Analytical Modelling and Experimental

Verification of Facing and Turning Processes for

Chatter Stability and Tool Wear Predictions

Milind A. Siddhpura

M.Eng.

This thesis is presented for the Degree of Doctor of Philosophy

The University of Western Australia

School of Mechanical and Chemical Engineering

March 2013

i

Abstract

Chatter vibration has been researched for more than a century and it is still a major

obstacle in achieving automation for most of the machining processes including turning,

milling and drilling. 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. In this thesis, some of the

chatter stability prediction and chatter detection techniques for the facing and turning

processes are reviewed to summarize the status of current research in this field. Chatter

stability prediction and chatter detection techniques are compared to find out the most

suitable technique/s. After this rigorous review, 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.

After the review process, the thesis focuses on the stability of chatter vibrations

and tool wear prediction by considering a single degree of freedom model of the

orthogonal turning process. Chatter-free (stable) cutting parameters are obtained

analytically for a sharp and a worn tool case respectively and stability lobes of an

orthogonal turning operation are constructed using simulations. The effects of tool wear

on chatter vibrations have been studied widely in the past, but the study of the effects of

chatter vibration on tool life is very limited. Tool wear tests are usually mainly

conducted under stable cutting conditions, which cannot explain the wear behaviour

under vibratory cutting conditions. An attempt is made to predict the wear and life of a

turning tool under chatter vibrations. A tool wear equation is derived which investigates

the effects of self-excited chatter vibrations on tool wear in order to predict the tool life.

This new tool wear equation clearly indicates that the tool wear increases very rapidly in

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the presence of chatter. The proposed analytical model and the tool wear equation have

been validated with orthogonal turning experimental results.

The thesis then focuses on the chatter stability prediction for a flexible tool-

workpiece system in a turning process by considering a two degree of freedom model.

The dynamic model of the turning process presented here considers two end-conditions

of the flexible workpiece. Chatter-free (stable) cutting parameters are obtained

analytically and stability lobe diagrams (SLDs) of a turning operation are constructed

using simulations to distinguish between the stable and unstable regions. The SLDs are

constructed for a variety of tool and workpiece parameters affecting the

flexibility/compliance of the tool-workpiece system to investigate the effects of these

parameters on the stability of the turning process. The proposed analytical model and its

simulations have been validated through the turning experimental results.

Overall, the proposed single degree of freedom and two degree of freedom

analytical models of the facing and turning processes predicted the process stability

accurately which are verified with the chatter experiments. A close agreement between

analytical model predictions and experiments was observed. A relationship between tool

wear and chatter has been established theoretically by deriving a new tool wear equation

considering mainly the dynamics and the contact mechanism of the turning process.

This accurately predicted excessive tool flank-wear in the presence of chatter, which

was confirmed experimentally.

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Table of Contents

Abstract.............................................................................................................................i

Table of Contents...........................................................................................................iii

Acknowledgements........................................................................................................vii

Statement of Candidature contribution.......................................................................ix

List of Symbols.................................................................................................................x

1 Introduction.........................................................................................................1

1.1 Background…………………………..…………………………………..1

1.1.1 Metal cutting theory……………………………………………...2

1.1.2 Turning process………………………………….........................4

1.1.3 Regenerative chatter vibrations………………………………….6

1.2 Turning dynamics during chatter………………………………………..7

1.3 Tool wear and tool life………………………………………………….12

1.4 Tool condition monitoring……………………………………………...14

1.5 Scope of the research…………………………………………………...17

1.6 Objectives of the research………………………………………………18

1.7 Thesis organisation……………………………………………………..18

2 Literature Review..............................................................................................19

2.1 Overview……………………………………………………………….19

2.2 Analytical techniques for chatter prediction……………………………21

2.2.1 Stability lobe diagram (SLD) ………………………………….21

2.2.1.1 Analytical models based on the number of DoF……….22

2.2.1.2 Analytical models based on compliance/flexibility

of tool-workpiece system……………………………….25

2.2.1.3 Analytical models considering tool-wear /

process-damping………………………………………..27

iv

2.2.2 Nyquist plot…………………………………………………….31

2.2.3 Finite element method/analysis (FEM/FEA) …………………..32

2.3 Experimental techniques for chatter prediction and detection…………34 2.3.1 Signal acquisition and processing approaches………………….35

2.3.1.1. Force and vibration measurements…………………….37

2.3.1.2 Sound and acoustic emission (AE) measurements..........44

2.3.2 Chip analysis approach…………………………………………48

2.3.3 Artificial intelligence approaches………………………………50

2.3.3.1 Artificial neural network (ANN) approach……………..50

2.3.3.2 Hidden markov model (HMM) approach........................53

2.3.3.3 Fuzzy logic approach…………………………………...53

2.4 Chatter suppression/control techniques...................................................55

2.5 Review of chatter and tool wear relationship research............................64

2.6 Summary and conclusions……………………………………………...67

3 Mathematical Modelling, Stability Analysis and Tool Wear Predictions in the presence of Chatter Vibrations for an Orthogonal Turning (Facing) Process.............................................................69

3.1 Overview……………………………………………………………….69

3.2 Mathematical model……………………………………………………69

3.3 Stability analysis considering a sharp tool……………………………..73

3.4 Stability analysis considering a worn tool……………………………..75

3.5 Tool wear prediction…………………………………………………...77

3.6 Results and discussions………………………………………………...78

3.7 Summary and conclusions……………………………………………...82

4 Mathematical Modelling and Chatter Stability Analysis for a Flexible Tool-Workpiece system in a Turning Process.........................83

4.1 Overview……………………………………………………………….83

4.2 Mathematical model……………………………………………………83

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4.3 Stability analysis considering a flexible workpiece……………………86

