(sticking sliding region ) finite element simulation of orthogonal metal
TRANSCRIPT
FINITE ELEMENT SIMULATION OF ORTHOGONAL METAL
CUTTING USING AN ALE APPROACH
by
Abdulfatah Maftah
B.Sc.Eng. University of Seventh April, 1998
A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Engineering
in the Graduate Academic Unit of Mechanical Engineering
Supervisors: Dr. H. A. Kishawy, Mechanical Engineering Department
Dr. R. J. Rogers, Mechanical Engineering Department
Examining Board: Dr. A. Gerber, Mechanical Engineering Department, (Chair)
Dr. Z. Chen, Mechanical Engineering Department
Dr. A. Schriver, Civil Engineering Department
This thesis is accepted by the
Dean of Graduate Studies
THE UNIVERSITY OF NEW BRUNSWICK
April, 2008
© Abdulfatah Maftah, 2008
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ABSTRACT
Understanding of the fundamentals of metal cutting processes through the
experimental studies has some limitations. Metal cutting modelling provides an
alternative way for better understanding of machining processes under different cutting
conditions. Using the capabilities of finite element models, it has recently become
possible to deal with complicated conditions in metal cutting. Finite element modelling
makes it possible to model several factors that are present during the chip formation
including friction at the chip tool interface, temperature, stress, strain, and strain rate. The
aim of improved understanding of metal cutting is to find ways to have high quality
machined surfaces, while minimizing machining time and tooling cost.
In this study, an Arbitrary Lagrangian Eulerian (ALE) finite element formulation
is used to simulate the continuous chip formation process in orthogonal cutting. The ALE
is an effective way to simulate the chip formation as it reduces element distortion that
causes several numerical problems. Several ALE models are available in the open
literature. Using an ALE approach one needs to understand the various options in order to
reach the best results. The combination of Lagrangian and Eulerian formulations has been
utilized in the current model to achieve the benefits of both formulations.
The study involves the turning of AISI 4140 steel using a cutting tool made of
carbide material. All the material properties are extracted from previously published
work, including the Johnson-Cook parameters. The effect of initial chip geometry, feed
rate of friction coefficient on cutting forces, stresses, strains, temperature, and formed
chip geometry have been studied. Model solutions were obtained by using the
commercially available finite element package ABAQUS/Explicit, version 6.7. The
ii
model verification is accomplished by comparing the predicted results to published
experimental results.
The current study showed that the effect of the initial chip height does not have
major effects on the results. The new formulation with no initial chip is shown to give
reasonable prediction of cutting force, feed force and chip thickness. To date all
simulations underestimate the chip contact length.
Friction behaviour at the chip-tool interface is one of the complicated subjects in
metal cutting that still needs a lot of work. Several models have been presented in the past
with different assumptions. In the current model, the Coulomb friction model, which
assumes a constant friction coefficient, is used to model the friction in order to simplify
the model. The effect of the constant friction model is considered by analyzing the results
for several friction coefficient values and comparing them to the previous work. The
comparison illustrates some weak points in this model that need to have more study.
in
ACKNOWLEDGMENTS
I would like to express my feelings and gratitude to my great supervisors Dr.
Hossam A. Kishawy and Dr. Robert J. Rogers for their support and guidance and thank
them for offering me the chance to work under their supervision. I truly appreciate their
time that is offered to me whenever I need their assistance and their assistance in writing
my thesis. I would like to thank all members of my committee, Dr. Z. Chen, Dr. A.
Gerber, and Dr. A. Schriver for their review and helpful suggestions. My appreciation
goes to the Department of Mechanical Engineering, faculty and staff for their help. Also,
I would like to thank my great friend Lei Pang for his help and suggestions. I do not
forget to thank the Libyan Embassy for supporting me to finish my study.
Finally, I would also like to thank my family for the support they provided me
through my entire life and in particular, I must acknowledge my wife for her patience,
and assistance. With out all, I would not have finished this thesis.
IV
I would like to dedicate this thesis to my great father, Mohamed Maftah, and my
great mother, Amina Salm who are trying to offer me the best in all my life, to my wife
Sara Elfatouri for her patience, and last but not least to my little boy whom I am excited
to see soon.
v
TABLE OF CONTENTS
Abstract u
Acknowledgments 1V
List of Figures X1
List of Tables x v
Nomenclature XV1
1- INTRODUCTION
1-1 Motivation and Background 1
1-2 Scope of Work 2
1-3 Thesis Objectives 2
1 -4 Thesis Outline 3
2- INTRODUCTION TO METAL CUTTING
2-1 Introduction 5
2-2 Machining Geometry 6
2-3 Orthogonal Cutting 11
2-4 Forces in Metal Cutting 12
3- LITERATURE REVIEW
3-1 Introduction 15
3-2 Finite Element Formulations 16
3-2-1 Lagrangian formulation 16
3-2-2 Eulerian formulation 18
vi
3-2-3 Arbitrary Lagrangian Eulerian formulation 19
3-3 Friction Models 21
3-3-1 Friction characteristics 23
3-3-2 Albrecht's Coulomb friction coefficient 27
3-4 Heat Generation and Deformation Zones 29
3-5 Residual Stresses 31
4- GOVERNING EQUATIONS OF THE NUMERICAL MODEL
4-1 Introduction 33
4-2 Coupled Thermal - Stress Analysis 34
4-3 Equations of Motion 34
4-4 Flow Stress 36
4-5 Heat Generation 38
4-5-1 Convection heat transfer 38
4-5-2 Conduction heat transfer 39
4-5-3 Friction energy and gap conductance definition 39
4-6 Friction Characteristics 41
4-6-1 Simple Coulomb friction definition 41
4-6-2 Shear limited friction factor 42
4-7 Contact Algorithms 43
4-7-1 Kinematic algorithm 44
4-7-2 Penalty Algorithm 44
vii
5- FINITE ELEMENT MODELLING
5-1 Introduction 46
5-2 Model Definition and Assumptions 47
5-3 Material Properties 48
5-3-1 Tool material properties 48
5-3-2 Workpiece material properties 48
5-3-3 Cutting conditions 50
5-4 Modelling Description 50
5-4-1 Elementtypes 50
5-4-2 Geometry and boundary conditions 51
5-4-3 Mesh and chip formation 54
5-4-4 Contact algorithms 58
6- RESULTS AND DISCUSSION
6-1 Introduction 60
6-2 Effect of the Initial Chip Geometry 63
6-2-1 Chip thickness 66
6-2-2 Contact length 68
6-2-3 Cutting and feed forces 70
6-3 Results with No Initial Chip 74
6-3-1 Chip formation 74
6-3-2 Cutting and feed forces 77
6-3-3 Stress and strain distribution 77
viii
6-3-3-1 Von-Mises stress distribution 78
r ~ - ~ Shear stress distributions __ 6-3-J-z /y
6.3.3.3 Normal and friction shear stress along the chip tool interface
6-3-3-4 Equivalent of the plastic strain 81
6-3-4 Temperature distributions 82
6-3-4-1 Temperature distribution in the chip 82
6-3-4-2 Temperature distribution along the rake face 83
6-4 Effect of Friction Factor 86
6.4. i Contour stress, strain and temperature distribution gg
6-4-1-1 Von-Mises stress distributions g7
6-4-1-2 Distribution of shear stress go
6-4-1-3 Distribution of equivalent plastic strain g\
6-4-1-4 Distribution of temperature 93
6.4-2 Chip thickness 95
6-4-3 Contact length 97
6-4-4 Cutting and feed forces 99
6-5 Effect of Mass Scaling 103
7- CONCLUSIONS
74 Summary 1 05
7_2 Conclusions 107
7.3 Contributions 108
7.4 Recommendation for Future Work 108
ix
REFERENCES
APPENDIX A
INPUT FILE FOR ABAQUS EXPLICIT
Curriculum Vitae
LIST OF FIGURES
Figure Page
2.1 Orthogonal cutting geometry 7
2.2 Oblique cutting geometry 7
2.3 Schematic illustration of two-dimensional orthogonal cutting 8
2.4 Thin shear plane model 9
2.5 Thick shear plane model 10
2.6 Pisspanen's shearing process 11
2.7 Velocity diagram 12
2.8 Forces acting on a cutting tool in two-dimensional cutting 13
3.1 Lagrangian definition 17
3.2 Eulerian definition 19
3.3 Arbitrary Lagrangian Eulerian (a) undeformed shape, (b) deformed 20
shape
3.4 Explanation of contact between two surfaces (a) Two bodies with 22
friction after applying the load (b) Free body diagram for the block on
a rough surface
3.5 Variation of the friction force between two bodies 23
3.6 Distribution of normal and shear stress at chip-tool interface 25
3.7 Force decomposition in the Albrecht's model 27
3.8 Corresponding cutting for different feeds 28
3.9 Definition of the critical feed rate 29
3.10 Heat transfer definition in metal cutting and the deformation zones .... 31
4.1 Gap conductance model 40
XI
4.2 Coulomb friction model with a limiting shear stress 43
4.3 Master and slave surfaces in contact 45
5.1 Four-node solid element 51
5.2 Two-node rigid element 51
5.3 Boundary conditions and partition scheme for the previous model .... 52
5.4 Boundary conditions and partition scheme for the new model 54
6.1 Schematic of both models 63
6.2 Chip formation of orthogonal machining at different times with initial 65
chip (f = 0.2 mm, h = 0.5 mm, V = 200 m/min, \i = 0.23)...
6.3 Chip thickness and contact length measurement 66
6.4 Chip thickness obtained by different models 67
6.5 Percentage error ofthe chip thickness for different models 67
6.6 Comparison between the models for the contact length 69
6.7 Percentage error of the contact length 69
6.8 Cutting forces versus time for all initial chip height cases (f = 0.2 mm, 71
V = 200 m/min, [i = 0.6)
6.9 Comparison between the models for the cutting forces 71
6.10 Percentage error of the cutting force 72
6.11 Feed forces versus time for all initial chip height cases (f = 0.2 mm, 72
V = 200 m/min, n = 0.6)
6.12 Comparison between the models for the feed forces 73
6.13 Percentage error of the feed force 74
6.14 Chip formation of orthogonal machining at different times with no 76
initial chip (f =0.3 mm, V = 200 m/min, u. = 0.23)
6.15 Cutting and feed force versus time (f= 0.3, V = 200 m/min, u, = 0.23). 77
xii
6.16 Distribution of Von-Mises stresses in the chip and the workpiece (Pa). 78
6.17 Distribution of shear stresses in the chip and the workpiece (Pa) 79
6.18 Normal contact pressure and friction shear stress distribution over the 80
rake face (f=0.3, V=200 m/min, u = 0.23)
6.19 Friction shear stress and normal contact pressure for the Coulomb 80
friction model identification
6.20 Distribution of equivalent plastic strain in the chip and the workpiece.. 81
6.21 Distribution of temperature in the chip and the workpiece 82
6.22 Distribution of temperature in the tool 83
6.23 Temperature distribution on the rake face (f = 0.3, V = 200 m/min, u = 84
0.23)
6.24 Location of the selected nodes in the rake face of the tool 85
6.25 Rake face temperature versus cutting time 86
6.26 Contour plots of Von-Mises stress for different coefficients of friction 88
(f= 0.3 mm, V = 200 m/min)
6.27 Contour plots of shear stress for different coefficients of friction (f = 90
0.3 mm, V = 200 m/min)
6.28 Contour plots of equivalent plastic strain distribution for different 92
coefficients of friction (f = 0.3 mm, V = 200 m/min)
6.29 Contour plots of temperature distribution for different coefficients of 94
friction (f= 0.3 mm, V = 200 m/min)
6.30 Chip thickness obtained for the experimental and numerical models ... 96
6.31 Percentage of error of the obtained chip thickness for numerical 96
models
6.32 Contact length along the chip-tool interface obtained for the 97
experimental [4] and numerical models
6.33 Percentage error for contact length for numerical models compared to 98
published experimental values
Xlll
6.34 Measured and predi cted force values for di fferent feeds 100
6.35 Percentage of error for the obtained cutting force of the numerical 101
models
6.36 Percentage of error for the obtained feed force of the numerical 101
models
6.37 Cutting force vs. feed 102
6.38 Feed force vs. feed 103
6.39 6.39 Chip thickness vs. feed 104
6.40 6.40 Contact length vs. feed 104
xiv
LIST OF TABLES
Table Page
5.1 Cemented carbide tool physical properties 48
5.2 Workpiece steel AISI4140 physical properties 49
5.3 Johnson Cook equation coefficients 49
5.4 Cutting conditions 50
xv
NOMENCLATURE
General Symbols
A B C d
Del
E F Fs
Fc
Ff Fn
FN
f
fr g h H k K lc m n N P
Pfr q
Qpl
R R' t tc V Vc
vs
Yield stress constant Strain hardening coefficient Strain rate sensitivity Gap clearance Elastic matrix Effusivity Friction force Shear force Cutting force Feed force Force normal to the shear force Normal force Weighting factor for distribution of the heat between interacting surfaces Average of any predefined field variable External body force vector Reference film coefficient Hardness of the metal asperities Gap conductance Conductivity Contact length Mass Normal vector Strain hardening component or Normal force Surface pressure Rate of friction energy dissipation per unit area Heat flow rate per unit area Heat flow rate per unit volume Force between the tool rake face and the chip or the Resultant force Force between the workpiece and the chip along the shear plane Uncut chip thickness (feed) Chip thickness Cutting velocity Chip velocity Shear velocity
XVI
Greek Symbols a P
*P<
• ^ 0
a a°
°y
°N ael
(7 eqv
a
<t> e
"melt
e° 0 6 M T
7 f P
Rake angle Friction angle
Rate of plastic strain
Reference plastic strain rate
Cauchy stress tensor Static yield stress
Yield stress
Normal stress
Total true elastic stress
Equivalent stress Yield stress at nonzero strain rate Shear angle or clearance angle Temperature Melting temperature
Reference sink temperature Average temperature Nondimensional temperature Coefficient of friction Shear stress Fraction coefficient of energy converted into heat Slip rate Density
XVll
CHAPTER 1: INTRODUCTION
CHAPTER 1
INTRODUCTION
1-1 Motivation and Background
The machining process includes the effect of coupling the plastic deformation and
the friction zone at the workpiece, chip, and cutting tool. Any study of metal cutting
models by a finite element method should consider some parameters such as simulation
geometry and material properties. During machining, the material will reach a high
temperature and therefore the finite element method considers how the analysis includes
the changes in temperature. The flow stress can be determined by a combination of the
temperature, strain and strain rate. The Johnson-Cook model can include the
aforementioned to calculate the flow stress. Most researchers usually make friction
1
CHAPTER 1: INTRODUCTION
assumptions based on the experimental data. Many researchers have come up with
different techniques to model the chip-tool interface.
One of these studies has been done by Arrazola el al. [1, 2]. They divided the
chip tool interface into two parts and were able to finally obtain good agreement of the
cutting and feed forces, as well as the chip thickness. Haglund [3] continued this work by
developing a finite element model with a range of friction models. In all cases, the
simulations underestimated the chip-tool contact length. As well there was some concern
that the choice of the initial chip geometry may have affected the results somewhat.
These results provided motivation for the present work.
1-2 Scope of Work
The goal of this thesis is to evaluate the role of initial chip geometry and, if
possible, to develop a finite element model where there is no initial geometry of the
undeformed chip. This model is performed as a two-dimensional Arbitrary Lagrangian-
Eulerian finite element model using ABAQUS Explicit version 6.7. Another goal is to
study the effect of the constant friction coefficient on cutting and feed forces, chip
thickness, and contact length.
1-3 Thesis Objectives
The specific objectives for the thesis are as follows:
• To develop a finite element model by using more realistic initial chip geometries
using the Arbitrary Lagrangian Eulerian technique.
• To compare the obtained results of the proposed finite element model with the
previously published measured data during the cutting of AISI 4140 [1, 2]. The
2
CHAPTER 1: INTRODUCTION
comparison includes the feed force, cutting force, chip thickness, and contact
length, as well as the shear stress, normal stress, and temperature distribution
along the rake face.
