Analysis of tool chatter in turning operation on lathe machine

Analysis of tool chatter in turning operation on lathe machine

Submitted in partial fulfilment for the award of the degree of

BACHELOR OF TECHNOLOGY In

Mechanical Engineering

(28 May 2014- 14 July 2014)

Submitted by: -

Aakash Gautam(111601)Abhay Rai(111603)

Aditya Kr. Singh(111610)Devanshu Yadav(111628)

Vijay Pratap Singh(111689)

DEPARTMENT OF MECHANICAL 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 workpiece for analytical modelling of

a turning process. The flexible workpiece which is supported only at one end undergoes elastic

deformation reducing allowable depth of cut in the process. The results also show the impact of

not having a tailstock on cylindricity of the workpieces due to the effects of numerous forces

generated by the cutting tool. Although there is a qualitative agreement between analytical and

experimental results which supports the cutting mechanism of the work, the quantitative

performance in terms of measured deflections of the workpiece was not satisfactory due to the

fact that the boundary conditions of the analytical model assumed zero elastic deflection of the

workpiece which is not true in reality.

Chen and Tsao [18, 19] presented 2DoF dynamic models of a cutting tool with and without the

tailstock supported workpiece using beam theory. The effects of workpiece parameters are

studied on the dynamic stability of the turning process by treating the workpiece as a continuous

system. The effect of the critical chip width under different spindle speed was investigated. By

considering the deformation of the workpiece under different conditions, the results showed that

the critical chip width of the deformed case was always larger than the rigid body case especially

at lower natural frequencies. Although these 2DoF models are very good at predicting the

stability and evaluating the influence of the elastic deformation and the workpiece natural

frequency on the critical chip width for two different workpiece end conditions, they are very

complex for studying the three- dimensional model and nonstationary cutting conditions,

particularly in the case of the vibratory situations.

Vela-Martınez et al. [20] developed a multiple degrees of freedom model based on the

compliance between the cutting tool and the workpiece, which was compared with an SDoF

model. This compliant model predicts a larger stability area when compared with the SDoF

model, but this result is not yet experimentally validated. This model can be used to predict

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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 workpiece. Different geometries were designed and analyzed giving as a

result a final workpiece of 35,516 elements. Afterwards a FE analysis was carried out to produce

a workpiece and the modal parameters were periodically updated to consider workpiece

evolution during machining within the stability algorithm.

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 turning process.

The model estimates the discrete transfer functions used for simulation and/or calculation of

frequency domain characteristics of the system. Also, the neural network can represent nonlinear

structures better than the conventional time series models and the stability conditions could be

more accurately evaluated by using the neural network cutting dynamics simulator. The accuracy

of the predictions was found to be much greater at higher cutting speeds. The neural network

model also represents the nonlinear characteristics of cutting dynamics, while the time series

methods use only the linear models.

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 workpiece and the static cutting forces on the tool by a series of

experiments. After measuring the dynamic cutting forces, surface roughness and critical chatter

lengths, the relations between the input and output parameters were established using radial-

basis function (RBF) neural network model and it was further employed to genetic algorithms

(GA) to optimize the machining data. Use of neural network technique in micro-cutting

operations by several researchers is very well summarized by Chae et al. [64] and the estimation

of tool condition in micro- machining of steel and aluminium has been explained. However,

chatter detection was not carried out using ANN techniques in this work. The neural network

technique requires extensive experimental data for a specific process and material condition,

which can be inconsistent for different processes, cutting conditions and material conditions.

The neural network is becoming the most powerful simulation tool for cutting dynamics with

respect to accuracy, flexibility, and computational speed when synthesized with sophisticated

algorithms and multi-processor neural network hardware.

2.2.2.2 Fuzzy logic technique

Fuzzy logic can process information like our brain. Fuzzy logic systems base their decision on

inputs in the form of linguistic variables derived from membership functions which are formulae

used to determine the fuzzy set to which a value belongs and the degree of membership in that

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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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



35



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 preprocessor, the time–frequency spectrum of the

simulated chatter signal using the HHT is presented in both 2 and 3-D time frequency spectrum

as shown in Fig. 4.10. From these plots it is quite evident that by adopting the proposed

methodology, noise frequency is eliminated. Peaks are only for the chatter frequency. Moreover,

it is also clear that without the WPT pre-processor, the Hilbert–Huang spectrum cannot reveal

the chatter phenomenon.

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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