4.4 Results and discussions………………………………………………...89

4.5 Summary and conclusions ……………………………………………100

5 Experimental Verification of Simulation Results.........................................102

5.1 Overview……………………………………………………………...102

5.2 Equipment and test materials……….………………………………...102

5.2.1 The lathe machine……………………………………………..102

5.2.2 Workpieces……………………………………………………103

5.2.3 Cutting tools and tool holders…………………………………106

5.2.3.1 Cutting tools and holder in orthogonal turning……….106

5.2.3.2 Cutting tools and holder in turning……………………108

5.2.4 Measurement equipment..……………………………………..111

5.2.4.1 Modal testing equipment……………………………...111

5.2.4.2 Dynamometer and charge amplifiers………………….114

5.2.4.3 Accelerometers and ICP conditioning amplifiers..........115

5.2.4.4 Microphone and amplifier…………………………….116

5.2.4.5 DAQ and LabVIEW……………………………….….117

5.2.4.6 Microscope……………………………………………118

5.3 Orthogonal turning experiments………………………………………121

5.4 Turning experiments…………………………………………………..125

5.5 Data acquisition and pre-processing…………………………………..127

5.5.1 Test run procedure…………………………………………….127

5.5.2 Sampling rate……………………………………………….…127

5.5.3 Interval………………………………………………………...127

5.5.4 LabVIEW and PXI……………………………………………128

5.5.5 Data storage…………………………………………………...129

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5.5.6 Signal processing……………………………………………...129

5.5.6.1 Time domain analysis…………………………………129

5.5.6.2 DC average and trend removal………………………..132

5.5.6.3 Frequency domain analysis…………………………...132

5.6 Concluding remarks.………………………………………………….134

6 Experimental Results and Discussions..........................................................135

6.1 Overview………………………………………………………….......135

6.2 Orthogonal turning experiments…………………………………........135

6.3 Turning experiments…………………………………………………..149

6.4 Summary of results and discussions…………………………………..165

7 Conclusions and Future Work.......................................................................167

7.1 Conclusions…………………………………………………………...167

7.1.1 Conclusions from literature review...........................................167

7.1.2 Conclusions from the SDoF model and the experiments..........167

7.1.3 Conclusions from the 2DoF model and the experiments..........169

7.2 Future Work..........................................................................................171

8 Appendices.......................................................................................................172

9 References........................................................................................................176

10 Publications Originated from this Thesis......................................................184

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Acknowledgements

I would like to express my sincere gratitude and appreciation to my supervisor,

Professor R. Paurobally for his invaluable inspiration and motivation throughout this

thesis work. I really appreciate his willingness to meet me at short notice every time and

going through several drafts of my thesis. Without his advice, encouragement and

support, this work could not have been a reality.

I will forever be thankful to my guru Dr. Shrikant Bhave who inspired me to

initiate research in the field of vibration and condition monitoring. He will always

remain my best role model for a scientist, mentor and teacher.

I would like to thank all the academic, administrative, IT and workshop staff

members of the School of Mechanical and Chemical Engineering for the direct and

indirect support they provided me to complete this research project during the past four

years. I heartily thank Mr Sebastian Daszkiewicz and Mr Gavin Criddle from IT as they

were always helpful when I had troubles with my computer or software. I am thankful

to Mr Mark Henderson, Michael Armstrong and all other technical staff from the

Mechanical engineering workshop for providing me anything I needed immediately for

my research experiments.

I would like to thank the Graduate research scholarships office (GRSO) and

CRC for Infrastructure and Engineering Asset Management (CIEAM) for providing

financial support in the form of scholarships, without which I wouldn’t have survived.

Words cannot express the feelings I have for my parents, Arun and Uma

Siddhpura for their constant unconditional love, encouragement and support at every

stage of my personal and academic life. I am thankful to my brother Naimish and his

wife Rutika for their encouragement and support throughout - and Haimie is a delight to

have around. I would like to heartily thank to my in-laws who have provided moral

support through their prayers, which was really needed to accomplish this gigantic

viii

thesis. I would like to acknowledge the most important person in my life – my wife

Arti, who was also my fellow PhD student. She has been a constant source of strength

and inspiration throughout the study. I would like to thank my lovely son, Ansh, who

has sacrificed his school holidays fun as he had to come to the university with us while

me and my wife were extremely busy with our PhD. I consider myself the luckiest in

the world to have such a supportive family, standing behind me with their love and

support.

Many friends have helped me stay sane through these difficult years. Their

support and care helped me overcome setbacks and stay focused on my study. I greatly

value their friendship and I deeply appreciate their belief in me.

Finally, I would like to thank God almighty who has been giving me everything

to accomplish this thesis: Strength, patience, health, wisdom, and blessing. Thank you,

Lord.

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Statement of Candidature Contribution

This dissertation is the original work of the author. It is not previously been submitted

for a degree at this or any other institution. To the best of the author’s knowledge, this

thesis contains no material previously published or written by another person, except

where due reference is made in the text.

Milind Siddhpura,

(Submitted for examination on .......................)

x

List of Symbols

A Area of workpiece A* Amplitude b Width of cut (chip width) blim Limiting width of cut c Damping coefficient C Constant d Depth of cut E Modulus of elasticity f Feed rate F Total Cutting force Ff Cutting force in feed direction fn Fr Natural frequency, Hz Cutting force in radial direction Ft Cutting force in tangential direction G(ω) Real part of the FRF (Transfer function) h Height of the workpiece H Interval frequency difference H(ω) Imaginary part of the FRF (Transfer function) h0 Mean chip thickness I Cross sectional moment of inertia k Stiffness Kf Cutting coefficient in the feed direction Ksp Proportionality coefficient l Tool overhang length L Total length of workpiece between two centres L1 Distance of cutting location on workpiece from headstock L2 Distance of cutting location on workpiece from free/tailstock end lc Clearance length lw Tool wear length/flat m Mass N Spindle speed n Number of lobes in a Stability Lobe Diagram (SLD)

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n* Constant R(ω) Denominator in the Transfer function. T Cutting time or Tool life T* Time delay between current revolution and previous revolution Or Spindle period T0 Tool life under vibration free condition Td Tool life under vibrating condition V* Volume of material displaced V, & Cutting velocity Vchip Chip velocity v0 Nominal cutting speed VB Average width of flank wear-land VBmax Maximum width of flank wear-land x* Constant y(t) Wave generated during current revolution y(t-T) Wave generated during previous revolution y* Constant αr Rake clearance angle β Constant cutting angle in turning Γ(s) Transfer function ζ Damping ratio θ Phase shift ρ Material density σ Standard deviation σ1 Coefficient σ2 Coefficient τ Decomposition form φ Constant ψ Phase angle ω Frequency of chatter vibration ωn Natural frequency, rad/sec Фc Shear angle

xii

1

Chapter 1

Introduction

1.1 Background

Material removal with tools is one of the oldest and most widely used methods to

produce components with desired dimension, quality and shape in the manufacturing

industry. Deformation processes, such as forging, rolling and casting are mostly

followed by a series of metal removal operations. The cutting operations, referred to as

‘chip removing’ represent the largest class of manufacturing activities in the production

of various components. Out of many metal removal processes, turning is the most

popular one. In any metal cutting operation, one of the most important and critical

parameter is the tool life, which affects the economics of any manufacturing operation.