• To study the contact mechanism at the chip-tool interfaces in order to obtain
better understanding of the friction behaviour by considering a range of friction
coefficients.
1-4 Thesis Outline
The thesis consists of seven chapters which are listed below:
First, a brief introduction of the principles of metal cutting processing is given in
chapter 2. The introduction includes machining geometry, orthogonal cutting, and the
force model. In the orthogonal cutting section, a short description of the shear plane and
the velocity model is illustrated. In addition, the force model is presented with analysis of
all forces that act in the shear plane and the friction plane.
Chapter 3 is a literature review of numerical models. First, the finite element
formulations are shown with different types of formulations and followed by the friction
models, which includes definitions of sticking and sliding. Also, a brief description of
the Albrecht assumptions [4] is introduced. Next, the heat generation at the primary and
secondary deformation zones is presented. The final point in the literature review section
considers the residual stress, which occurs on the product surfaces.
Chapter 4 describes the governing equations of the finite element model. These
are used in simulations with the Dynamic Temperature Explicit step. As well, the
material model and the contact algorithms are explored.
3
CHAPTER 1: INTRODUCTION
Chapter 5 shows the finite element model in detail. All parameters that are
contained in the simulation, such as the material properties, and model geometry are
illustrated in this section. In addition, boundary conditions and applied loads are
explained.
Chapter 6 discusses several cases of results with and without an initial chip. The
results are compared to the previously published experimental data. The main
comparisons include the chip thickness, contact length, and the cutting and feed forces.
The trends in the results for a range of friction coefficients are presented.
Chapter 7 includes a brief summary of this work. It is followed by a list of
conclusions, contributions and recommendations for future work.
4
CHAPTER 2: INTRODUCTION TO METAL CUTTING
CHAPTER 2
INTRODUCTION TO METAL CUTTING
2-1 Introduction
Metal cutting is the process of removing unwanted material from the workpiece to
obtain a part with high quality surfaces and accurate dimensions with acceptable
tolerances. This process has represented a very large segment in industry since the last
century. It is estimated that 15% of the value of all mechanical components manufactured
worldwide is derived from machining operations [5]. The metal cutting process includes
different forms of machining processes such as grinding, turning, milling, sawing, etc.
For all these types of machining, the productions of chips have different forms and each
process has unique chip morphology. Therefore, it is important to understand the
mechanism of chip formation in order to understand the machining process.
5
CHAPTER 2: INTRODUCTION TO METAL CUTTING
Many studies have been performed in the area of metal cutting. In the middle of
the 19th century, the old (trial and error) experimental method was the earliest way to
develop models of the metal cutting process. The simplified models were also presented
and used based on the shear zone theory [6]. The chip formation was assumed to take
place as the result of shear actions in the shear zone. Later, finite element analysis was
utilized, trying to optimize metal cutting processes. This opened a new way to investigate
the state of stresses, strains, temperatures, and feed and cutting forces in the deformation
zones. These models provide a better understanding of metal cutting and provided ways
to do detailed studies of the effect of different parameters where the magnitude of some
parameters such as the temperature cannot be easily measured experimentally.
2-2 Machining Geometry
Metal cutting processes can be divided into two basic categories: orthogonal and
oblique metal cutting. In orthogonal metal cutting, the cutting edge is perpendicular to the
relative cutting velocity and also normal to the feed direction, as shown in Figure 2.1.
However, in oblique cutting, the cutting edge is inclined at an acute angle to the direction
of the cutting velocity as shown in Figure 2.2. During the machining, the tool will be
given a certain position to obtain the amount of feed that will be removed from the
workpiece. In general, the cutting edge of the tool will engage into the workpiece;
therefore, high pressure and high temperature will occur at the front of the tool.
6
CHAPTER 2: INTRODUCTION TO METAL CUTTING
Chi
Cutting edge a
Tool
Motion of Workpiece
Workpiece
Figure 2.1 Orthogonal cutting geometry
Cutting edge axis
Tool
Cutting edge inclination
Motion of Workpiece
Workpiece
Figure 2.2 Oblique cutting geometry
The easiest way to present the fundamentals of the orthogonal metal cutting
process is by the two dimensional metal cutting geometry as shown in Figure 2.3. As the
workpiece starts moving, the cutting edge penetrates into the workpiece and forces the
chip to grow up so that the chip will be formed and move along the rake face of the tool.
7
CHAPTER 2: INTRODUCTION TO METAL CUTTING
This process causes high pressure and plastic deformation is expected to take place in
front of the cutting edge. The shape of the formed chip will be affected by the cutting
conditions (cutting speed, feed and depth of the cut), tool geometry and material
properties.
Or it
Motion of Workpiece ,
ti
Shear deformation zone
Cutting edge
Figure 2.3 Schematic illustration of two-dimensional orthogonal cutting
The uncut chip thickness t is known as the feed while the deformed chip has a
different chip thickness ^c. The tool will be defined by rake face angle a and flank
angle/? . The rake angle is defined to be positive on the right side (clockwise from
vertical) and negative on the left side (counter clockwise). The contact length lc is defined
as the distance from the tip of the tool to the point where the chip loses contact with the
tool on the rake face. The friction between the chip and the tool plays a significant role in
i Motion of chip
Chip ,--'<X -
Cutho toof
final surface RMC face
_____ * » ..' , A
: ' • : ' • • ' . ' " ' • • Batik fees J. Produced surface ' »- * 0 * >
"' "' " ' ""'""" * ¥ *" '
8
CHAPTER 2: INTRODUCTION TO METAL CUTTING
the cutting process because of the heat energy that is transferred into the workpiece. It
may be reduced by optimized tool geometry, tool material, cutting speed, rake angle, and
cutting fluid. Because of the high pressure and temperature, a built up edge (BUE) may
exist near the tool tip. As a result of the built up edge, welded material will become a part
of the cutting tool and may lead to tool wear. The shear angle if) is affected by the welded
material so the size of the welded material grows until it reaches a critical size. Then, it
breaks and starts the new welded material.
In orthogonal machining the shearing action takes place along the shear plane so the
chip will start to flow over the rake face. The shearing zone has been modelled using
either one of two assumptions. Merchant [7] developed an orthogonal cutting model by
assuming the shear zone to be thin as shown in Figure 2.4. Once the material approaches
the shear plane, the plastic deformation begins. A thin shear zone is usually created at
high cutting speeds.
Figure 2.4 Thin shear plane model
Some other researchers had different assumptions where the shear zone would be
thick as shown in Figure 2.5. This kind of shear zone is more complicated and normally
seen when using low cutting speeds.
9
CHAPTER 2: INTRODUCTION TO METAL CUTTING
Thick shear plane
Workpiece
Figure 2.5 Thick shear plane model
Both models have been used to analyze metal cutting processes where the thin
shear zone relates to the shear plane angle, cutting condition, material properties, and
friction behavior, while the thick shear zone model is based on the slip-line theory [6].
Many researchers have focused on chip formation. One side of the chip is in
contact with the rake face and as result of the relative motion and friction it forms what is
called the secondary shear zone. On the other side of the chip, the free surface is mainly
affected by the primary shear zone. Because of the high speed of machining, the primary
zone will have high pressure and temperature. From the geometry shown in Figure 2.3,
the cutting ratio can be calculated from this equation [6]:
r = L = ABsint ( 2 1 )
tc AB cos(^ - a)
where t is uncut chip thickness, tc is the deformed chip thickness, a is the rake angle and
<j) is the shear angle which can be determined such that [6]:
rcosor tan^ = (2.2)
1 - r sin a
10
CHAPTER 2: INTRODUCTION TO METAL CUTTING
2-3 Orthogonal Cutting
The single shear plane model was proposed to explain the chip formation in the
metal cutting process. From the earlier approaches the concept of shear plane has been
developed analytically in several models such as Pisspanen's model [6]. He described the
shearing process as a deck of cards such as when the first card slides forward, it will be
followed by the second card and so on as far as the cutting process keeps going. See
Figure 2.6.
Chip 1 a :
Parallel shear cards
(J) Tool
Shear plane
Figure 2.6 Pisspanen's shearing process [6]
The main velocity components in metal cutting can be seen in Figure 2.7. The
velocity of the cutting tool relative to the workpiece is known as cutting velocity (V ) .
The velocity of the chip relative to the tool is known as shear velocity (Vs). The velocity
of the chip relative to the workpiece is called the chip velocity (Vc).
11
CHAPTER 2: INTRODUCTION TO METAL CUTTING
9 0 - ( a - ^ )
a ••^Is
V I r
\T
Figure 2.7 Velocity diagram [6]
The velocity diagram shows the summation of the cutting velocity and the chip velocity
equals to the shear velocity. V^ and V~ are given by:
V, sin^
C V cos I m - a
(2.3)
VS = COS Of
COS (4-a) (2.4)
2-4 Forces in Metal Cutting
Knowing the forces that are acting in metal cutting is important for many reasons
such as for the power requirement. Some parameters including the cutting speed, feed,
and the depth of the cut influence the forces. Most likely, the forces can be reduced to
two main forces in 2-D instead of three forces in 3-D. There are two main forces we can
consider in orthogonal metal cutting. The force between the rake face and the chip (R),
12
CHAPTER 2: INTRODUCTION TO METAL CUTTING
and the force along the shear plane (R'). The two forces R and R' are equal but opposite
to each other.
These forces are decomposed into three sets as illustrated in the free body diagram
of the chip shown in Figure 2.8. The study of these forces can help us to estimate the
power requirement, tool geometry and material properties of the tool.
In general, the horizontal and vertical forces are called cutting force component
(Fc) and feed force component (Fj), respectively. In the shear plane the force (R') can be
resolved into the shear force (Fs) and the normal force to the shear force (Fn). On the rake
face the force (R) can also be resolved into two components: friction force (F) and normal
force (TV).
Chip
Figure 2.8 Forces acting on a cutting tool in two-dimensional cutting
13
CHAPTER 2: INTRODUCTION TO METAL CUTTING
In 1945, Merchant developed the most popular analytical model used in metal
cutting. The relations among the shear and friction components of forces in terms of
cutting and feed force can be obtained as follow [6]:
Fs = Fc c o s (/> - Ff s in </> (2.5)
Fn = Ff c o s </)-Fc s in <f> (2.6)
F = Fcsina + Ffcosa (2.7)
N = Fccosa-Ff since (2.8)
where Fc and Ff are the cutting and feed forces, respectively; Fs is the shear force, Fn
is the normal force along the shear plane; F is the friction force and the normal
force along the rake face.
14
CHAPTER 3: LITERATURE REVIEW
CHAPTER 3
LITERATURE REVIEW
3-1 Introduction
Finite Element Models (FEM) have been involved in manufacturing fields
because of the advantages that can be achieved from modelling processes such as metal
cutting. The FEM has the ability to solve complicated calculations of metal cutting by
detailed modelling of parameters such as the material properties and friction
characteristics. For example, the material properties can be incorporated by the Johnson-
Cook formula, which contains strain, strain rate, and temperature.
Creating FEM with different formulations can provide better results. Researchers
have utilized two formulations to model orthogonal metal cutting. The comparison shows
some weak points in each model. The latest formulation was created by combining the
15
CHAPTER 3: LITERATURE REVIEW
two formulations, Lagrangian and Eulerian, and is called Arbitrary Lagrangian Eulerian.
The advantages of FEM are explained in the following section.
As explained above, complicated friction is involved in the FEM of orthogonal
metal cutting to study the interactions between the surfaces of two different bodies, the
tool and workpiece. The reality shows that friction behavior is hard to estimate in
machining. Some other models present the friction coefficient in terms of shear limit and
temperature dependence. Friction characteristics require more studies because the
obtained results of all models show some weak points.
The temperature effect is one of the most important parameters that might cause
trouble to the product surface and the tool as well. The temperature changes result in
thermal stresses in the workpiece so that many studies focus on the residual stresses
where the stress remains in the product surface after the machining.
3-2 Finite Element Formulations
The specific mesh formulations used for models of orthogonal machining are
Lagrangian, Eulerian, and Arbitrary Lagrangian Eulerian. The advantages and
disadvantages of these formulations will be discussed in this section as follows.
3-2-1 Lagrangian formulation
The Lagrangian or updated-Lagrangian method is often used in FEM. These
formulations are similar. The only difference is that updated-Lagrangian uses an adaptive
mesh technique to reduce mesh distortion. The updated-Lagrangian formulation was first
used for machining model by Klamecki in 1973 [8].
16
CHAPTER 3: LITERATURE REVIEW
The basic concept of the Lagrangian definition is that the mesh will follow the
material. The deformation can happen by increments in time. After each increment the
reference domain is updated based on material coordinates. In this way, the history of the
material is easily taken into account. This updated position situation is used as an initial
condition for the next increment, so the FE mesh is connected with its material. However,
the updated-Lagrangian method can be costly because of the mesh distortion during the
large deformation in these calculations (see Figure 3.1).
I
2 k
=M
(a) Initial Mesh (b) Deformed Mesh
Figure 3.1 Lagrangian definition
Carroll et al. [5] formulated two models. The first one was Updated-Lagrangian
and the second was Eulerian. The updated-Lagrangian model successfully determined the
deformed chip, stress, and the temperature under the failure criteria to control the chip
formation process. Shih and Yang [9] have developed an FEM for metal cutting based on
Updated-Lagrangian which includes the effect of elasticity, visco-plasticity, temperature,
strain rate and the effect of frictional force. Marusich and Ortiz [10] presented an
interesting FEM analysis of machining, based on a Lagrangian formulation with adaptive
mesh processing for modelling high speed machining work. Recent work with the
17
CHAPTER 3: LITERATURE REVIEW
Updated-Lagrangian formulation was done by Ozel in 2005 [11]. He used this
formulation to simulate a continuous chip formation process in orthogonal cutting by
presenting different friction models based on the experimental data.
3-2-2 Eulerian formulation
Another FEM option is to use the Eulerian formulation. The simple definition of
the Eulerian formulation is that the mesh will be fixed in space and the material will flow
through the mesh. The advantage of the Eulerian formulation is that this formulation does
not have any mesh distortion because the mesh is spatially fixed during the simulation
(see Figure 3.2). However, the mesh does not connect to the material. It is difficult to
obtain accurate data from free surfaces, which is an important result of the simulation of
the forming process as seen in Figure 2.3. Some researchers [12, 13, 14] used the
Eulerian formulation model in metal cutting because this model can use fewer elements
and reduce the time of the analysis. Leopold et al. [27] has developed an Eulerian
analysis of 3D oblique machining with a single cutting edge. Carroll et al. [5] compared
the Eulerian model with Lagrangian model and they found that the advantage of the
Eulerian model is that it does not need failure characteristics. Also, the mesh cannot have
high distortion. Strenkowski an Moon [14] built an FEM of orthogonal metal cutting with
an Eulerian formulation. The model predicted temperature distribution. He found that the
shear stress occurred over a finite region in front of the tool. In the same year, Childs and
Maekawa [13] used the Eulerian formulation to create an FEM to study the tool wear of
cemented carbide tools in high speed machining. The results of the model were very good
except there are small percentage of errors in the cutting forces.
18
CHAPTER 3: LITERATURE REVIEW
/ \
(a) Initial Mesh (b) Deformed Mesh
Figure 3.2 Eulerian definition
3-2-3 Arbitrary Lagrangian Eulerian formulation
Recently, researchers have been focusing on the Arbitrary Lagrangian Eulerian
(ALE) formulation to combine the best features of both the Lagrangian and Eulerian
formulations. The concept of ALE was first proposed lately. This formulation was called
"the coupled Eulerian-Lagrangian method" and later on was changed to "the Arbitrary
Lagrangian Eulerian Model." The ALE method was introduced into the finite element
method by Belytschko and Kennedy [15]. It was applied to finite strain deformation
problems in solid mechanics. The ALE formulation helps to solve problems with large
deformation in solid mechanics
The ALE adaptive meshing is a helpful feature that can smooth the deformation
throughout the analysis by allowing the material to flow with the mesh. The mesh has
some limitations during the analysis; however, ALE helps to avoid these limitations. The
ALE formulations shown in Figure 3.3 uses re-meshing techniques to keep the analysis
19
CHAPTER 3: LITERATURE REVIEW
going. Other formulations such as the Lagrangian formulation have difficulty avoiding
high distortion of the workpiece.
(a) (b)
Figure 3.3 Arbitrary Lagrangian Eulerian (a) undeformed shape, (b) deformed shape
Wang and Gadala [16] investigated the ability and the accuracy of mesh
formulation. They ended with the conclusion that many problems occurred during
extensive mesh distortion, load fluctuation, and inaccurate description at the boundary
condition with a corner (tool tip). With ALE, most problems have been avoided;
however, at the time, ALE was not developed carefully for solid mechanics problems.
Olovsson et al. [17] developed FEM by using the ALE formulation so that the large strain
that is caused from the high deformation in metal cutting does not affect the element
distortion at the tool tip. Movahhedy et al. [18] presented that the arbitrary Lagrangian-
Eulerian (ALE) formulation offers the most efficient modelling approach. He included
the features of an ALE analysis of the cutting process in his conclusion. Movahhedy et al.
[19] focused on the chamfered cutting edge in their FEM simulation that utilized ALE.
The results of the simulation show that the chamfer angle does not have a large effect on
20
CHAPTER 3: LITERATURE REVIEW
the chip removal process. The successful results of the ALE motivated many researchers,
such Arrazola et al. [1] who studied the friction on the chip tool interface, to keep
developing this model. After that, the majority of researchers have followed the ALE
procedure to build new ideas into their research.
In recent work, Kishawy et al. [20] in 2006 considered the effects of different
cutting edge radii on the rake face of the tool by using the ALE formulation. They
concluded that the cutting edge significantly affects the cutting forces, the chip thickness,
chip contact and the temperature.
3-3 Friction Models
A general conception of friction can be considered as the tangential force
generated between two surfaces. Friction can be represented as a resistance force acting
on the surface to oppose slipping. Figure 3.4 (a) shows a simple example of friction
where a block is pushed horizontally with mass m over rough horizontal surface. As
showing in the free body diagram, Figure 3.4 (b), the body has distributions of both
normal force N and horizontal force/along the contact surface. From the equilibrium, the
normal force N acts to resist the weight force of the mass mg and the friction force/acts
to resist the force F.
21
CHAPTER 3: LITERATURE REVIEW
mg mg
B
(a) (b)
Figure 3.4 Explanation of contact between two surfaces (a) Two bodies with friction after
applying the load (b) Free body diagram for the block on a rough surface
Basically, there are two types of friction, which are static and kinetic as shown in
Figure 3.5. By increasing the force F, friction force /increases too. The blocks cannot
move until the force F reaches the maximum value. This is called the limiting static
factional force. Increasing of the force F further will cause the block to begin to move. In
the static portion, the limiting friction force can be expressed as:
F«a,ic=V,N
where jus is called the coefficient of static friction
(3.1)
When the force F becomes greater than Fstaljc, the frictional force in the contact
area drops slightly to a smaller value, which is called kinetic frictional force. Machining
models generally just consider the kinetic friction coefficient which can be calculated by
the following equation:
22
CHAPTER 3: LITERATURE REVIEW
J1 kinetic ~ Mk^ (3.2)
No motion
o
a) o c
"55 w
Motion
Force required to start sliding
Kinetic friction
- • p
Applied force (F)
Figure 3.5 Variation of the friction force between two bodies
3-3-1 Friction characteristics
The contact region and the friction coefficient at chip-tool interface are affected by
parameters such as feed rate, cutting speed, and rake angle. The reason for this effect is
that high normal pressures act on the surface. Many researchers have tried to explain
what happens at the chip-tool interface where different friction models were employed in
finite element models [11, 20, 21]. Some of them investigated reliable predictive models
based on experiments. Other researchers such as Johnson [22] summarized different
models and applications to model dynamical contact problem with friction.
23
CHAPTER 3: LITERATURE REVIEW
Friction at the tool-chip interface is a complicated problem. It is hard to estimate
the fiction coefficient at the chip-tool interface based on the relationship between the
normal stress and the shear stress. The basic Coulomb friction model is stated as the
relation between the friction force and the normal force. From the metal cutting
geometry, the Coulomb friction coefficient can be calculated from the measured cutting
and feed forces as an average value follows [6]:
F r + Fc tan a
Fc - Ff tan a
where F f is the feed force, Fc is the cutting force, and a is the rake angle.
The best way to obtain the friction coefficient at the tool-chip interface is to
directly measure the normal and shear stresses during the actual metal cutting process.
Usui and Takeyama [23] studied the distribution of the normal and shear stresses along
the tool face by using the photo elastic method at low speed. They found that the shear
stress was constant over half of the contact length at the chip-tool interface (sticking
region) and then decreased to zero (sliding region).
Most popular FEM have been developed based on the basic Coulomb friction law:
the friction force is proportional to the normal load. Merchant and Zlatin [6] defined the
friction coefficient along the chip sticking and sliding regions. Over the chip-tool
interface at the sticking region is used a constant shear stress x. Over the remaining
sliding region, the shear stress can be calculated using the friction coefficient ju. The
normal and shear stress distributions can be illustrated in the two regions. See Figure 3.6.
24
CHAPTER 3: LITERATURE REVIEW
n . T
f , t i ! t )
"X.
{^•swT***
Figure 3.6 Distribution of normal and shear stress at chip-tool interface
The values of the shear stress can be calculated in the sliding and sticking zones
such that:
T = jUa when //O" < Tmax (sliding) (3.4)
T = rmax when Ma - rmax (sticking) (3.5)
Previously, FEM of metal cutting used the friction coefficient as a constant based
on Coulomb's law over the entire chip-tool interface [8, 24]. Some researchers assumed
the limit of shear stress to be 7max - —j= where ov is the yield stress [24, 25]. The shear
stress along the chip tool interface can be calculated from equations 3.4 and 3.5 but the
problem is how the sticking and the sliding regions can be defined analytically.
25
CHAPTER 3: LITERATURE REVIEW
Other researchers developed Coulomb friction models based on dependent
temperature [3, 26, 27]. The critical shear stress would be modelled as function of the
temperature along the chip tool interface. Astakhov and Outeiro [28] presented a model
to show the contact stress distribution at the chip tool interface. This study includes a
comprehensive investigation of many attempts to define the stress distributions. After the
comparison between the FEM and the experiment, the normal and shear stresses were not
uniform. Studying the stresses along the chip tool interface helps to understand the
behaviour of the friction coefficient.
Some models have been formed based on variable shear friction along the chip-
tool interface. One of the models was simulated by Usui and Shirkashi [23] who derived
the empirical stress characteristic equation as a variable friction model as follows:
T - k 1-exp \ k )
(3.6)
where k is the shear flow stress, // is the friction coefficient obtained from experiments,
Tf and &N are the shear and normal stresses, respectively. The idea of variable shear
friction was developed by several researchers such as Ozel et al. [11] who extended
further modification to equation (3.6) so that the sticking stresses in that region can be
different from the shear strength as follows:
T = wk 1-exp f \n
\ wk J (3.7)
26
CHAPTER 3: LITERATURE REVIEW
where w and n are correction factors. The correction factors help to keep the friction
stress less than the shear flow stress of the material.
3-3-2 Albrecht's Coulomb friction coefficient
In order to define the Coulomb friction coefficient, Albrecht's analysis has been
used to estimate the coefficient of friction along the chip-tool interface by eliminating the
cutting edge effect [4]. Figure 3.7 illustrates the basic concept of Albrecht's model.
Undeformed chip thickness
Workpiece
Figure 3.7 Force decomposition in the Albrecht's model [4]
The forces are resolved into two components where P is close to the cutting edge
and Q is applied on the rake face. With the sharp cutting tool, the ploughing force P has
insignificant value. But for the tool that is not sharp, the force P will affect significantly
the force model. For uncut chip thickness greater than the critical uncut chip thickness,
Albrecht assumes that the force P has a constant value; however, at feeds less than the
critical uncut chip thickness, the force P will affect the feed force significantly. After
passing the critical chip thickness, the force P slightly affects the feed force. Example
27
CHAPTER 3: LITERATURE REVIEW
feeds and chip thickness are shown in Figure 3.8. The sum of the two force components
(cutting and feed) can be obtained by the sum of two vectors P and Q.
Figure 3.8 Corresponding cutting for different feeds
Figure 3.9 illustrates the cutting force and the feed force relation at different uncut
chip thicknesses. At the smallest feeds in Figure 3.9 (A and B sections), a non-linear
relation will describe the behaviour of the cutting and feed forces. Below the critical
point, the P force will cause a relatively large feed force. The section C where the relation
takes a linear behaviour is used to approximate the value of the Coulomb friction
coefficient. The friction coefficient along the chip tool interface can be defined by taking
the slope of section C as tan (A - a) and then ju = tan X [ 1 ].
28
CHAPTER 3: LITERATURE REVIEW
Figure 3.9 Definition of the critical feed rate [3, 4]
Arrazola et al. [1, 2] used the previously presented model by Albrecht [4]. In this
study the friction was defined at a variety of feeds. Arrazola et al. [1, 2] applied the dual
friction idea to the chip-tool interface. More recently, these studies were followed by
different investigations. Some other researchers also used the idea of the dual friction
model [3].
3-4 Heat Generation and Deformation Zones
During machining, high pressure and shear stress occur in the contact surface.
Most of the plastic deformation energy is converted into heat, which is usually
approximated at 90% [20, 21, 29]. The mechanical work that is done in the machining
process in the primary deformation zone can be predicted analytically or measured
experimentally. The higher temperature that exists in the secondary deformation zone is
caused by the hard contact and friction. Because of raised temperature in metal cutting,
29
CHAPTER 3: LITERATURE REVIEW
the heat energy will influence the tool wear, tool life, and chip formation [11, 30].
Increasing the temperature of the workpiece at the primary deformation zone will soften
the material. Also, the temperature at the secondary deformation zone will affect the
contact process at the chip tool interface. Finally, the heat generated in the tertiary
deformation zone will influence the produced surface as shown in Figure 3.10.
Temperatures in the primary and secondary zones are mainly affected by the cutting
conditions [6, 31].
Measuring temperature during metal cutting is extremely difficult but some
researchers are trying to develop ways to measure the temperature of the models
experimentally. Blok [32] was one of the researchers who developed energy partition
analysis to study the heat sources in metal cutting. The measured temperature due to
machining was obtained from a thermal imaging camera [32]. Basically, the assumption
is that all the mechanical work done in the machining process is converted into heat.
Increasing the temperature in the workpiece, chip, and tool will affect the product
surface, since the temperature has an effect on the surface quality and the tool wear.
Some of the heat will be removed from the primary and secondary zones by the
chip (see Figure 3.10). The temperature at the tool will be raised in the secondary heat
zone. Also, the heat that comes from the primary deformation zone will affect the
temperature of the cutting tool, so that part of the heat generated at the shear plane will be
carried by the chip through the rake face into the tool.
30
CHAPTER 3: LITERATURE REVIEW
Convection Boundary
Tool Holder
Primary deformation zone
Tertiary deformation Z O n e , A , , •
Workpiece
Figure 3.10 Heat transfer definition in metal cutting and the deformation zones [31]
3-5 Residual Stresses
Due to the thermal effect in orthogonal metal cutting, an important subject has
been noticed inside the workpiece which is residual stress. Some of the heat energy
comes from the plastic deformation zones and the thermal stress goes to the surface layer
of the workpiece.
Genzel [42] studied the residual stress by creating a numerical model and
compared the obtained results with the experimental data obtained with X-rays. He found
that the influence of the cutting speed and feed causes tensile residual stress over the
productive surface of the workpiece. Liu and Guo [25] investigated the effect of
sequential cuts and the friction at the chip tool interface on residual stresses in the
machined layer. They found that the residual stress is sensitive to the friction at the chip
tool interface. In their analysis, they performed more than one cut to predict the effect of
sequential cuts on the residual stress. M'Saoubia et al. [32] considered the residual
31
CHAPTER 3: LITERATURE REVIEW
stresses in a wide range of cutting feeds including cutting speed, feed rate, tool geometry
and tool coating. By taking consideration the hardness of the material, they found a high
tensile stress on the workpiece surface. This tensile stress is caused by local thermal
effects that are generated from heat energy. Some other influences could come from the
mechanical and feed rate effects [33, 34].
Hua et al. [35] focused on the effects of workpiece hardness by using a newly
proposed hardness flow stress model. Also, they included different cutting edge shapes
such as sharp edge, honed, and chamfered and different cutting conditions. They ended
with a brief presentation of residual stresses in the axial and circumferential directions of
the machined surface. A more compressive residual stress was achieved at higher
workpiece hardness. In addition, a larger hone radius or a chamfered edge generated more
compressive residual stresses; however, the effect of the chamfered was less than the
honed.
Nasr et al. [36] in 2006 studied the effect of the tool edge using an Arbitrary
Lagrangian Eulerian formulation. They found that the cutting edge geometry had a major
effect on the cutting process. As a result, a higher tensile residual stress in the produced
surface layer was caused by a high cutting edge radius. With a large cutting edge radius, a
high compressive residual stress was generated beneath the surface. The maximum
compressive residual stress occurred deeper into the workpiece surface. The development
of non-sharp cutting edge caused a stagnation zone underneath the tool.
32
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
CHAPTER 4
GOVERNING EQUATIONS OF THE
NUMERICAL MODEL
4-1 Introduction
An understanding of the system solution is important to form a complete input file
for ABAQUS Explicit. With its many of options, ABAQUS can model the very
complicated conditions of metal cutting. It is important to understand how to use its tools
which are available such as element types, material models, mesh density (coarse or fine),
adaptive meshing techniques, boundary conditions, etc. Stress and thermal characteristics
at the contact area are the greatest challenges with this type of model. The constitutive
equations for the model are described below.
33
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
4-2 Coupled Thermal - Stress Analysis
In the metal cutting process, fully coupled thermal-stress is a requirement for the
analysis because the stress depends on the temperature distribution and the temperature
depends on the stress solution. The contact condition exists in the secondary deformation
zone where the heat is conducted between the chip tool interfaces, depending on the
pressure. The thermal and mechanical solutions can be solved simultaneously [3, 37, 38].
4-3 Equations of Motion
The explicit dynamic analysis procedure is based on using very small time steps.
The dynamic equations are integrated using the explicit central difference integration
method, which uses a diagonal mass matrix. The velocity estimated equation is integrated
through the time as follows [37]:
At,. ,, + At,., "(1+1/2) ~ M ( i - l /2 ) + n. U(i) V*A>
And the displacement is determined as
<.)="(0+ AV.)"(J)+ l /2) <4'2)
where the subscript (i) refers to the increment number, uN represents the displacement
vector, and At represents the time increment. The central difference integration operator
is explicit in that the kinematic state may be advanced using known values of u^_V2] and
u^ from the previous increment.
34
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
The explicit integration rule provides high computation efficiency due to the use
of diagonal element mass matrices so that the accelerations at the beginning of the
increment may be computed by
^ = ( M - ) - * ( F ( ^ ) (4.3)
where M ^ i s the diagonal lumped mass matrix, F J i s the applied load vector, and IJis
the internal force vector. The explicit procedure integrates through time by using many
small time increments.
The explicit forward difference time integration method integrates for the current
temperature using the value of 0{" from the last increment. The heat transfer is
integrated as
$ , ) = < + A W & . / 2 ) (4"4)
N
where 9,., is the temperature at node Nand the subscript /refers to the increment number
in an explicit step. The values of 9,", are calculated at the beginning of the increment by
^ = ( C - ) " ' ( ^ - ^ ) (4.5)
where CNJ is the lumped capacitance matrix, P,i is the applied nodal vector, and F,i is
the internal flux vector.