Tool wear is the most common cause of damage to the tool, which also reduces

the tool life. Tool wear is highly dependent on the friction and vibration produced

during the cutting operation. Tool life is one of the critical factors which affect cost and

productivity.

Self-excited (chatter) vibrations are very critical in machining operations and also

one of the conditions that accelerates the tool wear. Chatter may be present in any

machining operations. Chatter may generate high pitch noise, cause poor surface finish,

tool wear, tool fracture and damage to the machine tool system. Metal removal rate has

to be reduced in order to avoid chatter, which in turn reduces productivity. Chatter has

detrimental effects on product quality, machine tool assembly and production rate,

which makes analysis of chatter vibration an essential activity. Turning is a machining

process in which chatter vibrations occur frequently and affects machining quality and

tool life. So, this research focuses on chatter vibrations and its effects on tool wear/life

in a turning operation.

2

This research work will give important information about tool wear in the

presence of chatter vibrations. Condition monitoring of the tool-workpiece system will

be useful to find out the occurrence of chatter and tool wear rate. From tool wear

observations, tool life can be calculated using standard tool life criteria. Thus, tool life

predictions could be possible. It will also be very useful in estimating the total cost of

chatter due to a reduced tool life in machining operations. This information will also be

useful in justifying additional cost of chatter suppression activities.

1.1.1 Metal cutting theory

Metal cutting operations are industrial operations in which metal components are

shaped by removing unwanted material from them. For most of the metal cutting

processes like turning, milling, boring and grinding, the mechanics of cutting is similar

but the geometry of the operations is very different.

There are two general models of metal cutting processes like turning, namely

orthogonal and oblique cutting as explained by Altintas (2000). Although the most

common cutting operations are three dimensional and geometrically complex, the

simple case of two-dimensional orthogonal cutting is used to explain the general

mechanics of metal removal. In orthogonal cutting, the material is removed by a cutting

edge that is perpendicular to the direction of the relative tool-workpiece motion. The

geometry of an orthogonal cutting process is shown in Figure 1.1. Where, b and h are

chip width (width of cut) and thickness of cut, V is the cutting velocity, Ft and Ff are the

forces in the tangential and feed directions.

3

Figure 1.1: Geometry of orthogonal cutting process.

In orthogonal cutting, the cutting operation is assumed to be uniform along the

cutting edge. So, it is a two-dimensional plane strain deformation process without side

spreading of the material according to Armarego and Brown (1969) and Trent (2000).

The metal cutting operation is basically a plastic deformation process. In the cutting

region, there are three main deformation zones as shown in Figure 1.2. The material

being cut shears over the primary zone to become chip as the cutting tool edge moves

into the workpiece material. The newly created chip moves along the rake face of the

tool which is called the secondary deformation zone. The contact zone between the

flank face of the cutting tool and the newly-machined surface is called the tertiary zone.

4

Figure 1.2: Deformation zones in orthogonal turning process.

1.1.2 Turning process

Turning is the most common and very basic machining operation in the manufacturing

industry. As the focus of this research is on the turning operation, it is essential to

understand the basic mechanics of the turning operation.

In a turning process, a workpiece rotates about its longitudinal axis on a lathe

machine-tool which is shown in Figure 1.3. The workpiece is supported by a chuck at

one end and by a tailstock at the other. A cutting tool mounted rigidly on a tool post on

the lathe is fed along the workpiece axis to remove material and produce the required

shape. The geometry of a turning process is shown in Figure 1.4. If the cutting tool is

fed perpendicular to the workpiece axis, it is called orthogonal turning (facing).

In addition to the cutting geometry, the major operating parameters to be specified

in turning are the cutting speed (V), feed rate (f) and depth of cut. The cutting speed is

the rate at which the uncut surface of the workpiece passes the cutting edge of the tool.

The feed rate f is the tool advancement per revolution along its cutting path. Depth of

cut is the thickness of the metal removed in the radial direction.

5

Figure 1.3: A Lathe machine (Source: American Machine Tools).

Figure 1.4: Geometry of oblique turning process (Altintas, 2000).

6

1.1.3 Regenerative chatter vibrations

From the very beginning, metal cutting processes like turning have had one troublesome

obstacle in increasing productivity and accuracy, namely chatter. In machining, chatter

is perceived as unwanted excessive vibration between the tool and the workpiece,

resulting in a poor surface finish and accelerated tool wear. It also has a deteriorating

effect on the machine tool life and the reliability and safety of the machining operation

as explained by Wiercigroch and Budak (2001).

In a turning process, three different types of mechanical vibrations are present due

to a lack of dynamic stiffness/rigidity of the machine tool system comprising the tool,

tool holder, workpiece and machine tool itself as explained by Tobias (1961). These are

free, forced and self-excited vibrations. Free vibrations are induced by shock and forced

vibrations are due to unbalance effects in machine tool assemblies like gears, bearings,

spindles. Free and forced vibrations can be easily identified and eliminated. But self-

excited chatter vibrations are still not fully understood due to its complex nature. They

are most harmful for any machining process including turning. Self-excited vibrations

are generally classified into primary chatter and secondary chatter as described by

Wiercigroch and Budak (2001). Primary chatter is caused by friction between tool and

workpiece, thermo-mechanical effects or by mode coupling. Secondary chatter is

caused by the regeneration of wavy surface on the workpiece. Regenerative vibration is

the most destructive among all other vibrations.

Chatter is easily recognized by the noise associated with these vibrations, by the

chatter marks on the cut surface, and by the appearance of the chips according to

Schmitz (2003). Machining with chatter causes unstable cutting and is mostly

unacceptable because of the chatter marks on the machined surface and because the

large peak values of the variable cutting force might cause breakage of the tool or of

some other part of the machine (Huang, 2006). Correspondingly, the chip width and

7

also the metal removal rate must be kept below the limit at which chatter occurs. In this

way, chatter is often the factor limiting metal removal rate below the machine’s capacity

and hence reduces the productivity of the machine.

1.2 Turning dynamics during 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 1990 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 the machine-tool dynamics and as a result the prediction accuracy was low

(Cardi et al. (2008; Clancy and Shin (2002)). But over the last few decades (after

1990s), other 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 the 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 chapter 2.

Regenerative chatter vibration arises due to the interaction between the metal

cutting process and the machine tool structure as shown in Figure 1.5 (a) and it is a

major obstacle in achieving maximum material removal rate (MRR). Self excited

chatter vibrations are much more detrimental to finished surfaces and cutting tools due

to their unstable behavior which results in large relative displacements between the tool

and workpiece (Kayhan and Budak, 2009).

8

(a) (b)

Figure 1.5: (a) Machine tool, cutting process interaction (b) Mechanism of regeneration.

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. Figure 1.5 (b) displays the relative motion between the tool

and the workpiece in turning. 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,

y(t) is the wave generated during the current revolution and y(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 y(t-T) and in the current revolution y(t) is the key

factor governing the occurrence of chatter in the turning process. If the two waves are in

phase (θ=0), the undulations on the workpiece will not grow and the process will

remain stable because the chip thickness variation is negligible resulting in a relatively

constant force on the tool. From the point of view of energy transfer in the turning

system, the onset of chatter can be regarded as the stability threshold of the system in

which the energy supplied to the system is equal to the energy dissipated by the system.

So, when there is no phase delay/shift (θ=0), there is no surplus energy in the system

resulting in a stable cutting process. However, when the waves are not in phase (θ≠0),

the undulations on the workpiece grow due to energy being supplied to the cutting tool

9

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.

It is a challenging task to identify/measure dynamic parameters of the dynamic

chatter model. There are basically two approaches to formulate analytical expressions

describing the turning process dynamics (Das et al., 1970). The first has been to specify

incremental cutting force equations of suitable form, and to derive the values of the

coefficients of these expressions from steady-state cutting tests (Das and Tobias, 1967;

Knight, 1968; Tobias and Fishwick, 1958) or by fitting to experimentally derived

stability charts (Sadek and Tobias, 1970; Tobias, 1959) or by fitting the expressions to

the results of dynamic/vibratory cutting tests (Vanbrussel and Vanherk, 1970; Wallace

and Andrew, 1965). It is clearly much more straightforward to use steady-state tests, if a

wide range of cutting conditions have to be investigated. A unified mathematical model

was presented by Kaymakci et al. (2012) which can predict cutting forces for turning,

boring, drilling and milling. This generalized model incorporates tool/cutter geometries

of these multiple cutting processes according to ISO standards and predicts cutting

forces considering oblique mechanics. The model seems quite promising because it can

even be used to develop unified chatter stability laws for multiple operations.

There are a number of parameters which influence the varying cutting forces, i.e.

effective rake angle, clearance angle and instantaneous direction of cutting. But in order

to determine the factors which affect the dynamic forces most, the second approach to

describe the vibratory turning process, in which the fundamental mechanics of metal

cutting are considered and which is based upon the cutting process model derived by

Meritt (1965). In this second approach, the cutting force variations are determined by

considering the total force at any point during the cyclic motion of the tool and

10

corresponding to the instantaneous values of the cutting parameters and tool geometry.

Based on this second approach, mathematical models have been formulated in chapters

3 and 4, which represents the complete dynamics of the chatter process and chatter

stability prediction of the turning operation.

These mathematical models are 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 Figure 1.6. The SLD distinguishes regions of stable (chatter-free) and unstable cutting operations 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 will be stable leading to a

smooth surface finish and less dynamic loads on the machine tool system as explained

by Altintas (2000). By selecting specific combinations of width of cut and spindle

speed, chatter vibrations can be avoided to achieve a stable turning process throughout.

Figure 1.6: Typical SLD showing the stability lobes for various speeds and widths-of-cut.

11

The most significant cutting parameter, which is decisive for the generation of

chatter in a turning process, is the width 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 width of cut) and becomes more energetic for all values of b>blim. Therefore, blim is the most important parameter for the stability of cutting. The value of blim depends on the dynamic characteristics of the structure, on the workpiece material, cutting speed and feed, and on the geometry of the tool as explained

by Tlusty (1986). SLD can be used for the prediction of chatter stability in a turning

process. The limiting width of cut blim is plotted against spindle speed (N) on the SLD as shown in a typical plot similar to Figure 1.6. Vibrations between the tool and

workpiece appear as different lobes (n = 1, 2, 3….) and any width 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 width of cut combinations for the

best MRR in a turning process.

To obtain the dynamic parameters of the turning process numerically, finite

element method can be used which is discussed in chapter 3. Impact testing is the most

conventional experimental method for obtaining dynamic parameters for the chatter

model. In particular, the natural frequency, damping ratio, Real and Imaginary parts of

the transfer function are determined by impact testing technique which has been used by

several researchers (Chiou and Liang, 1998; Kayhan and Budak, 2009; Kebdani et al.,

2008; Rao and Shin, 1999; Sekar et al., 2009; Serra et al., 2009; Thomas and

Beauchamp, 2003; Turkes et al., 2011). The structural stiffness (k) of the tool-workpiece

system can be obtained by simultaneous measurement of displacement and static force

applied at the end of the workpiece through the tool (Chiou and Liang, 1998; Kayhan

and Budak, 2009; Sekar et al., 2009).

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1.3 Tool wear and tool life

Selection of an appropriate tool for a machining operation is crucial for the process

efficiency. The productivity of any cutting process is highly dependent on tool wear and

tool life. If cutting speed and feed are increased to improve productivity, the tool life

will be shortened due to a higher tool wear rate. When the tool wear reaches a specific

limit, the tool or the tool insert has to be replaced with a new one; otherwise it will

break during the cutting operation.

Several types of wear occur during the cutting process. The most important types

are crater wear CW, flank wear FW and notch wear NW as described by Tlusty (1999).

The chip flows away on the rake face of the tool and the motion results in a severe

friction between the chip and the rake face. So, it leaves a scar on the rake face which is

parallel to the major cutting edge. That damage on the rake face of the tool is called

crater wear. The flank wear-land generally develops due to abrasion of the cutting tool

edge against the machined workpiece surface. Flank wear is measured by the average

and maximum width of wear-land size and denoted as VB and VBmax respectively. The

notch wear is a combination of flank and rake face wear which occurs on the primary

clearance face, adjacent to the width of cut line where the major cutting edge intersects

the workpiece surface. It generally accelerates more rapidly than the flank wear.

(a) (b)

Figure 1.7: (a) Flank wear on a turning tool. (b) Flank-wear profile.