Since both the forward difference and central difference integrations are explicit,
displacement and heat transfer solutions are obtained simultaneously so that no iteration
or tangent stiffness matrix are required [37]. One of the options with ABAQUS is the
time step increment. Chosen time step increments are based on the smallest element to
35
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
reach the stable time for the system. In addition, ABAQUS explicit will take the time
step increment that is less than the estimated one with a factor from 1 / v 2 to 1 for two
dimensions.
Mass scaling is a feature that is used when the finite element model contains very
small elements. Many finite element models contain complicated meshes that can have
very small elements. These small elements affect the time increment of the system and
can cause very small increments. By scaling the mass of these controlling elements at the
beginning of the step, the time increment can be increased. In fact, applying the mass
scaling should not be over the entire model because increasing the over all mass can
influence the accuracy.
ABAQUS Explicit has two types of mass scaling: fixed mass scaling and variable
mass scaling. Fixed mass scaling is used to define the element masses that are assembled
to the global mass matrix. The mass scaling can also be defined as a factor that can be
used to reach a desired time increment. Variable mass scaling is used to scale the mass at
specified solution times as an addition to any fixed mass scaling that is exists. Mass
scaling factors will be calculated automatically and applied through the desired steps.
4-4 Flow Stress
Workpiece material deforms extensively along the shear plane and the contact
area where the plastic deformation exists with high values. Strain rate dependence has
been assumed to model the plasticity region. Considering the strain rate based on the
previous work where the parameters are available, the Johnson-Cook plasticity model
will be explained in this section. The Johnson-Cook model is the perfect formula that can
36
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
be used to determine the flow stress. It is a function of strain, strain rate, and temperature.
This function can be utilized for high strain rate deformation of materials [3,37].
In the plastic regime, flow stress can be expressed primarily as written below:
= *°(spl,e) R s \ J
.PI
(4.6)
where a is the yield stress at nonzero strain rate, s is the equivalent plastic strain rate,
-pi G°\e ,0 is the static yield stress, and R
f±p'\ £
V J
is the ratio of the yield stress at nonzero
strain rate.
Johnson-Cook strain rate can be presented as [3, 37]
1 £ =£0 exp
C (*-l) for R>\ (4.7)
.pi
where £ is the equivalent plastic strain rate, and s0 and C are the material parameters
measured at or below the transition temperature, 9tmnsUion. The yield stress performed can
be written as
(T = IA + B(£P1)") ,pi
1 + Cln
v £ » ;
( l - # m ) (4.8)
where a is the material flow stress, sp the equivalent plastic strain, sQ the reference
plastic strain rate at 9tmnsition, A yield strength, B hardening modulus, C strain rate
sensitivity, n hardening coefficient, and m thermal softening coefficient
37
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
transition 0 for e<0lr
0 = \{0- Vra^on )/(#„„/, " ^™„WoB ) M 6><rnnsilio„ <&< 9melt (4.9)
i for e>emeh
where #is the current temperature, 9melt\% the melting temperature, and 0tmmiljm\s the
transition temperature defined as the one at or below which there is no temperature
dependence on the expression of the yield stress. The material parameters must be
measured at or below the transition temperature [37].
4-5 Heat Generation
In metal cutting, the heat is generated due to the plastic work in the primary zone
and by friction in the secondary shear zones. Due to high speed machining, heat
generated does not have sufficient time to diffuse along both bodies, the tool and the
workpiece. The plastic strain gives rise to a heat flow rate per unit volume, as shown
below [37, 38]:
Qpl=rioJs (4.10)
where Qpl is the heat flow rate per unit volume, 77 is the percentage of plastic work
transformed into heat which is approximated as 90%, a is the equivalent stress, and
.pi
e is the plastic strain rate.
4-5-1 Convection heat transfer
A convection heat transfer is applied on the free surface of the workpiece and the
flank surface of the tool. The convection heat is expected to affect the production surface.
q = h[e-B°) (4.11)
38
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
where q is the heat flux across the surface, h is a reference film coefficient, 6 is the
temperature at the surface, and 9° is the reference sink temperature [37].
4-5-2 Conduction heat transfer
Because of the heat energy from the primary and secondary deformation zones,
conduction heat transfer occurs inside the workpiece material. The conduction heat
transfer can be calculated basically from the equation below
q = k(OA-0B) (4.12)
where q is the heat flow per unit area crossing the interface from point A to point B, 6A
and 6B are the temperatures at A and B, and k is the thermal conductivity.
4-5-3 Friction energy and gap conductance definition
During the contact between the tool and the chip along the secondary shear zone,
heat generation and gap conductance models are used at the friction surface. The rate of
frictional energy rate per unit area can be calculated as:
pfr=T-r (4.13)
where r is the frictional stress and y is the slip rate. The frictional thermal energy that
goes into each surface is given as
qA=flPfi (4-14)
qB={\-f)r?Pfl. (4.15)
39
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
where / is the weight factor, qA is the heat flux into the slave surface (chip), and qB is
the heat flux into the tool. The fraction of the heat energy conducted into the chip is given
as[43]
f= fjjy I Hd /•>
^C,T yJ^-CjPc.T^CT
(4.16)
(4.17)
where the Kc T is the thermal conductivity, pc T is the density, and Cc T is the specific
heat capacity. The subscript symbol C indicates the chip, and T indicates the tool [3, 37,
43].
The gap conductance can be expressed as seen in Figure 4.1 in terms of the
distance d. The maximum conductivity can be reached when the two surfaces are in the
perfect contact so there is no gap and the distance d is equal to zero. When the gap
appears, the magnitude of conductivity decreases.
k
<±>->d
Figure 4.1 Gap conductance model [4]
40
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
When the distance d reaches a certain value, the conductivity magnitude can be
ignored because of the very small value. The lowest value of the conductivity can be
controlled by a constant. The possible variables affects gap conductance are
k = k{0,d,pjr) (4.18)
where 6 is the average temperature, d is the gap clearance, p is the surface pressure, and
/ is the average of any predefined field variable.
4-6 Friction Characteristics
Friction plays a very important role in metal cutting. Friction can change many
properties because of the heat energy gained from the contact. These effects include the
surface quality of the products and the rate of tool wear. Most researchers have used
simplistic simulations to present their models with the basic Coulomb friction role [11,
36, 39]. Others choose more complicated models with variable coefficients where the
shear limit or temperature dependency is developed.
4-6-1 Simple Coulomb friction definition
Basically, the definition of the Coulomb friction model is illustrated as a ratio
between the maximum shear force to the maximum normal force that act at the chip tool
interface. In this definition, the shear stress can be written in terms of the local forces
(shear and normal force) that exist along the chip-tool interface. The sliding shear stress
can be simplified as
r = MP (4-19)
41
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
where the ju is the coefficient of the friction and p is the contact pressure at the chip
tool interface.
The value of the coefficient of friction will affect the friction behaviour between
the contact surfaces at the chip-tool interface. In ABAQUS, the default model for the
friction coefficient is defined as
jU = jU fyeq,P,6,f^ v j
(4.20)
where Yeq-\Y\^Y2 ^s t n e equivalent slip rate, p is the contact pressure,
0 = —(6A+0B)\s the average temperature at the contact point, and / =—(/"+ fg ) is
the average of a predefined field variable a at the contact point. 6A, 6B, f", and f% are
the temperature and predefined field variables at points A and B on the surfaces.
4-6-2 Shear limited friction coefficient
The limiting shear stress is one of the friction options available in ABAQUS. The
contact pressure at the chip tool interface can be divided into two regions, sticking and
sliding. In the sticking region, the shear stress will reach the maximum shear stress as
shown in Figure 4.2. In the sliding region, the shear stress is less than the maximum shear
stress. The shear stress limit is typically introduced in cases when the contact pressure
stress may become very high (as can happen in some manufacturing processes such as
metal cutting) causing the Coulomb theory to provide a critical shear stress at the
interface that exceeds the yield stress in the material beneath the contact surface. The
maximum shear stress is sensitive to the temperature as seen in the Figure 4.2. By
42
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
increasing the temperature, the maximum shear stress decreases, (Tx < T4) .The limiting of
shear stress can be estimated as:
r = max V3~
where av is the Mises yield stress [37].
w w a> i_
•4—»
w CD (D -C CO
*•
cf 7 ^ /
''max a l ' 1
Tmax a ^ T 2
Tmax 3 * T 3
Tmax a ^ T 4
/
(4.25)
Normal Stress
Figure 4.2 Coulomb friction model with a limiting shear stress [3]
4-7 Contact Algorithms
There are two specific contact algorithms in ABAQUS Explicit: Kinematic and
Penalty contact that can be used to simulate surface to surface contact. By default,
ABAQUS Explicit uses the Kinematic contact algorithm. Penalty contact is the other
option that might be used in more general cases of contact between the surfaces.
43
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
4-7-1 Kinematic algorithm
The Kinematic contact algorithm is defined by the forces in a pure master-slave
contact. At each increment of the analysis, the algorithm determines which nodes from
the slave surface will penetrate the master surface so that it can apply the resistance force
(see Figure 4.3). During hard contact, the forces that are applied between the two surfaces
caused the slave nodes to exactly contact with the master surface before the penetration
occurs. The kinematic method will not affect the time increment as the Penalty method
will do.
4-7-2 Penalty algorithm
The Penalty contact algorithm is more general so that it is a common option. An
additional element will be added to the model where the stiffness for this part is neglected
when there is a gap between the two surfaces; however, the stiffness will have high
values when contact exists. The stiffness can influence the stable time increment. The
Penalty contact method considers one surface as a master and the other as a slave as
shown in Figure 4.3. The Penalty contact algorithm tracks the slave nodes that may
penetrate the master surface, so the contact applies forces to the slave nodes to prevent
the penetration. A finer mesh is recommended on the slave surfaces to minimize the
number of nodes of the master surfaces that will penetrate the slave surface.
Sliding formulation can be included in contact with three options: finite sliding,
small sliding, and infinitesimal sliding and rotation. The small sliding option can be used
to linear and nonlinear contacts similar to the finite sliding case. The only difference
exists that the slave nodes will interact small local area in the master nodes. The other
option is infinitesimal small sliding which is unavailable in this analysis because the
44
CHAPTER 4: GOVERNING EQUATIONS OF THE NUMERICAL MODEL
infinite small sliding cannot perform nonlinear geometry. For chip tool interface, using
finite sliding is appropriate.
Master surface (segments) *"
Slave nodes can not penetrate master segments Penetration
Gap Master node can penetrate slave segment
Figure 4.3 Master and slave surfaces in contact [37]
45
CHAPTER 5: FINITE ELEMENT MODELLING
CHAPTER 5:
FINITE ELEMENT MODELLING
5-1 Introduction
Finite element methods have been developed to solve many problems in many
applications. In metal cutting, the finite element models have been used to investigate
several aspects which include stresses and strain. In the current application, the finite
element model is created to analyze a metal cutting problem in terms of dynamic
displacement and temperature. After introducing all the governing equations in the
previous chapter, the choice of the finite element parameters is explained in this chapter
as follows.
46
CHAPTER 5: FINITE ELEMENT MODELLING
5-2 Model Definition and Assumptions
A two-dimensional finite element model was developed under the plane strain
assumption to simulate the orthogonal metal cutting of steel (AISI 4140) with a
continuous chip. ABAQUS can simulate large deformation accompanied by elastic,
plastic, thermal, and friction effects. The element type is bilinear (four-nodes) with
reduced integration and hourglass control to deal with the large deformation. The
dynamic displacement-temperature explicit method was used to analyze this model with a
combination of some input parameters such as temperature-dependence and heat transfer.
To simplify the analysis, a perfectly rigid cutting tool is assumed because of the
significantly high elastic modulus of most tool materials. This should be an acceptable
approach since the elastic properties of the cutting tool do not affect the large plastic
deformation at the workpiece.
To simplify the analysis, it is better to consider some parameters from the beginning
so that the goal of the analysis will be achieved efficiently. The model assumptions are
considered as follows:
1. The initial temperature of both the workpiece and tool is 25 °C (room temperature)
2. The cutting tool is sharp with a 5 urn cutting edge.
3. Constant cutting velocity is equal to 200 m/min.
4. Tool wear is neglected in this study so that the running time will be reduced.
5. The machining model does not include any coolant.
6. Homogenous material is used to model the workpiece material.
47
CHAPTER 5: FINITE ELEMENT MODELLING
5-3 Material Properties
This finite element model was developed with two materials: the cutting tool and
the workpiece. The cutting tool is modelled with a specific material with high modules of
elasticity; whereas, the workpiece material is simulated by the Johnson-Cook model. In
the current work the tool is defined as a rigid body with thermal properties.
5-3-1 Tool material properties
The tool was made of cemented carbide grade P10. The physical and mechanical
properties of the cutting tool material are presented in Table 5.1 [1, 2, 3]:
Table 5.1 Cemented carbide tool physical properties [1, 2, 3].
Density kg.m"
Young's modulus GPa
Poisson's ratio
Specific heat J.kg'.°C"'
Conductivity W m"1 °C"'
Expansion urn m"1 °C~'
10600
520
0.22
200
25
7.2
5-3-2 Workpiece material properties
The workpiece material used for the plane strain orthogonal metal cutting
simulation is steel AISI 4140. The physical properties of the used material are given in
Table 5.2 [1,2, 3].
48
CHAPTER 5: FINITE ELEMENT MODELLING
Table 5.2 Workpiece steel AISI 4140 physical properties [1, 2, 3].
Density kg.m"J
Young's modulus GPa
Poisson's ratio
Specific heat J.kg'.C"1
Melting temperature °C
Inelastic heat fraction
Conductivity W m"1 °C '
Expansion Urn m"1 °C"'
7800
210
0.3
473 at 200 °C. 519 at 400 °C. 561 at 600 °C.
1520
0.9
42.6 at 100 °C. 42.3 at200 °C. 37.7 at 400 °C. 33 at 600 °C. 12.2 at 20 °C
13.7 at 250 °C 14.6 at 500 °C
As discussed in section 4.4, the Johnson-Cook model is used to model the
workpiece material under thermo-viscoplastic behaviour. This model has been used
widely because it is suitable to obtain the flow stress as a function of strain, strain rate,
and temperature. The Johnson-Cook model is represented in the following equation [1,2,
3,40]:
- = M*")'\ -pi
1 + Cln
V £o J
1 0-0, ref
V @melt 0>ef J
(5.1)
And the Johnson-Cook parameters are written in Table 5.3.
Table 5.3 Johnson Cook equation coefficients [1, 2, 3, 40]:
Material
AISI4140
A(MPa)
598
B(MPa)
768
n
0.2092
C
0.0137
m
0.807
Z0
0.001
49
CHAPTER 5: FINITE ELEMENT MODELLING
5-3-3 Cutting conditions
The current work is based on the continuous chip model for different feed rates
and friction coefficients to study the effect of the friction coefficients and the initial
geometry. Through this work, the cutting conditions are given in Table 5.4
Table 5.4 Cutting conditions [1, 2, 3].
Cutting Conditions
Tool Geometry
Feeds (mm)
Cutting Speed (m/min)
Rake Angle (degree)
Clearance Angle (degree)
Cutting Edge Radius (pm)
0.1,0.2,0.3
200
6
6
5
5-4 Modelling Description
In order to build any simulation with finite elements, the understanding of the mesh
formulation, boundary conditions, and the initial geometry are very important. It can
clearly be seen that the new model utilizes a combination of mesh formulations to
achieve high deformation.
5-4-1 Element types
Figure 5.1 shows the two-dimensional four nodes plane strain element, (CPE4RT),
used to model both the workpiece and the tool with reduced integration and hourglass
control elements [3, 37, 39].
50
CHAPTER 5: FINITE ELEMENT MODELLING
4 o 3 o
c~-~ (2) Y 2
Figure 5.1 Four-node solid element
The two-dimensional, two-node rigid link element (R2D2) is shown in Figure 5.2.
The element is defined by two nodes with two degree of freedom in X and Y directions at
each node. This type of element is used to present the tool shank where it is tied strongly
to the tool insert as a part of the tool. There is no output associated with these elements
[37, 39].