13

Flank wear has been emphasized more than crater wear during analysis of cutting tool

wear. Flank wear also results in changes to the mechanics of the cutting process and

changes in the dimension of the product according to Thangavel et al. (2006). This is

why the single most significant type of wear that has drawn constant attention is flank

wear. Flank wear is generally used as a tool life criterion.

Figure 1.7 (a) illustrates the location of flank wear on a turning tool and Figure

1.7 (b) shows detailed flank wear profile where VB is the average flank wear width,

VBmax is maximum peak land width and lw is flank wear length/flat. The tool life

criterion is generally taken as VB≤0.3 mm and VBmax≤0.6 mm. The flank wear length

(lw) is very critical in positive damping in the occurrence of chatter vibrations as

explained by Tlusty (1999).

The development of flank wear can be split into three zones in the tool life curve

as shown in Figure 1.8.

Figure 1.8: Flank wear zones (Altintas, 2000).

14

Tool life was first investigated by Taylor (1907), who established the relation between

the cutting speed and the tool life in the following form

VTn* = C

where V [m/min] is the cutting speed, T [min] is the tool life and C and n* are

experimentally identified constants which depend on tool and work material.

The effects of depth of cut and chip thickness were neglected in this tool life equation,

which was then included in the tool life equation by Kronenberg (1966) as:

VTn* dx* fy* = C

where f [mm/min] is the feed rate, d [mm] is the depth of cut, C, x* and y* are

experimentally identified constants.

In conventional workshops, operators either visually inspect the cutting edge or rely

on previous experience with the tool life as described by Liu and Altintas (1999). But in

the unmanned machining environment, it is essential to predict tool wear/life

analytically, and with on-line monitoring using various sensors and automatic

replacement of the cutting tool.

1.4 Tool condition monitoring

For any machining process, timely detection of tool wear is very important and it can be

achieved by tool condition monitoring (TCM). According to Rehorn et al. (2005), TCM

is widely used in turning operations, because it can be simply described in two

dimensions. Secondly, turning cutters are the only machining tools that do not rotate.

Various sensors like Accelerometers or Laser sensors for vibration measurements, tool

dynamometers for force measurements, Acoustic Emission (AE) sensors for chatter or

tool breakage detection are used for tool condition monitoring.

The need of monitoring in a metal cutting process encompasses monitoring the

machine and the cutting process dynamics, cutting tools and workpiece to ensure

optimum performance of the systems according to Byrne et al. (1995). A tool condition

15

monitoring system can therefore be viewed as serving the following purposes (Dimla

and Lister, 2000):

1. Advanced fault detection system for cutting and machine tool.

2. Check and safeguard machining process stability.

3. Means by which machining tolerance is maintained on the workpiece to

acceptable limits by providing a compensatory mechanism for tool wear offsets,

and

4. Machine tool damage avoidance.

Tool condition monitoring can be performed on-line or off-line by either direct or

indirect means. The on-line designation for a sensing method refers to the fact that it is

performed while metal is being removed without the need for interrupting the process

according to Nayfeh et al. (1995). Off-line methods can be performed on the machine or

away from the machine. In either case, these methods require either scheduling idle time

for the measurements or actually interrupting the process.

TCM can also be classified as direct and indirect methods. In the direct methods,

the tool and the process are sensed directly by measuring tool-workpiece dimensions

and measurement of the distance to the tool post. Some of the explored direct methods

as presented by Nayfeh et al. (1995) are radioactivity tracers, optical scanning, electrical

resistance and probes. The direct methods have advantages of capturing actual

geometric changes arising from wear of the tool. But, direct on-line methods for tool

and process condition monitoring have been difficult to develop and implement since

the tool nose and flanks are obscured from vision during cutting. So, none of these

systems are practical for the shop floor. The indirect methods are practical and most

widely used. Indirect methods measure one or more of the parameters associated with

the cutting operation, such as tool forces, acoustic emission and vibration. The tool

16

condition is then inferred from the values of the parameters. They have the advantages

of less complicated setup and suitability for practical application.

The chatter onset detection and tool condition monitoring tasks can be divided

into the following categories: (1) Signal acquisition (2) Signal processing (3) Tool

chatter/wear state estimation.

Signal acquisition can be carried out using force, vibration and acoustic signals

which are very useful for the monitoring of the process. Signal processing is essential to

extract only useful sensor features by filtering redundant information/noise. There are

various methods like Time domain analysis, Frequency domain analysis (FFT- Fast

Fourier transform) and Time frequency domain (WT- Wavelet transform) analysis

methods.

In time-domain analysis, individual signals can be analysed in the time domain

either by studying the time records by themselves or by generating their auto-correlation

functions as explained by Norton and Karczub (2003). Signals can be readily observed

in the time domain on an oscilloscope, and this is a useful way of analysing the form of

the time histories and of identifying signals peaks. It is also a good engineering practice

to monitor the time histories and of recorded signals prior to performing a frequency

analysis so as to get an overall feel for the quality of the signals. However, Ramos et al.

(2009) described that in many applications (if not in the majority of applications), the

time domain representation is insufficient to gain insight as to what constitutes a signal.

For example, from the time domain representation (e.g., observed in an oscilloscope) a

user can see the basic shape of a signal, its amplitude, and eventually its frequency.

However, some smaller disturbances or distortion of the signal are difficult to spot and

even harder to classify and quantify.

Time domain data is often transformed to the frequency domain by the application

of discrete Fast Fourier Transform (FFT). The power associated with various frequency

17

bands or shifts in specific bands may then be considered as features as presented by

Heyns (2007).

One disadvantage of frequency domain is that the dynamics of the machining

operation and measurement hardware is not always fully understood. The frequency

domain representation is suited for the stationary signals. However, in many situations

the actual signal frequency composition changes with time and this must be measured.

To solve this issue, a mixed time–frequency domain representation can be used.

In tool condition monitoring, the aim is to apply appropriate sensor signal

processing techniques to identify and predict the cutting tool state, so as to reduce loss

brought about by tool wear or tool failure according to Zhu et al. (2009). An effective

tool condition monitoring (TCM) system can improve productivity and ensure

workpiece quality, and hence, has a major influence on machining efficiency according

to Geoffrey and Winston (1989). Tool wear can be estimated using statistical methods

and it can also be physically measured using microscopes.

1.5 Scope of the research

The main scopes of this research are described below:

(1) This research will focus on chatter prediction and experimental validation.

(2) This research will also focus on relationship between chatter vibration and tool

wear.

(3) This research will restrict to analysis of facing and turning operation only.

18

1.6 Objectives of the research

(a) To carry out a comprehensive literature survey to understand the recent

development in this field and to justify the objectives and define the scope of

this project.

(b) To formulate mathematical models of the turning process for chatter stability

and tool wear predictions.

(c) To verify the model predictions experimentally.

(d) To conduct chatter detection using tool condition monitoring (TCM) method and

to measure the tool wear off-line using an optical microscope.

(e) To establish correlation between chatter vibration and tool wear and tool life

predictions from that correlation.

1.7 Thesis Organization

The thesis is organized into 7 chapters. Chapter 1 covers the introduction and chapter 2

has a state-of-the-art literature review of chatter vibration research in a turning process.

In chapter 3 and 4, dynamic models of chatter vibration is presented by considering the

workpiece as a rigid member and then as a flexible member. Stability analysis is carried

out to obtain chatter free cutting parameters using MATLAB simulations. Chapter 5

covers experimental methodology and verification. Chapter 6 presents experimental

results and discussions. Chapter 7 presents the conclusions and future work.

19

Chapter 2

Literature Review

2.1 Overview

Chatter vibration has been researched for more than a century and it is still a major

obstacle in achieving automation for most of the machining processes including turning,

milling and drilling. Its catastrophic nature creates numerous problems like poor surface

finish, excessive noise, breakage of machine tool components, reduced tool life and

productivity. Turning is still one of the most widely used machining processes to

produce a variety of products by mostly cutting the metals. The machining of metals is

often accompanied by a violent relative motion between tool and workpiece which is

called chatter vibration.

Chatter was first identified as a limitation of machining productivity by Taylor

(1907), who carried out extensive studies on metal-cutting processes as early as in the

1800s. A 3/4 power law cutting force model was derived and it was stated that chatter is

the “most obscure and delicate of all problems facing the machinist”. Arnold (1946)

examined numerous influences to which a tool is subjected to during cutting analytically

as well as experimentally for lathes and other machines and explained the mechanisms

generating chatter and proposed cutting forces as a function of speed. It was shown that

the most important characteristic property of chatter vibration is that it is not induced by

external periodic forces, but rather that the forces which bring it into being and maintain

it are generated in the vibratory process (dynamic cutting process) itself. Chatter is

caused by instability in the cutting processes, which was first understood by Tobias and

Fishwick (1958) and Tlusty and Polacek (1963) almost simultaneously but

independently. It was observed that modulated chip thickness due to vibration affects

cutting forces dynamically, which in turn, increases vibration amplitudes yielding a

process known as regenerative chatter. It was also observed that the depth of cut was the

20

key process parameter in the cutting process stability. Tlusty and Polacek (1963)

presented a stability condition in which stability limits can be calculated based upon the

system dynamics for orthogonal cutting and analytically showed that for the depth of

cuts higher than the stability limit, the magnitude of the dynamic forces and oscillations

increases, yielding instability and thus chatter vibrations. The solution has been

approximated by resolving cutting forces and structural dynamics into one direction

only, i.e. the chip thickness direction and thus can only be valid for a one dimensional

process. Tobias (1965) and Meritt (1965) studied the modelling of the dynamic

response, structural aspects and stability limit aspects of regenerative chatter. These

studies are only applicable to orthogonal cutting, where the direction of the cutting

force, system dynamics and chip thickness do not change with time.

Most of the research has been carried out to avoid this regenerative chatter

vibration by either predicting its occurrence earlier or detecting it as soon as it occurs.

Many researchers tried active or passive control strategies to control chatter vibrations,

which are also reviewed in this chapter. Quintana and Ciurana (2011) recently presented

state-of-the-art review of chatter in machining processes and classified current methods

which ensure chatter-free (stable) cutting conditions. The process of chatter analysis,

chatter stability prediction and chatter detection is highly complex which needs to be

investigated independently for different cutting processes like turning, milling and

drilling. The literature available till date on each of these processes is tremendous and it

provides motivation to produce a state-of-the-art review focusing on the turning process

alone. In this chapter, some of the chatter stability prediction, chatter detection and

chatter control techniques are reviewed exclusively for the turning process.

21

2.2 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 SLD, Nyquist plots and Finite

element method/analysis are most frequently utilized techniques in the literature and are

reviewed critically here. Figure 2.1 shows the number of publications for each

technique. It should be noted that multiple citing is possible as some publications may

repeat in each category in Figures 2.1, 2.2, 2.3, 2.4 and 2.5 and these figures represent

publications reviewed in this thesis as shown in the reference list. 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.

Years SLD Nyquist FEM Total 1960-1970

1 1 0 2

1971-1980

2 0 0 2

1981-1990

0 1 0 1

1991-2000

3 1 0 4

2001-2010

20 5 5 30

TOTAL 26 8 5 39

Figure 2.1: Number of publications featuring analytical chatter prediction approaches and the table showing summary of the selected publications between years 1965 and 2010.

(Please refer to Appendix A).

2.2.1 Stability lobe diagram (SLD)

Meritt (1965) 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.

22

Linear chatter stability models presented by Das and Tobias (1967) and Tlusty (1978)

have considered the effects of instantaneous, regenerative chip thickness on the dynamic

force. To generate SLDs, analytical modelling can be done by considering different

parameters in the model, which are reviewed in the following subsections.

2.2.1.1 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

several researchers (Tobias and Fishwick, 1958: Meritt, 1965; Tobias, 1961; Tlusty,

1999; Altintas and Weck, 2004). In most of these research works, the turning tool is

represented by an SDoF spring–mass system which is cutting a rigid workpiece 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 (1974) 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 (2006) 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,

23

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 workpiece, 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 (2007) and Ozlu and Budak (2007) compared an SDoF and

multi-dimensional stability models by several simulations and chatter experiments. The

effects of three cutting angles, the insert nose radius and the dynamics of the

components were included in the cutting system in all directions in their 3DoF model.

As these parameters cannot be included in an SDoF model, it can give erroneous results.

It was also shown that when inclination angle or nose radius exists on the tool, a multi-

dimensional solution is needed since the SDoF stability formulation fails to represent

the dynamics of the process accurately. Dassanayake and Suh (2008) studied tool

chatter with turning dynamics using a 3DoF model and also compared it with an SDoF

model. In a 3DoF model the workpiece is modeled as a system of three rotors namely,

machined, being machined, and un-machined regions connected by a flexible shaft. It

was found that neglecting workpiece vibrations in modelling a fine turning operation

will 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 modelling of the turning

process.