2 P
/
0 1
Figure 5.2 Two-node rigid element
5-4-2 Geometry and boundary conditions
Figure 5.3 shows the geometry of the old model with the variable initial chip
height (h) in the case of feed 0.2 mm. The mesh of the workpiece is constrained in space
so the material will flow from the left side to the right side and over the rake face to form
51
CHAPTER 5: FINITE ELEMENT MODELLING
the chip. The old model is constrained in the Y direction along the bottom of the
workpiece. Also, the tool is fully fixed at the reference point (RP). The length of the
workpiece is 1.5 mm with width of 0.6 mm. The workpiece has 59613 nodes and the tool
has 1134 nodes. The element size is bigger if it is compared to the new model. The
calculation time for the case of feed 0.2 mm is 42 hours in the case of a computer with 3
GB of RAM memory and 2.4 GHz.
The old model shows a critical initial chip height. For a certain short value of h,
the model will not complete the analysis because the upper element of the chip at the
chip-tool interface will penetrate the tool surface. Also, at some high value of h, the
model cannot complete the analysis because of the high deformation that occurs.
RP
0.6 mm m&mmm
0.4 mm
1.5 mm
Figure 5.3 Boundary conditions and partition scheme for the previous model
52
CHAPTER 5: FINITE ELEMENT MODELLING
Figure 5.4 shows the basic geometry of the two-dimensional finite element model
that is used in this analysis for 0.3 mm feed with no initial chip height. The material
moves from the left to the right at cutting speed V, with boundary conditions fixed in Y
direction on the bottom of the workpiece. The tool is fully fixed at the reference point
(RP). Figure 5.4 shows that the workpiece material has been divided into two main parts,
A and B. These two zones are used to define the ALE boundaries as will be explained
later. The initial length of the workpiece was approximately 2.7 mm with a width of 0.6
mm and a feed equal to 0.2 mm. As the workpiece flows pass the tool, its length reduces.
This is different from the previous work [3] where the workpiece length was constant. In
the present model, the workpiece and the tool have 4153 and 1731 nodes, respectively.
The element size is chosen carefully such that small elements are used where the highest
deformation is expected. The calculation time for the case of feed 0.2 mm and p, = 0.23 is
9 hours in the same computer as mentioned above with mass scaling factor equal to 50.
The new model is a good contribution as it can avoid the initial chip geometry and
let the mesh perform the chip deformation. During the deformation, the upper element on
the side of the contact surface may penetrate the tool surface so the model cannot
complete the analysis. The idea that is used to avoid the penetration is ignore the friction
effect at the upper element. This will not cause any trouble because the upper element is
the first element that will lose contact with the tool face. The way to separate the first
element from the mesh is to perform the partition before the mesh is completed and then
make a small cut at the upper element with approximate size equal to the mesh seed of
the element below.
53
CHAPTER 5: FINITE ELEMENT MODELLING
RP
Tool
Workpiece
A " %mmf : ,4mn
;,/ mni
Figure 5.4 Boundary conditions and partition scheme for the new model
5-4-3 Mesh and chip formation
The Arbitrary Lagrangian Eulerian method is utilized in the proposed finite element
model. This technique is used to solve large deformation problems [3, 24]. One of the
critical issues in this type of modelling is the positions at which Lagrangian or Eulerian
regions are applied. Nasr et al. [36] presented an ALE model where they divided the
workpiece into different parts. In the present work, a similar idea has been applied to hard
steel AISI 4140.
The explicit method has been used here to simulate metal cutting with high
deformation; however, some researchers have used the implicit method [29, 41]. The
implicit method causes difficulty in convergence because the contact and the material
models with a high number of iterations cause more cost. The explicit integration method
54
CHAPTER 5: FINITE ELEMENT MODELLING
is more efficient than the implicit integration method for solving extremely discontinuous
events or processes.
Before starting to explain the geometry and the structure of the new model, a brief
explanation of the adaptive mesh technique that is used in the new model is given. The
selection of choices for the adaptive mesh can play a major role to enable the model to
run perfectly by choosing the optimum options. An Arbitrary Lagrangian Eulerian (ALE)
adaptive mesh domain can be applied with the following cases [37]:
• Can be used to analyze either Lagrangian or Eulerian problems.
• Can contain only first order, reduced integration, solid elements (4-node
quadrilaterals, 3-node triangles, 8-node hexahedra, and 4-node tetrahedra).
• Have boundary regions and surfaces where the applied loads and boundary
conditions can exist.
The choice starts with a defined mesh domain. In the current model, the adaptive
mesh domain was applied to the entire workpiece by selected region. The ALE Adaptive
Mesh Control is used where one chooses a file that was created earlier. Other options are
left in default.
The ALE Adaptive Mesh Constraint is used to apply the mesh boundaries in
region B by choosing the right direction boundaries. There are two types of boundary
region edges: Lagrangian and sliding. Note that the Eulerian boundary is not available in
the CAE files. The only way to apply the Eulerian boundary is to write it directly to the
input file. In all cases, the mesh just constrains the displacement of the boundary. For the
Lagrangian boundary definition, the nodes are allowed to move with the material and this
is what is called in a CAE file as flow of underlying material. The flow of underlying
55
CHAPTER 5: FINITE ELEMENT MODELLING
material is used in this analysis; it is altered to be Eulerian boundary later in the input file.
The other option is a sliding boundary which is called independent of underlying
material. A sliding boundary is similar to the Lagrangian boundary except that it has a
sliding edge. The mesh is constrained to move with the material in the direction normal to
the boundary region but it is completely unconstrained in the direction tangential to the
boundary region. Both Lagrangian and sliding boundaries can be viewed with
ABAQUS/CAE. Finally, the Eulerian boundary constrains the mesh in space and allows
the material to flow through it.
The last step with the adaptive mesh technique is mesh control. This is one of the
keys that is important to perform the new model. There are a lot of options here but the
most important one in the new model is the mesh constraint angle for boundary region
smoothing. This option controls the smallest angle in an element with default value equal
to 60°. Currently, the angle can be changed to be less than 60° because the simulation can
have smaller angles. It has been found that 20° works well.
In the current model, region A is modelled as a Lagrangian region with an
adaptive mesh domain. The mesh will follow the material while the re-meshing will
prevent the elements from being distorted exceedingly. Because the mesh deforms with
the underlying material, free surfaces can be modelled properly and the boundary
conditions can be applied in a simple way. The Lagrangian surface is applied along the
contact surface where the deformation is expected. A mapped mesh is applied to this
region so that the productive elements will have a uniform shape to deal with the
deformation. The initial mesh is made very small at the region, where the mesh expects to
grow (chip), to allow the model to reach steady state geometry.
56
CHAPTER 5: FINITE ELEMENT MODELLING
Region B is modelled as an Eulerian region. The simple definition to explain the
Eulerian region is as a fixed net in space that allows the material to flow through. The
mesh is constrained to make sure that there is no separation around the tool tip. The top
surface in region B should be higher than the tool tip but lower than the expected contact
length so that the material will flow around the tool edge as if it is a fluid. The mesh is
finely formed around the tool edge in order to allow high stress gradients, even though
region B in general has a coarse mesh.
In region A, the area above region B is where the chip is expected to grow and
from the final shape of the chip. The current model is running without any initial chip
height. The chip now has the ability to grow automatically where the only limitation is
the element distortion.
Reducing the computational cost by using mass scaling can be done in ABAQUS
Explicit by multiplying the density of the material by a factor/'. The mass scaling should
not apply to the entire model because it will increase mass of the workpiece. Based on the
previous study [3], the chosen factor is equal to 50. The mass scaling is applied just in the
region B (Eulerian region) and the small area above region B where mesh is expected to
grow. Because the smallest element occurs in that region, the scale factor is applied in
this portion of the workpiece. With mass scaling the file was solved in 9 hours for feed of
0.2 mm and friction coefficient 0.23; however, with no mass scaling, the simulation took
around 32 hours to complete running. Mass scaling results have a short running time that
saves the cost of the simulation.
Achieving the steady state temperature over the whole tool insert is not possible in
the short time of running but at least the contact temperature along the chip-tool interface
57
CHAPTER 5: FINITE ELEMENT MODELLING
reaches the steady state temperature at the contact area. Although, the previous models
[1, 2, 3] had a longer running time (4 ms), the new model reaches the same maximum
temperature with shorter time (0.6 ms). The temperature distribution on the rake face
grows gradually to reach the maximum values at the contact surface. In this study, the
temperature at the contact surface is studied to explain the heat energy in the friction
zones.
5-4-4 Contact algorithms
The interaction between two surfaces can be solved with ABAQUS by using the
contact algorithms as explained in section 4-6. When the surfaces make imperfect contact
the gap conductance applies between the surfaces as a gap exists. These surfaces may
separate after contact, such as in the metal cutting example. As explained in section 4.6
about the contact algorithm, either the kinematic or penalty contact algorithm must be
chosen. Both options can be used in this analysis if the tool and the workpiece are
modeled as elastic parts; however, the current model used the penalty contact algorithm
because the tool is model as a rigid body. The penalty contact algorithm is useful in more
general cases of contact. A further difference between kinematic and penalty contact is
that the critical time increment is unaffected by the kinematic contact but can be affected
by penalty contact.
During the hard contact between the two surfaces, tool and workpiece, the contact
algorithm applies distributed forces to nodes of the slave surfaces. There are three
approaches for the relative motion of the two contact surfaces which include finite
sliding, small sliding, and infinite small sliding. Using the finite sliding allows the nodes
of the slave surface either to separate or to slide when they come into contact anywhere
58
CHAPTER 5: FINITE ELEMENT MODELLING
along the rake face of the tool. ABAQUS Explicit tracks the position of these nodes
relative to the master nodes. The choice of finite sliding is used in the current work
because it is useful for the nonlinear geometry that has large deformation.
At high values of the friction coefficient, the maximum temperature will reach more
than 1000 °C in a very short time. This high temperature will considerably affect the
properties of the workpiece and make the study more complicated. The friction along the
chip-tool interface is present in the two regions that affect the surface, sticking and
sliding. Different approaches have been considered to determine the shear stress in these
zones at the contact surface [3]. These approaches include a constant shear stress along
the entire chip-tool interface, a constant shear stress in the sticking region, Coulomb
friction in the sliding region, variable Coulomb friction along the entire chip-tool
interface, constant friction along the chip-tool interface. In the current model, the constant
Coulomb friction model is selected to simplify the analysis.
For the thermal boundary conditions, the workpiece and the tool are initially set at
25 °C. The convection heat transfer coefficient has been calculated. It is 10 W/m2oC for
the free surface of the workpiece and 157 W/m2oC along the flank face of the tool [3].
The gap conductance model along the chip tool interface has thermal conductance of
0.1GW/m°C with zero gap distance and zero at gap distance of 0.01 jam along the chip
tool interface. Using equations 4.17& 4.18, the fraction of heat energy conducted to the
chip and the tool are 0.623 and 0.377, respectively.
59
CHAPTER 6: RESULTS AND DISCUSSION
CHAPTER 6:
RESULTS AND DISCUSSION
6-1 Introduction
In this chapter, the results of the finite element models that are used to investigate
the effect of the friction coefficient and the initial chip geometry are presented for the
AISI 4140 workpiece and carbide tool. The main results include the cutting and feed
forces, chip thickness, and contact length. The behaviour of the friction at the chip-tool
interface is also shown to affect some other parameters.
In order to discuss the results of the FEM, the basic Coulomb friction coefficient
was utilized with friction coefficient equal to 0.23 based on the previous work [1, 2, 3].
The experimental data were obtained from reference [1,2] with same material at the same
cutting conditions from feeds 0.01 mm to 0.4 mm. The initial part of this chapter is
60
CHAPTER 6: RESULTS AND DISCUSSION
focused on the analysis of the obtained results with friction coefficient 0.23 at feed 0.3
mm. The results of reference [2] were obtained by scanning the charts and then
measuring from CorelDraw by choosing the right scale.
At the beginning of the analysis, different models will be presented based on the
initial chip height. These models will be compared to a new model without initial chip
height and the experiment results [2]. The analysis results include the chip formation,
cutting and feed forces, stress, strain, and temperature. The chip formation is presented at
six different time steps. The maximum deformation of the chip in this specific cutting
condition (feed 0.2 mm, friction coefficients 0.23 and 0.6, and cutting velocity 3.33 m/s)
is presented at time step 0.6 ms. By 0.6 ms, the chip has reached the final form and the
interaction keeps acting steadily at the chip-tool interface.
The results of the simulation show slightly different data with different initial chip
heights. This study is verified by comparing the current model with the previous model
for a variety of initial chip heights. The comparison includes the chip thickness, contact
length, and cutting and feed forces. The results present some interesting problems
especially the force results.
With the new model, the chip starts forming from the beginning of the deformation
with the correct chip thickness. One of the advantages of the new model is that the final
chip thickness occurs sooner. The maximum deformation of the chip in this specific
cutting condition (feed 0.3 mm, friction coefficient 0.23, and cutting velocity 3.33 m/s) is
presented at time 0.6 ms. After 0.6 ms, the chip will have more curl and this curl will
cause damage in the mesh (see Figure 6.14).
61
CHAPTER 6: RESULTS AND DISCUSSION
The obtained forces are presented first by plotting cutting and feed forces versus
time. The plot shows that the stability exists early before 0.1 ms. The forces change as a
result of parameters such as the friction coefficient, feed and velocity. The primary results
had been chosen in specific cutting conditions. The next section shows the stresses acting
in the chip and workpiece. The analysis of the contour plots illustrates the maximum and
minimum stress locations.
The next section is mainly focused on the temperature, which is one of the most
important issues because of the tool life. The contour plots help to study the distribution
of temperature in the workpiece and the chip. The maximum temperature occurs in the
friction zone. Steady temperature is one of the goals that needs to be achieved for steady
state at the chip-tool interface. Also, studying the contact surface shows the distribution
of friction and normal stresses along the chip-tool interface.
Since the friction behaviour along the chip-tool interface is not clear, many studies
were focused on a variety of friction models that could be used in metal cutting analysis.
In this study, the simple friction coefficient is utilized based on Coulomb's low.
Basically, the magnitudes of different values of friction coefficient, which are used in this
work, are chosen from force data of Arrazola et al. [1]. The friction coefficient is selected
to be 0.23, 0.4, 0.5 and 0.6 according to Albrecht's definition where the plot of feed
forces versus the cutting forces is presented.
62
CHAPTER 6: RESULTS AND DISCUSSION
6-2 Effect of the Initial Chip Geometry
The traditional method for the ALE model includes initial chip height and
thickness as an assumption. Although the predicted results were successful, the assumed
initial chip usually depends on the feed and the friction coefficient. In this work, an
attempt has been made to model the cutting process without defining the chip height.
Before the comparison starts, it is important to state the differences between both models.
Figure 6.1 shows the schematic diagrams of the new model and the previous model. The
previous model will be presented with several initial chip heights.
Chip thickness
Contact length
(a) The previous nrxM (b)Therewrrrxtel
Figure 6.1 Schematic of both models
The initial geometry has some effect on the results. The following graphs show the
percentage error of the chip thickness, contact length, cutting force, and feed force with
different models for a feed of 0.2 mm. In each case, different initial chip heights (L) are
used. For each chip height, the results are presented for two different friction coefficients
(u=0.23, u=0.6). This analysis has been done for both 0.23 and 0.6 friction coefficient
with the same parameters (cutting conditions). The new model, which has no initial chip
height, is represented with L = 0 and all others are presented with different initial chip
63
CHAPTER 6: RESULTS AND DISCUSSION
heights from 0.3 up to 0.8 mm with an initial chip thickness of 0.35 mm. In some cases,
the new model gives the best agreement with experimental results as will be explained in
the following sections.
Figure 6.2 shows the deformation process for an initial chip height case (L = 0.5
mm). The time step starts from 0.1 ms up to 0.6 ms. The chip geometry changes until it
reaches the steady state. The free surface of the chip shows the chip deforms gradually
from the bottom left of the chip to upper. It is obvious that the mesh does not have any
severe distortion due to adaptive meshing and the Eulerian region.