Suzuki et al. (2010) 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

clockwise and counter clockwise rotation processes were significantly different from

24

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. (2011) 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 workpiece 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, it seems 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 will 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.

25

2.2.1.2 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 (1976) proposed a general

method for the analytical evaluation of the stability limit in oblique turning of a slender

workpiece, held between the centres. 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. (2006) 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 (2006a; 2006b) presented 2DoF dynamic models of a cutting

tool with and without the tailstock supported workpiece using beam theory. The effects

of workpiece parameters on the dynamic stability of the turning process by treating the

workpiece as a continuous system were studied. 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

26

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 non-stationary cutting

conditions, particularly in the case of the vibratory situations.

Vela-Martínez et al. (2008) developed a multiple degrees of freedom model

based on the compliance between the cutting tool and the workpiece, which was

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

when compared with the SDoF model, but this result is not yet experimentally

validated. This model can be used to predict stability limits more accurately when the

dynamics of both the cutting tool and the workpiece are similar or when slender cutting

tools must be used.

Sekar et al. (2009) 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 the model. But both the workpiece end-conditions along with their stiffness

expressions were not considered in the modelling. These will be included in the 2DoF

model in chapter 4.

Urbikain et al. (2012) presented an algorithm to predict stability in straight

turning of a flexible workpiece by the 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 a concentrated mass workpiece was

analyzed using ANSYS to find the dynamic parameters. The compliant model is useful

27

for low order lobes and provides accuracy in stability prediction for up to 87.5% but

inaccuracies arise from modelling and the input parameters of the model like cutting

coefficients and modal parameters. There are very few research works which considered

compliance of the tool–workpiece system and the tool–workpiece compliance should

always be considered to constitute a more realistic model.

2.2.1.3 Analytical models considering tool-wear / process-damping

Tool wear phenomena occur during a cutting process and it changes the tool geometry

resulting in a drastic change in the dynamics of the cutting process. Sisson and Kegg

(1969) found that high stability at low speed is caused by the damping generated at the

tool–workpiece interface and reported that the finite radius of the tool nose, clearance

angle and cutting speed are the most important factors affecting the process damping

and which cause deviation of experimental results from the predicted results. The

preparation of the tool cutting edge can have a dramatic influence on the damping

produced by the cutting process. Thus, changes in the edge radius of the cutting tool

may produce the desired effect on the cutting process. It was also recognized that the

process damping caused is due to the interference between the cutting tool flank face

and the undulated machined surface. Wu (1989) presented a model of the tool–

workpiece interaction where the tool is indenting the workpiece surface and generates

undulations on it. The ploughing force which acts on the flank face of the tool is

assumed to be proportional to the volume of the material extruded on the workpiece.

Elbestawi et al. (1994) and Lee et al. (1995) showed that the ploughing force acts like

an additional damper in the system after applying the ploughing force model in

numerical simulations.

Ahmadi and Ismail (2010; 2011) proposed that the numerical calculations of the

extruded volume requires high resolution in discretizing the surface undulations, which

makes establishing the SLD a time consuming task. It was stated that the indentation

28

model is nonlinear since the extruded volume is computed only for the part of the

vibratory cycle when the tool is moving into the workpiece and it is zero when the tool

is moving away from the workpiece. It is nonlinear because it depends on the surface

undulations amplitude. Due to these facts, it is still not possible to implement this model

directly in analytical modelling to predict the stability of the cut.

Chiou and Liang (1998) and Chiou et al. (1995) approximated this indentation

model with a linear model with first order Fourier transform. A small amplitude

vibration was assumed in this model. The stability lobes were generated by integrating

the approximate linear model into their analytical development. It was demonstrated

that chatter instability is delayed to a greater overhang distance as a result of flank wear.

And at lower cutting speeds, the chatter limit increases as the tool wear increases. The

effect of tool wear on chatter stability was investigated and it was found that the chatter

stability increases as the tool-wear-flat enlarges.

Clancy and Shin (2002) presented a three-dimensional frequency domain chatter

stability prediction model for face turning by including tool wear in the model. This

model could predict the magnitude and direction of the process damping force, which

was also used to analytically calculate stability limits. The results showed that the flank

wear and the stability limit were directly proportional to each other. As wear developed

on the flank of the tool the stability limit was increased due to the process damping

effect. This means that the larger the flank wear area becomes, the higher the stability

limit will be. It was also found that the process damping has a larger effect at lower

spindle speeds resulting in very high stability for a worn tool compared to a fresh tool.

And at a very high speed this effect is negligible resulting in lower stability limits.

Fofana et al. (2003) investigated stability of a turning process analytically as

well as experimentally by using worn tool inserts. Cutting forces were investigated with

varying depth of cut and feed rate, whereas cutting force coefficients were investigated

29

as the tool wear progresses. It was shown that tool wear and dynamic instability are both

due to the combined effect of the contact and friction mechanisms between tool–

workpiece, tool–chip and workpiece–tool–machine–tool interactions.

Altintas et al. (2008) presented a linear model, and verified that the damping

coefficient is approximately proportional to the ratio of vibration and cutting speeds.

Controlled oscillation tests were carried out using a fast tool servo to identify the

proportionality constant of the process damping. The stability charts were obtained

using the Nyquist criterion considering the process damping. It was found that accurate

prediction of chatter stability at low speeds is dependent on the identification of the

dynamic cutting force coefficients. The coefficients were found to be sensitive to the

work material properties, cutting edge preparation, tool clearance angle, tool wear,

cutting speed, tool–workpiece contact mechanics, shearing process, wavelength and the

frequency of vibration during machining.

Moradi et al. (2009b) presented an SDoF model of a turning process. In this

model, an orthogonal cutting configuration is used to set up the nonlinear delay

differential equation of motion that includes the effects of tool flank wear. Modelling

and stability analysis were carried out by considering a sharp tool and a worn tool where

tool flank-wear was modeled as the contact force. It was shown that the introduction of

tool wear to the model adds damping to the system and creates a speed-dependent

variation in the critical width of cut, showing higher stability limits at lower speeds.

Tool wear length was the parameter representing tool wear in the model. It was also

found that the critical value of width of cut increases by a parabolic trend when the tool

wear length is increased.