64
CHAPTER 6: RESULTS AND DISCUSSION
(a) Time = 0.1 ms (b) Time = 0.2 ms
(c) Time = 0.3 ms (d) Time = 0.4 ms
(e) Time = 0.5 ms (f) Time = 0.6 ms
Figure 6.2 Chip formation of orthogonal machining at different times with initial chip (f = 0.2 mm, L = 0.5 mm, V = 200 m/min, \i = 0.23)
65
CHAPTER 6: RESULTS AND DISCUSSION
6-2-1 Chip thickness
Before presenting the chip thickness results, it is important to illustrate how it is
measured (see Figure 6.3). After picking point A, which is away from the contact surface,
measuring the distance between that point and several points at the free surface like B, C,
and D is done to figure out the shortest distance. Because of the chip is curled, the
shortest distance is expected to be the distance perpendicular to the point A
'Contact length
Figure 6.3 Chip thickness and contact length measurement
Figures 6.4 and 6.5 show the obtained results for the chip thickness. The left hand
bars are the experimental results of Arrazola et al. [1, 2]. It can be seen in the figure that
the results illustrate the effect of the friction coefficient where the percentage of error has
higher values for the higher friction coefficient. The new model without any initial chip
height presents the best result at lower friction coefficient with less than 3% of error;
however, at the higher friction coefficient, the data do not show the best results (see
Figure 6.5). The results agree with the above explanation that increasing the friction
coefficient causes a thicker chip because of the increase in the shear angle.
66
CHAPTER 6: RESULTS AND DISCUSSION
0.5 0.45
-g- 0.4 £ 0.35 S 0.3 J= 0.25 | 0.2
.9- 0.15 O 0.1
0.05 0
B|j = 0.23 I p = 0.6 DExp
EXP L=0 L=0.3 L=0.4 L=0.5 L=0.6 L=0.7 L=0.8
Initial chip height
Figure 6.4 Chip thickness obtained by different models
The maximum magnitude of the chip thickness at 0.23 friction coefficient occurs in
0.6 mm initial chip height with percentage of error equal to 10%. The percentage of error
increases at the higher friction coefficient to reach the maximum value at the initial chip
height of 0.5 mm with percentage of error over 25%.
g in
L=0 L=0.3 L=0.4 L=0.5 L=0.6
Initial Chip Height (mm)
P|j = 0.23 i p = 0 . 6
L=0.7 L=0.8
Figure 6.5 Percentage error of the chip thickness for different models
67
CHAPTER 6: RESULTS AND DISCUSSION
6-2-2 Contact length
The results of contact length are obtained by measuring along the chip-tool interface
(see Figure 6.3). Figures 6.6 and 6.7 display the contact length for all cases of initial
chip. The average percentage of error with the smaller friction coefficient is 43% and for
the higher friction coefficient it is close to 27%. It is obvious that the contact length has a
high percentage of error. The results of the contact length with different initial chip
heights from 0.3 to 0.8 mm have close results to each other. Some improvement has been
gained by using the new model as will be explained below.
The new model presents the best results with contact length for both friction
coefficients with 44% percentage of error at 0.23 friction coefficient and 23% percentage
of error at 0.6 friction coefficient. The advantage of the new model shows the better
results when the highest node of the chip interacts with the rake face and slips over the
rake face in short distance during the deformation as illustrated in section 6.2 when the
chip is deformed at different times. Generally, the figures demonstrate that friction
coefficient has big effects on the contact length in all simulations. Also, using the new
model avoids having to decide the initial chip geometry and simplifies initial meshes.
Sometimes the node in the highest location will lead the simulation to stop because
of the high deformation that might occur in the element that will separate first from
contact with tool. The reason for that high deformation is some extra force will be applied
at the highest element in the chip-tool interface. This deformation can exist even in some
cases of the initial chip height. One of the keys that might help to build a numerical
model is to avoid applying friction in the highest element at the chip-tool interface during
the analysis at high friction coefficients.
68
CHAPTER 6: RESULTS AND DISCUSSION
H|J = 0.23 ^ M = 0.6 DExp
c
u c o o
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 EXP L=0 L=0.3 L=0.4 L=0.5 L=0.6 L=0.7
Initial Chip Height
L=0.8
Figure 6.6 Comparison between the models for the contact length
l|j=0.23 B|J=0.6
0
-10
-20
o
£ -30
-40
-50
-60
L+0 l i i l tills L= M BH • L=P6 L= W L=t>.8
Initial Chip Height (mm)
Figure 6.7 Percentage error of the contact length
69
CHAPTER 6: RESULTS AND DISCUSSION
6-2-3 Cutting and feed forces
The force results are easy to obtain from the software because the reference point
(RP) collects the entire force vectors that act in the simulation. There are several results
presented in this section. The first part is the force time histories for six different initial
chip heights. The average cutting and feed forces (over the last 0.5 ms) are then compared
between these models and the experiment [1]. First, the cutting forces versus time for the
cases for \i = 0.6 are illustrated as shown in Figure 6.8. Obviously, there is no big
difference between these cases.
Figure 6.9 shows the comparison of the average cutting forces for (i = 0.23 and \i =
0.6 for various initial chip heights. By increasing the friction coefficient, the cutting
forces increases higher than the experiment value of the cutting force on the one hand,
while using the lower friction coefficient gives smaller values of the cutting force than
the experiment. Figure 6.10 shows the percentage differences for the cutting force. The
cutting forces for all models have quite good agreement with the experiment for both
friction coefficients. The maximum percentage error of around -10% at friction
coefficient 0.23 for the model L = 0.4 mm and 15% at friction coefficient 0.6 for the
model L = 0.5 (see Figure 6.10).
70
CHAPTER 6: RESULTS AND DISCUSSION
cnn -r~-
480 -460 -440 -
% 420 -8 400 -£ 380-
360 -340 -320 -inn -
L-0.3 L-0.4
fli^k % C w
T ^ •Wr' y 'CTy^iidw^.VsS^Q^
i i i
0 0.0005 0.001 0.0015
L-0.5 L=0.6 L-0.7
^ ^ ^ ^ ^ ^ ^ ^ ^
0.002 0.0025 0.003 0.0035
Time (s)
L-0.8
srf
1
0.004 0.0045
Figure 6.8 Cutting forces versus time for all initial chip height cases (f = 0.2 mm, V =
200 m/min, \x = 0.6)
Hu=0.23 Hu=0.6 DExp
EXP L=0 L=0.3 L=0.4 L=0.5 L=0.6 L=0.7 L=0.8
Initial Chip Height
Figure 6.9 Comparison between the models for the cutting forces
71
CHAPTER 6: RESULTS AND DISCUSSION
Su=0.23 H|J=0.6
20
,2 10
-10
-15
'-If •0 L = • L= . 1 L= ) 5 L= t
9 1
L=
3L ).7 L= 3.8
Initial Chip Height (mm)
Figure 6.10 Percentage error of the cutting force
The feed forces versus time for the cases of the initial chip height are illustrated in
Figure 6.11. Obviously, there are big differences with feed forces.
? i n -.
190 -
_ 170 -2^
Forc
e
o
o
110 -
Qf)
L-0.3 L-0.4
In i ^^^^^^^^^^^
0 0.0005 0.001 0.0015
L-0.5 ^ - 0 . 6 L-0.7 L-0.8
^^^t^ff^^^^u^r^^^f^Si
0.002 0.0025 0.003 0.0035 0.004
Time (s)
0.0045
Figure 6.11 Feed forces versus time for all initial chip height cases (f = 0.2 mm, V
200 m/min, (j, = 0.6)
72
CHAPTER 6: RESULTS AND DISCUSSION
The results for the feed forces are shown in Figure 6.12 and 6.13. The feed forces
for the low friction coefficient demonstrate very high percentage of error. The maximum
percentage of error is 80%. It is apparent that the lower friction coefficient cannot model
the feed force. Well, the feed forces have improved results with less than 30% as a
maximum percentage of error when the friction coefficient is 0.6. The presented data
shows that the friction coefficient affects the feed force significantly; the average
percentage of error for the lower friction coefficient is 76%, while the average is 14% for
the higher friction coefficient.
Generally, the new model shows the best average results for both cases of friction
coefficient (|a, = 0.23, u=0.6). The new model will be presented in more details in section
6.3. Results with no initial chip present some progress in the contact length and forces as
well.
Figure 6.12 Comparison between the models for the feed forces
73
CHAPTER 6: RESULTS AND DISCUSSION
• |j=0.23 B|j=0.6
0
-10
8 -20 -30
$ -40
o -50 --
t -60 --UJ
5? -70
-80
-90
mo L= L= )4 p D.5 L* •I LH fe^m. M
Initial Chip Height (mm)
Figure 6.13 Percentage error of the feed force
6-3 Results with No Initial Chip
The results of the new model will be emphasized in current section where there is
no initial chip geometry. The study shows the new model can perform the metal cutting
problems efficiently. The primary results are calculated at friction coefficient 0.23 with
the same cutting conditions and tool geometry as reference [1]. The results of no initial
chip have a good agreement with the published [1] and previous work [3] for the case of
friction coefficient 0.23. The results will show several interesting points that can be
considered in machining as follows:
6-3-1 Chip formation
The chip formation process of orthogonal cutting is explained in the section (see
Figure 6.14). Before the deformation starts, the tool is in perfect contact with the
74
CHAPTER 6: RESULTS AND DISCUSSION
workpiece to reduce the running time and make sure that the contact occurs from the
beginning. As the tool starts to move into the workpiece, more plastic deformation of the
workpiece material exists along the chip-tool interface and the primary deformation zone.
The chip starts increasing gradually along the rake face of the tool. The deformed chip
has a high density of elements so these elements can be stretched to the chip geometry;
however, the elements outside the primary deformation zone from the workpiece side are
larger because these elements shrink during the deformation.
Figure 6.14 (b) demonstrates that the top of the chip starts separating from the
contact area while the continuous chip is still growing. During machining, the simulation
reachs the steady state in both deformation zones so the shear plane softens the material
to flow as a chip. The resistance to the tool penetration decreases because of the effect of
the high temperature. The chip thickness achieves steady state (chip thickness and contact
length) before 0.2 ms as seen in Figures 6.14 a, b, c. Figures 6.14 d, e present the curl of
the chip during the deformation later. The model stopped running when the supply of
material stopped (see Figure 6.14 f).
75
CHAPTER 6: RESULTS AND DISCUSSION
(a) Time = 0.1 ms (b) Time = 0.2 ms
(c) Time = 0.3 ms (d) Time = 0.4 ms
L, L.
(e) Time = 0.5 ms (f) Time = 0.6 ms
Figure 6.14 Chip formation of orthogonal machining at different times with no initial chip (f = 0.3 mm, V = 200 m/min, \i = 0.23)
76
CHAPTER 6: RESULTS AND DISCUSSION
6-3-2 Cutting and feed forces
The engagement of the tool with the workpiece causes high deformation zones at
the shear zone and along the friction zone. As a result of machining, the contact pressure
on the chip-tool interface increases at different time increments (see Figure 6.14).
Increasing the contact pressure affects the cutting force and the feed force as well. Figure
6.15 shows the predicted feed and cutting forces during steady state at 0.3 mm feed and
200 m/min cutting speed. The forces reach steady state before 0.1 ms. The average
cutting force was 528 N and the feed force was 55 N for friction coefficient 0.23.
S
600
500
400
300
200
100
0
0.1
-Cutting_ Feed-F
0.2 0.3 0.4
Time (ms)
0.5 0.6 0.7
Figure 6.15 Cutting and feed force versus time
(f = 0.3 mm, V = 200 m/min, u = 0.23)
6-3-3 Stress and strain distributions
In this section, the contour plots of Von-Mises stress, shear stress, contact stress and
equivalent plastic strain at friction coefficient 0.23 (f = 0.3 mm and V = 200 m/min) are
77
CHAPTER 6: RESULTS AND DISCUSSION
shown in Figures, 6.16, 6.17 and 6.18. The distribution of these variables will be
discussed to obtain better understanding of chip formations.
6-3-3-1 Von-Mises stress distribution
One of the stresses that is considered in the analysis is the Von-Mises stress. The
analysis shows the maximum stresses occur in the primary deformation zone due to high
strain and strain rate (see Figure 6.16). The stress decreases gradually on both sides of
the shear zone. Along the chip-tool interface, where the surfaces interact, smaller stress is
noticed in the friction zone. The stresses are still decreased and reach low values when
the chip is separated from the contact region. It is easy to observe that stress still occurs
in the chip after the separation. The contour of Von-Mises stress is shown below with
five interval stresses lines.
S, Mises
1- +1.166e+09 2- +9.382e+08 3- +7. !08e+08 4- +4 833e+08 5- +2 559e+08
Figure 6.16 Distribution of Von-Mises stresses in the chip and the workpiece (Pa)
(f = 0.3 mm, V = 200 m/min, u. = 0.23)
78
CHAPTER 6: RESULTS AND DISCUSSION
6-3-3-2 Shear stress distribution
One of the results that are presented in this section is the shear stresses (see Figure
6.17). The highest stress was located in the primary deformation zone in front of the
cutting tool edge and the end of the primary shear zone (region 1). The significance of the
shear stress study was to focus on the friction shear zone because of the high interaction
effect between the tool surface and the chip surface. A smaller shear stress is noticed in
the shear zone despite the high temperature (region 3).
s SI 1-2-i-4-5_
T
+2 716e+08 +7.549e+07 -1 206e+08 -3.167e+08 -5.128e+08
Figure 6.17 Distribution of shear stresses in the chip and the workpiece (Pa)
(f = 0.3 mm, V = 200 m/min, (x = 0.23)
6-3-3-3 Normal and friction shear stress along the chip tool interface
Figure 6.18 shows the normal and shear stress distributions along the chip tool
interface. The contact pressure along the rake face demonstrates that the maximum
pressure occurs at the edge of the tool. It seems that the contact pressure is almost
constant with slight decrease while moving away from the tool edge. The same trend is
79
CHAPTER 6: RESULTS AND DISCUSSION
observed for the shear stress with smaller values. It has nearly constant values where the
sticking region occurs and decreases along the sliding region.
1 .
eg onnn _, 35 ^uuu w 1800 -, ~i 1600 -• | ^ 1400 -£ | 1200 -* 7 1000 -3 2 800 -
$ ^ 600 -
i 400 1
JS 200 -c o n -C
k —•— Contact Pressure —•— Friction Shear Stress
) 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Distance along Chip-Tool interface (mm)
0.4 0.45
Figure 6.18 Normal contact pressure and friction shear stress distribution over the rake
face (f=0.3 mm, V=200 m/min, \i = 0.23)
450 _.- - - —.- -
^ 400-ra S 350 -
$ 300 -
5> 250 -
2 200 •
Fric
tion
Sh
o
o
o
n <
( ) 200 400 600 800 1000 1200
Contact Pressure (MPa)
1400 1600 1800 2000
Figure 6.19 Friction shear stress and normal contact pressure for the Coulomb friction
model identification
80
CHAPTER 6: RESULTS AND DISCUSSION
The relation between the contact pressure and the fiction shear stress is illustrated in
Figure 6.19. The slope of the chart presents the Coulomb friction model due to sliding
with friction coefficient equal to 0.23.
6-3-3-4 Equivalent plastic strain
Plastic strain is observed after the flow material passes the shear plane. Once the
material enters the shear zone, the magnitude of plastic strain increases rapidly with
different values depending on the friction zone. Figure 6.20 shows the distribution of the
plastic strain in the chip and workpiece. It is obvious that plastic strain decreases rapidly
from the contact area (the right side of the chip) to the free surface at the left side of the
chip. The maximum strain occurs in the contact area at the friction zone where the high
temperature is experienced.
~^° I / >v i-+2.357e+00 / / X 2-+1.885e+00 / 5 ^ / / A i-+1.414e+00 / ^ / f\ 4- +9 427e-01 — 4 ^S \3 \ 5- +4.714e-01 J>^ \ \
u
Figure 6.20 Distribution of equivalent plastic strain in the chip and the workpiece
(f = 0.3 mm, V = 200 m/min, \i = 0.23)
81
CHAPTER 6: RESULTS AND DISCUSSION
6-3-4 Temperature distributions
The contour plots of temperature distribution of both the workpiece and the tool are
shown during steady state for f = 0.3 mm, V = 200 m/min, and \i = 0.23. This study
shows the location of the maximum temperature and where the temperature decreases
along the rake face of the tool. Studies of temperature distribution helps to obtain the
optimum cutting condition of the tools to avoid the tool wear.
6-3-4-1 Temperature distribution in the chip
The contour plot in Figure 6.21 demonstrates the temperature distribution in the chip
during steady state orthogonal machining. The undeformed workpiece was initiated to be
at room temperature (25 °C ). The temperature increased as a result of the heat generated
by the plastic deformation and the friction at the secondary deformation zone. The
highest temperature was located at the friction zone (region 1) with an approximate value
equal to 940 °C. The lowest temperature was located in the primary shear zone (region 5).
T E M P I-2-.1-4-5-
+7.776e+02 +6.27le+02 +4,766e+02 +3.261e+02 + l.755e+02
Figure 6.21 Distribution of temperature in the chip and the workpiece
(f = 0.3 mm, V = 200 m/min, u. = 0.23)
82
CHAPTER 6: RESULTS AND DISCUSSION
6-3-4-2 Temperature distribution along the rake face
The temperature rise occurs at the chip-tool interface where some of the heat energy
is held in the tool and other is carried out with the chip. The magnitude of the heat that is
carried out with the chip is higher than what is held in the tool because of the flow of the
chip. Besides, the properties of the tool and the workpiece such as the conductivity and
the specific heat will significantly affect the heat energy which is transferred to both.
Figure 6.22 shows that the maximum temperature exists almost in the middle of the rake
face (region 1).
TEMP 1- +7.846e+02 2- +6.327e+02 3- +4.808e+02 4- +3.288e+02 5- +1.769e+02
Figure 6.22 Distribution of temperature in the tool
(f = 0.3 mm, V = 200 m/min, \i = 0.23)
83
CHAPTER 6: RESULTS AND DISCUSSION
A tool's temperature plays a very important role in the tool's life. It is important to
use the tool for a long time as long as the properties of the tool have not changed and the
shape matches the perfect cutting geometry. Due to friction, the tool life will decrease, so
the tool life should be managed by using the optimum cutting conditions such as the
velocity and the feed [6].
Figure 6.23 shows the temperature distribution along the chip tool interface. It
illustrates that a maximum temperature of 940 °C will be reached at a distance away from
the cutting edge. Away from the maximum temperature point, the temperature values
start to decrease close to the zone where the chip physically leaves the tool at 0.4 mm.
1000 -|
900 -
800 -
8 700-
T 600 -
1 500-
a 400 * E £ 300 -
200 -
100 -
o-l C
> Y
) 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Distance along the Rake Face (mm)
0 8
Figure 6.23 Temperature distribution on the rake face
(f = 0.3 mm, V = 200 m/min, \L = 0.23)
84
CHAPTER 6: RESULTS AND DISCUSSION
TKMP 1 -.?.-3 -
5 -
-7 .846e-02 6 . 3 2 7 C 0 2 •4.808c-'-02 •3.288e-:02 -1.76<V -02
Node - 4
Node - 3
Node - 2
Node - 1
Figure 6.24 Location of the selected nodes in the rake face of the tool
(f = 0.3 mm, V = 200 m/min, \L = 0.23)
Figure 6.24 shows the location of selected nodes at the rake face. The nodes are
selected to be in different zones to show the distribution of the temperature along the
entire rake face. The steady state will be achieved at different times at these nodes. The
maximum temperature is expected to be somewhere in region 1. In Figure 6.25, the
maximum temperature seems to reach a reasonable steady state after 0.5 ms. After 0.5 ms
the temperature still increases but with very small values.
85
CHAPTER 6: RESULTS AND DISCUSSION
Node-1 Node-2 Node-3 Node-4
0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007
Time (s)
Figure 6.25 Rake face temperature versus cutting time
(f = 0.3 mm, V = 200 m/min, u = 0.23)
6-4 Effect of Friction Factor
During machining, the interaction between the tool and the chip includes forces in
the normal and tangential directions. In this study, the simple Coulomb friction model
was applied along the chip-tool interface with different friction coefficients. The results
show different responses when using different friction coefficient. The effect of the
friction will be shown in the following sections.
6-4-1 Contour stress, strain and temperature distributions
The results of the contour plots of stresses, equivalent strains, and temperature for
different friction coefficients are shown in the following plots from Figures 6.26 to 6.29.
The distribution of these variables at the workpiece and tool are explained to explore the
effect of friction in orthogonal machining. These results can be used to gain good
information that may be used in understanding chip formation.
1000 y 900 -800 -
o 700 -
| 6 0 0 "
<5 500 -E 400 -£ 300 -
200 -100 -0 --0
86
CHAPTER 6: RESULTS AND DISCUSSION
6-4-1-1 Von-Mises stress distributions
Figure 6.26 shows the steady state Von-Mises stress in the chip for four friction
coefficients, 0.23, 0.4, 0.5, and 0.6 during machining. The stress was calculated based on
the strain, strain rate, and temperature (Johnson-Cook formula). The maximum and
minimum stress contour values were constrained in the four cases to simplify the
analysis. The location of any stresses over the whole chip is defined by six lines as shown
in the plots. The maximum stresses occur in the primary shear plane with approximated
stress equal to 1.34 GPa. The only differences that can be noticed are the sizes of the
stress regions. Lower stresses are shown near the contact surface at the friction
deformation zone. As far as the friction coefficient increase, the secondary deformation
zone will show clearly that the stresses will increase at the friction surface.
In general, the plots look similar; however, the stress distributions show some
differences. Also, the geometry of the chip is affected by the friction coefficient as it
becomes thicker with higher friction coefficients. The stresses decrease after the
separation at the chip tool interface and increase gradually after a while because of the
curl. Some effect of the stresses will influence even the produced surface and the
workpiece itself. The influence for the workpiece is important because high stress near
the produced surface is what it is called residual stress.
87
CHAPTER 6: RESULTS AND DISCUSSION
S, Mises '- +1.340e+09 2- +1.117e+09 3- +8.945e+08 4- +6.718e+08 5- +4.490e+08 6- +2.263e+08
u
S, Mises 1-2-3-4-5-6-
+1.340e+09 +1.117e+09 +8.945e+08 +6.718e+08 +4490e+08 +2263e+08
u
(a) n = 0.23 (b) p, = 0.4
S, Mises
1-+1.340e+09 2- +1.117e+09 3- +8.945e+08 4-+6.718e+08 5- +4.490e+08 6- +2.263e+08
i L
(c) ji = 0.5 (d) \i = 0.6
Figure 6.26 Contour plots of Von-Mises stress for different coefficients of friction (Pa)
(f = 0.3 mm, V = 200 m/min)
88
CHAPTER 6: RESULTS AND DISCUSSION
6-4-1-2 Distribution of shear stress
The shear stress distribution in the chip and the workpiece during the steady state is
presented in Figure 6.27 for different friction coefficient. The friction coefficient has
some effects on the shear stress as seen from the plots. As a result of the interaction
between the surfaces at the friction zone, the stress increases gradually by increasing the
friction coefficient from 0.23 to 0.6 (regions 4, 5) (negative values). Increasing the
coefficient of friction will generate higher temperatures at the chip-tool interface, which
will be explained later.
The shear stress acts at the friction zone by applying tangential loads over the chip
contact surface to make the separation harder. High shear stresses occur just where the tip
of the tool contacts the workpiece. The whole interior chip, regions 1, 2, and 3, has a
positive shear stress; however, the regions, 4, 5 and 6 have negative shear stress. It can be
seen that the stress diffuses gradually from negative shear stress at the primary and
secondary zone to the positive shear stress. The stress will gradually affect some layers of
the produced surface.
89
CHAPTER 6: RESULTS AND DISCUSSION
S.S12 1 -2-3-4-5-6-
+3.540e+08 +1.781e+08 +2.200e+06 •1.737e+08 -3.496e+08 -5.255e+08
Lx
S.S12
1- +3.545e+08 2- +1 785e+08 3- +2.515e+06 4- -1.735e+08 5- -3.495e+08 6- -5.255e+08
Lx
S.S12 1 - +3.540e+08 2 - +1.781e+08 3 - +2.200e+06 4 - -1.737e+08 5 - -3.496e+08 6- -5.255e+08
(a) p, = 0.23
S.S12
1- +3.540e+08 2- +1.781e+08 3- +2.200e+06 4--1.737e+08 5- -3.496e+08 6- -5.255e+08
Lx
(c) n = 0.5
(b) n = 0.4
(d) n = 0.6
Figure 6.27 Contour plots of shear stress for different coefficients of friction (Pa)
(f = 0.3 mm, V = 200 m/min)
90
CHAPTER 6: RESULTS AND DISCUSSION
6-4-1-3 Distribution of equivalent plastic strain
The effect of the friction coefficient on the distribution of equivalent plastic strain
over the whole workpiece is illustrated in Figure 6.28. The pattern of the equivalent
plastic strain looks similar; however, the magnitude is different as shown in the contour
plots. The plastic strain starts after the workpiece material passes the shear plane.
Extensive plastic strains occur in the secondary deformation zone. The maximum plastic
strain occurs in the layer at the chip-tool interface.
The magnitude of the equivalent plastic strain is significantly affected by the
friction coefficient. The highest value of the equivalent plastic strain occurs in a thin layer
near the chip tool interface in the sticking region close to the transition into the slip
region (see Figure 6.28 a). In the Figures 6.28 b, c, d the starting point is not clear
because of the use of 6 lines of equivalent plastic strain in the contour plots. The peak
values of the plastic strain are 5, 18.6, 19.9, and 20.2 for coefficients of friction 0.23, 0.4,
0.5, and 0.6, respectively.
A high plastic strain also appears in the tertiary deformation zone near the tool tip
position. The magnitude of this strain in the tertiary is related to the friction coefficient,
so by increasing the friction coefficient, the tertiary zone reaches a higher magnitude
plastic strain.
91
CHAPTER 6: RESULTS AND DISCUSSION
PEEQ l-+5.000e+00 2- +4.167e+00 3- +3.333e+00 4- +2.500e+00 5-+1.667e+00 6- +8.334e-01 7- +5.000e-05
U
PEEQ i-+1.866e+01 2- +5.000e+00 3-+4.167e+00 4 - +3.333e+00 s-+2.500e+00 6-+1.667e+00 7-+8.334e-01 s-+5.000e-05
(a) [i = 0.23 (b) \i = 0.4
PEEQ i-+1.994e+01 2- +5.000e+00 3- +4.167e+00 4- +3.333e+00 5- +2.500e+00 e-+1.667e+00 7- +8.3346-01 8- +5.000e-05
1-x
PEEQ i-+2.020e+01 2 - +5.000e+00 3 - +4.167e+00 4 - +3.333e+00 s- +2.500e+00 e-+1.667e+00 7- +8.334e-01 8- +5.000e-05
Lx
(c) (x = 0.5 (d) n = 0.6
Figure 6.28 Contour plots of equivalent plastic strain distribution for different
coefficients of friction (f - 0.3 mm, V - 200 m/min)
92
CHAPTER 6: RESULTS AND DISCUSSION
6-4-1-4 Distribution of temperature
Figure 6.29 presents temperature distributions in the chip during the steady state.
The temperature rise is a result of converted heat energy from both the plastic
deformation and friction effect. As explained above, most of the plastic work will transfer
to heat (assumed 90%). In the primary deformation zone, the chip and the workpiece
material are considered as one body; however, the chip and the tool material are two
different bodies that should be emphasized because of the large influence at the contact
surface.
Although the temperature at the shear plane is high to soften the material, the
temperature at the friction zone will be even higher because of the interaction between
the tool surface and the chip surface. The contour plots show that the maximum
temperature occurs not at the tool tip but on the chip-tool interface in some distance over
the tool tip. The friction coefficient clearly affects the maximum temperature. Figure
6.29 shows that the maximum temperature values along the chip-tool interface increase as
the friction coefficient increases in a uniform distribution as seen in the contour plots.
For the friction coefficient 0.23, 0.4, 0.5, and 0.6, the maximum temperatures are
equal to 936.5, 1151, 1163, and 1184 Celsius, respectively. The temperature decreases
gradually from the contact surface to the free surface of the chip. The maximum plastic
strain also occurs at the maximum temperature region as seen in Figure 6.28 and 6.29. By
increasing the temperature, the crystal structure of the workpiece may be more free to
deform and result in large plastic strains.
93
CHAPTER 6: RESULTS AND DISCUSSION
NTH MaxT:9.365e+02
1 - +9.736e+02 2- +7.839e+02 3- +5.942e+02 •4- +4.044e+02 5 - +2.147e+02 6 - +25006+01
L
NT11 MaxT: 1.151e+03
1-2-3-4-5-6-
+9.736e+02 +7.839e+02 +5.942e+02 +4.044e+02 +2.147e+02 +2.500e+01
u (a) ji = 0.23 (b) n = 0.4
NT11 MaxT: 1.163e03 1- +9.736e+02 2- +7.839e+02 3- +5.942e+02 4- +4.044e+02 5- +2.147e+02 6- +2.500e+01
L
NT11 MaxT: +1.184e+03
1- +9.736e+02 2- +7.839e+02 3- +5.942e+02 4- +4.044e+02 5- +2.147e+02 6- +2.500e+01
L_x
(c) n = 0.5 (d) n = 0.6
Figure 6.29 Contour plots of temperature distribution for different coefficients of friction
(f = 0.3 mm, V = 200 m/min)
94
CHAPTER 6: RESULTS AND DISCUSSION
6-4-2 Chip thickness
The comparison between the measured chip thickness [1, 2], and the predicted
values is shown in Figure 6.30 for six different feeds for four friction coefficients. The
obtained chip thickness is measured as explained in section 6-2-1. As expected when the
feed increases, the chip thickness increases linearly. The results of the current model are
very close to the experiment done by Arrazola et al. [1, 2] and the simulation work done
by Hagland [3]. In fact, increasing the friction coefficient alters the simulation results of
the chip thickness, so as the friction coefficient increases the chip thickness as well. The
results show that the simulations can have a good agreement with the experiment if the
friction model uses the right assumptions. The presented models seem to have excellent
results compared to the published experiment, especially for friction coefficient u=0.23
where the magnitude of percentage of error is less than 6% (see Figure 6.31).
Figure 6.31 shows that maximum error occurs for the highest friction coefficient
u=0.6 where the maximum magnitude error is located at feed 0.25 mm with value equal
to 30%. As a result of increasing the friction coefficient, the friction force will be
increased along the chip-tool interface; consequently, the shear angle decreases and
causes the chip thickness to increase. The present model shows the steady state chip
thickness from the beginning of the deformation, which makes the measurement of the
chip thickness easier.
95
CHAPTER 6: RESULTS AND DISCUSSION
Figure 6.30 Chip thickness obtained for the experimental [1,2] and numerical models
B |J=0.23 • |J=0.4 • M=0.5 D |J=0.6
35
30 a c o i -Q.
O «*-o o k
Ill
3?
25
20
15
10
5
0 0.1 0.15 0.2 0.25 0.3 0.35
Feed (mm)
Figure 6.31 Percentage of error of the obtained chip thickness for numerical models
96
CHAPTER 6: RESULTS AND DISCUSSION
6-4-3 Contact length
Figure 6.32 shows the contact length at different feeds with different friction
coefficient. The results of the contact length have the same trend of the chip thickness as
explained in section 6.4.2 where the obtained contact length is plotted against the feed
and compared with the published experimental data [1, 2]. In all cases the contact length
is under predicted. It can be observed that better contact length can be reached by
increasing the friction coefficient.