Budak and Tunc (2010) determined the indentation force coefficient responsible

for the process damping through energy analysis. This coefficient is identified from the

chatter test and it is used for process damping and the stability limit predictions. It was

30

demonstrated that decreasing the clearance angle increases the process damping which

is a well-known effect in practice. The process damping was only observed at very low

speeds with sharp tools. It exists at relatively higher cutting speeds for honed tools.

Process damping was found to be the significant source for increased stability at low

speeds in an orthogonal turning process which was verified by time domain simulations

and experiments.

Kurata et al. (2010) have also identified the process damping force coefficient

from the plunge turning tests. The process damping coefficient is estimated by inverse

solution of the stability law using the characteristic equation of the turning process

when it is critically stable during cutting tests. Stability lobes were constructed using

this identified process damping coefficient. It was found that once tool wear reaches a

level that covers the vibration wave left on the surface, process damping becomes fully

effective and additional tool wear does not significantly change the damping during the

process. Very recently, Tunç and Budak (2012) have extensively explored the process

damping phenomena with some additional insights by focusing on the effect of cutting

conditions and tool geometry on process damping and stability analytically as well as

experimentally. Cylindrical flank face geometry was suggested over planar flank

geometry to achieve higher process damping and stability. Higher vibration frequency

and amplitude increased indentation volume on the flank face resulting in a higher

process damping and thus stability. This clearly indicates that the process damping

phenomena is still being exploited and has potential to achieve higher process stability

through its precise modelling.

Process damping is a very important phenomenon which occurs at low speed but

it is very crucial to consider it at the modelling stage as it significantly affects the

stability limit predictions. Identification of the process damping coefficient either

analytically or by dynamic testing is also quite essential. After reviewing different

31

analytical models/techniques it was observed that an analytically obtained SLD usually

changes with the machine tool, work material and tool geometry. So it is difficult to

apply such SLD in practice since the SLD is different case by case. Moreover, any

analytical technique used in obtaining the SLD cannot describe the high stability

property at lower spindle speed due to the use of a static model of the cutting (turning)

process. However, the SLDs are still very useful and important in the analytical studies

as they give a ‘global’ picture of the stability behaviour for the turning process.

2.2.2 Nyquist plots

Some researchers used control theory to predict chatter vibrations. It includes the use of

Nyquist plots. Nigm (1981) proposed a method based on the feedback control theory

which was conceptually similar to that of Meritt (1965), but it has the advantage of

accounting for the dynamics of the cutting process. The analysis method was strong

enough for implementation either graphically or analytically and it could account for the

full range of regeneration. The Nyquist criterion was used to predict the stability. The

method only requires plotting the operative receptance instead of 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. (1991) 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 (2002) also performed stability analysis

using the Nyquist criterion. The chatter stability of the dynamic cutting process is

solved using the Nyquist criterion by Altintas et al. (2008) 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.

32

Eynian and Altintas (2009) presented an SDoF and 3DoF turning model for

stability prediction by modelling 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. Turkes et al.

(2011) predicted chatter vibrations in orthogonal cutting with an SDoF turning system

by modelling the process according to OTF (oriented transfer function) and τ

decomposition forms. The stability of the system by applying OTF and τ decomposition

form to the Nyquist criteria was also investigated. The analytical technique (Nyquist

technique) was compared with the TDS (time domain simulation) technique.

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.

2.2.3 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 (2002)

presented a finite-element beam model of a spinning stepped shaft workpiece to perform

stability analysis using the Nyquist criterion. Baker and Rouch (2002) analyzed 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 (2005) predicted the

33

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. (2007) proposed a FEA-based 3-dimensional turning model.

This 3D-FEA model has the potential to determine the resulting cutting forces for even

complex- shaped tool geometries. An approach was used to reduce the calculation time

by using characteristic diagrams for the calculated process forces in the FEA-model by

focusing on the thrust and feed forces. FEM/FEA technique is quite useful in predicting

the stability at the design stage of any process, which saves heaps of time and money in

any production environment. Urbikain et al. (2012) 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

34

2.3 Experimental techniques for chatter prediction and detection

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 operations, 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 the off-line mode and detecting chatter onset in the online mode. These

experimental techniques have potential to establish an unmanned machining

environment. Some experimental techniques are employed off-line 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 will be a semi-analytical one. A true/realistic SLD will rather be obtained with the

help of actual cutting tests, however the task involved in obtaining a SLD by direct

cutting test is very tedious and time consuming. The experimental

validation/verification 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 verification (detection). Figure 2.2

provides information about the number of publications for the most frequently used

experimental techniques like signal processing, chip analysis and artificial intelligence

methods.

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.

35

(2008). Tool condition monitoring can be carried out using force, vibration and acoustic

signals which are very useful for the monitoring of the process. Armarego and Brown

(1969) and Armarego and Whitfield (1985) 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 (1972) 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.

Years Signal processing

Chip analysis

Artificial Intelligence

Total

1941-1950

1 0 0 1

1951-1960

0 0 0 0

1961-1970

2 0 0 2

1971-1980

3 0 1 4

1981-1990

8 1 0 9

1991-2000

14 0 2 16

2001-2010

31 4 5 40

TOTAL 59 5 8 72

Figure 2.2: Number of publications featuring experimental chatter detection approaches and the table showing summary of the selected publications between years 1946 and 2010.

(Please refer to Appendix B).

2.3.1 Signal acquisition and processing approaches

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. Figure 2.3 provides

information about the number of publications for each of these signal acquisition

techniques. 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.

36

Tlusty and Andrews (1983) 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 it is difficult to measure with a vibration transducer.

The cutting force however, 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.

Years Force Vibration Acoustic Total

1941-1950

1 1 0 2

1951-1960

0 0 0 0

1961-1970

2 0 0 2

1971-1980

2 2 1 5

1981-1990

5 3 5 13

1991-2000

13 11 2 26

2001-2010

18 24 8 50

TOTAL 41 41 16 98

Figure 2.3: Number of publications featuring signal acquisition approaches and the table showing summary of the selected publications between years 1946 and 2010.

(Please refer to Appendix C).

Heyns (2007) reviewed these signal processing approaches 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. (2009)

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

37

information in a time-localized fashion. WT has great potential in detecting abrupt

changes in tool conditions in TCM. It is robust and in-sensitive to changing working

conditions.

2.3.1.1 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

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