The influence of the friction coefficient is shown in Figure 6.32. As explained
above in section 6-3-3-3, the contact shear stress along the chip-tool interface will have
the highest magnitude at the tip of the tool and stay almost constant over the sticking
region then the shear stress decreases gradually, so when the friction coefficient has a
high value, the shear force will increase and prevent the chip from separating. While
increasing the friction coefficient gives a better contact length, it will badly affect other
parameters such as chip thickness.
Q. -I _.. 2 1
O 0.9 J | ? 0.8 -1 g>£ 0.7 -5 8 0.6 -t l 0.5 -•* a> g> "£ 0.4 -3 o ° 3 " t3 ,2 0.2 i •g 0.1 -,9 r> -O u
0.05
A ll 9
' 0.1
# M=0.23
A
•
I
0.15
O|j=0.4 •(J=0.5 A M :
A A
i o
A 1 • •
1 ' 0.2 0.25
Feed (mm)
=0.6 A EXP
A
1
0.3
A
8
1
0.35
i
0.4
Figure 6.32 Contact length along the chip-tool interface obtained for the experimental [1,
2] and numerical models
97
CHAPTER 6: RESULTS AND DISCUSSION
At feed 0.1 mm for example, the maximum percentage error is 50% at friction
coefficient 0.23 and will drop to 22% for friction coefficient 0.6. The big jump of the
percentage error really comes from the friction coefficient effect (see Figure 6.33). These
results illustrate that the simulations do not have a good agreement with experiment in the
contact length. The contact length still needs some study since the simulation shows poor
results. Even the previous work in which dual friction was used [1, 2, 3], the results
poorly presented the contact length. In the current work, the contact length shows some
response to the friction coefficient. The reason for these poor results might be the friction
model or the material model.
t-10 c 0)
i -20
o -30
I -40
-50
-60
I |J=0.23 • M=0.4 D |J=0.5 O (J=0.6
iJBiial O Ksj
Feed (mm)
m Iffiffrl
Figure 6.33 Percentage error for contact length for numerical models compared to
published experimental values [1,2]
98
CHAPTER 6: RESULTS AND DISCUSSION
6-4-4 Cutting and feed forces
In Figure 6.34, the average cutting and feed forces, obtained from the last 0.05 ms
of the solution, are plotted to illustrate the effect of friction coefficient on these forces.
Before starting the discussion, it is important to know that the constant Coulomb friction
model has been utilized in this analysis. The obtained results at friction coefficient 0.23 at
different feeds show the same trend if they are compared to the experimental results. The
feed and cutting force show high sensitivity to the friction coefficient (see Figure 6.34).
The results present less than 10% error in the cutting forces and over 70% error in the
feed forces (see Figure 6.35, 6.36). The amount of error, especially in the feed force, is
not acceptable. Increasing the friction coefficient, the feed force demonstrates a better
response. For example, friction coefficient 0.4 gives less error in both cutting and feed
force: the maximum percentage error is equal to less than 10% for the cutting force with
feed 0.2 mm and less than 20% for the feed force at the same feed.
At friction coefficient 0.5, the results show some improvment for the feed force;
however, the cutting force increases the percentage of errors. The same trend will occur
for the friction coefficient 0.6. In general, the increasing of the friction coefficient means
that the feed forces will have better results but not in the all cases, as seen in Figure 6.33.
The friction coefficient 0.4 gives the best obtained results in the feed forces generally. In
some cases, friction coefficient 0.5 and 0.6 have better results than the friction coefficient
0.4. Also, friction coefficient 0.4 has good results but not the best for the cutting force.
99
CHAPTER 6: RESULTS AND DISCUSSION
Figure 6.34 Measured and predicted force values for different feeds
It is obvious that a big jump for the feed force at higher friction coefficient at feed
of 0.15 mm occurred. This may be what is called the critical feed. Below that feed, the
tool tip force will have higher magnitude, which causes a rapid increase in feed force.
The tip force vector will affect the feed force significantly. Below the critical feed, the
feed force can include the tip force, but after that the tool tip vector will have
insignificant values to affect the feed force so this may be the reason of higher values of
the feed force. This explanation explores the assumptions of Albrecht [4] who explained
the affect of two forces that act in the tip and the rake face of the tool, as discussed in
section 3-3-2.
100
CHAPTER 6: RESULTS AND DISCUSSION
H|j=0.23 H|j=0.4 D|j=0.5 D|J=0.6
35
30
S 25
£ 20 O)
.E 15
§ 10 o 5 -§ 0 ill
S? -5
-10
-15
0.1 0.15 0.2
Hi i l l • ! m ' ' ' J 0.25 0.3
0.35
Feed (mm)
Figure 6.35 Percentage of error for the obtained cutting force of the numerical models
l|j=0.23 B|j=0.4 D|j=0.5 D|j=0.6
60
40
S 20 A
•a 0 0) <u "- -20 o o -40
UJ
g= -60
-80
-100
^ P15
dl •2 0.25 0.3
Feed (mm)
0.35
Figure 6.36 Percentage of error for the obtained feed force of the numerical models
101
CHAPTER 6: RESULTS AND DISCUSSION
6-5 Effect of Mass Scaling
In order to explore the effect of mass scaling, the numerical results for friction
coefficient 0.5 and 0.6 for the cases with and without mass scaling are shown in Figures
6.37 to 6.40. Figure 6.37 shows the cutting forces versus feed. All numerical results of
the cutting force are very similar. The numerical results have larger values compared to
the experiment because of the high values of friction coefficient. The maximum error of
the cutting forces is less than 30% compared to the experiment. Figure 3.38 shows the
feed forces versus feed. Again the effect of mass scaling is quite small. The trend of the
feed force shows some noise especially for feeds 0.15 mm and 0.25 mm. The reason may
be that the solution without mass scaling needs more running time. For example, at 0.15
mm feed and 0.6 friction coefficient with mass scaling, the maximum error jumps from
48% to 60 %.
—A— p=0.5 •--•"••• |j=0.6 —•— (j=0.5 + Mass scaling —•— (j=0.6 + Mass scaling —*— EXP
800 -r
700 -
£- 600 -
"g 500-
£ 400 -O)
•j= 300 -
O 200 -
100 -
0 -0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Feed (mm)
Figure 6.37 Cutting force vs. feed
102
CHAPTER 6: RESULTS AND DISCUSSION
—*— M-0.5
o c n
200 -F
orc
e(N
)
o
•g 100-LL.
50 -
n
0
—#— (j=0.6 -
0.05
-•— (j=0.5 + Mass scaling —•— (j=0.6 + Mass scaling —*-
j .
/ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ - * "
Y^
0.1 0.15 0.2 0.25 0.3 0.35
Feed (mm)
-EXP
0.4
Figure 6.38 Feed force vs. feed
The chip thickness and the contact length for the cases of mass and non-mass
scaling are shown in Figures 6.39 and 6.40. The numerical results are very similar with
maximum error for the chip thickness 25% and for the contact length around 25%
compared to the experimental results. It seems there is no big effect for the mass scaling
for both chip thickness and contact length for the cases that are shown in Figures 6.39 and
6.40. The difference between the numerical results of mass and non-mass scaling is less
than 10%.
103
CHAPTER 6: RESULTS AND DISCUSSION
-A—|j=0.5
n o
0 .7 -<-—. | 0 . 6 -
¥ 0.5 -a> 5. 0.4-o jE 0.3 -a. !E 0.2 -o 0.1 -
n
0
-®~- |j=0.6 —•— |j=0.5 + Mass Scaling —•— p=0.6 + Mass scaling - - * -
M ~^?8l&
< ^ ^ ^ ^ > > ^
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Feed (mm)
-EXP
0.4
Figure 6.39 Chip thickness vs. feed
-4r~-|j=0.5 © u=0.6 —•—|j=0.5 + Mass scaling - •— u=0.6 + Mass scaling -as— EXP
1 0.9
-g" 0.8 E. 0.7
o 0.5
i 0.4 re £ 0.3 o O 0.2
0.1 -I 0
0 0.05 0.1 0.15 0.2 0.25
Feed (mm)
0.3 0.35 0.4
Figure 6.40 Contact length vs. feed
104
CHAPTER 7 CONCLUSIONS
CHAPTER 7
CONCLUSIONS
7-1 Summary
An Arbitrary Lagrangian Eulerian approach (ALE) has been used to develop a
finite element model of orthogonal metal cutting using ABAQUS in order to study the
behaviour of the friction along the chip-tool interface. During this investigation, some
parameters such as the geometry of the workpiece were included in the study to see the
effect of the initial geometry. The finite element model includes nonlinear features such
as the material properties. The Johnson-Cook material model is one of the options that is
available in ABAQUS. It is easy to input this model after obtaining the right parameters,
which are obtained experimentally [1,2]. The finite element method can provide detailed
105
CHAPTER 7 CONCLUSIONS
results of different variables that cannot be obtained from experiments such as the
distributions of contact stress and temperature.
The current finite element model was developed by using no initial chip
geometry. By allowing the chip to grow over the rake face of the tool, the mesh is
deformed to the shape of the chip. The deformed chip is affected by the interaction at the
chip tool interface, so increasing friction coefficient influences the results. The obtained
results of no initial chip height were compared to the old models with initial chip
geometry and published experimental results for AISI 4140 steel [1,2]. The comparisons
include chip thickness, contact length, cutting force, and feed force for different models
for a feed of 0.2 mm, and u=0.23, u=0.6. The model of no initial chip height showed
improving results that give the best agreement with experimental results.
Friction at the chip tool interface was studied to investigate the effect of friction
coefficient. Constant friction coefficient was applied to the entire chip-tool interface to
simplify the analysis. Albrecht theory [4] was discussed as a way to estimate the friction
coefficient as the feed changed. The friction model was used with different coefficient
values, 0.23, 0.4, 0.5, and 0.6, for the same cutting conditions and tool geometry as
reference [1,2] for six different feeds from 0.1 mm up to 0.35 mm in order to investigate
the mechanism of machining process.
The effect of mass scaling was explored briefly. Although it considerably reduced
the solution time, its effect on the results was quite small.
106
CHAPTER 7 CONCLUSIONS
7-2 Conclusions
In this study, an ALE finite element simulation is used to simulate the continuous
chip formation process in orthogonal cutting of steel AISI 4140. The conclusions of this
work based on the obtained results can be drawn as follows:
1. The initial geometry of the workpiece has a little influence on the results;
however, the new model, which is presented with no initial chip height, shows
some improved results compared to the old models. These improved results
include the contact length and the cutting forces.
1. The chip thickness has the best results with no initial chip model at the lowest
friction coefficient compared to the other models; however, with friction
coefficient 0.6, the result is not the best.
2. Using constant Coulomb friction coefficient over the chip-tool interface with the
Albrecht definition (JJ, = 0.23) cannot give good results for the feed force
compared to the experimental results. The reason for poor results of the feed force
and contact length may be due to either the cutting edge or the friction model.
3. Raising the friction coefficient improves the prediction of the contact length;
however, it changes the other results, cutting and feed force as well as the
temperature. The contact length is always underestimated, compared to the
experimental results.
107
CHAPTER 7 CONCLUSIONS
7-3 Contributions
The contributions of this research include the following:
1. An ALE two-dimensional finite element model capable of simulating orthogonal
metal cutting processes using a mechanical and thermal explicit solution was
further developed.
2. The no initial chip model avoids issues related to defining initial chip geometry.
The chip presented by the deformed mesh and material grows smoothly along the
chip-tool interface. This model reaches steady state sooner than the old models
with initial chips and so saves computer time. The comparison study focused on
the effect of the chip height and showed that the no initial chip model often gives
the best results for chip thickness, contact length, cutting force and feed force.
3. Constant friction coefficient was used along the chip-tool interface with four
different values to obtain detailed analysis of the effect of the friction during
machining. Six different feed values were simulated.
4. This work defined a way to create the right input file by using the interactive
software ABAQUS.CAE. Nearly all the input data is entered to the simulation by
CAE so that there is no way to make mistakes with nodes position and number of
elements that are needed for the model.
7-4 Recommendations for Future Work
The following points are suggested for further work:
1. Review heat transfer coefficient values used on all surface and investigate need
for radiation heat transfer.
108
CHAPTER 7 CONCLUSIONS
2. Study different friction models that can be applied along the chip-tool interface
such as limiting shear stress model, temperature dependence, and variable friction
model can be used.
1. Consider the residual stress that may affect the product surface because of the
high temperature that is generated along the chip tool interface. The thermal
stresses occur in a layer close to the machined surface, after the relaxation to the
room temperature.
2. Perform more complicated models of metal cutting by using three-dimensional
geometry. The cost of this kind of model will be high because of the long solution
time.
3. Use different materials to represent the workpiece material for successful metal
cutting model. Some materials have the Johnson-Cook parameters available in the
published literature.
4. Study the effect of the workpiece hardness in the metal cutting model because this
may influence the results of the cutting and feed forces and the shape of the chip.
Study also the hardness effect on the residual stress.
109
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117
APPENDIX A
INPUT FILE FOR ABAQUS EXPLICIT
A finite element code is defined by using ABAQUS Explicit. The data of the
model is entered to the input file by using ABAQUS CAE. The input file is made up of
comment lines, keyword lines and data lines. Frequently, the block lines of the input file
starts with common lines which have a description to the current common. Next, the
keyword lines which have parameters. Finally, data lines are used to provide data that are
more easily given in lists. Most options require one or more data lines which have the
numeric entries.
*Heading
** Job name: Model name:
*Preprint, echo=NO, model=NO, history=NO, contact=NO
**
** PARTS
**
*Part, name=SHANK
*End Part
**
*Part, name=TOOL
*End Part
**
*Part, name=WORKPIECE
*End Part
**
** ASSEMBLY
118
*Assembly, name=Assembly **
* *
*Instance, name=TOOL-l, part=TOOL
*Node
* Element, type=CPE4RT
*Nset, nset=TOOLL, instance=TOOL-l
*Nset, nset=_PickedSet2, internal, generate
*Elset, elset=_PickedSet2, internal, generate
** Section: TOOL
*Solid Section, elset=_PickedSet2, material=TOOL
*End Instance
instance, name=WORKPIECE-l, part=WORKPIECE
*Node
* Element, type=CPE4RT
*Nset,
*Elset,
nset=
, elset=
PickedSet2,
=_PickedSet2:
internal,
, internal
generate
, generate
** Section: WP
119
*Solid Section, elset=_PickedSet2, material=WP
*End Instance
•Instance, name=SHANK-l, part=SHANK
*Node
*Element, type=T2D2
*Node
*Nset, nset=SHANK-l-RefPt_, internal
*Nset, nset=_PickedSet4, internal, generate
*Elset, elset=_PickedSet4, internal
** Section: SHANK
*Solid Section, elset=_PickedSet4, material=TOOL
*End Instance
**********************rrQQT -ET-ESET- EXAMPLE ************************
*Nset, nset=ALL, instance=TOOL-l, generate
•Elset, elset-ALL, instance=WORKPIECE-l, generate
*Elset, elset=ALL, instance=TOOL-l, generate
*Nset, nset=TOOLL, instance=TOOL-l
120
*******************WORKPIECE-NSET-ESET'EXAMPLE *******************
*Nset, nset=INFLOW, instance=WORKPIECE-l
*Elset, elset=INFLOW, instance-WORKPIECE-1
*Nset, nset=S-l, instance=WORKPIECE-l
*********************gjl^-^j^_^ggy_gggy. EXAMPLE **********************
*Nset, nset=SHANK, instance=SHANK-l, generate
*Elset, elset=SHANK, instance=SHANK-l
*Nset, nset=REF-P, instance=SHANK-l
**********DEFINED-SURFACES-IN-THE-WORKPIECE: EXAMPLE************
*Elset, elset=_0UT-S_S2, internal, instance=WORKPIECE-l
*Elset, elset=_0UT-S_S4, internal, instance=WORKPIECE-l
* Surface, type=ELEMENT, name=OUT-S
*Elset, elset=_EULERCHIP0UT_S3, internal, instance=WORKPIECE-l
* Surface, type=ELEMENT, name=EULERCHIPOUT
121
*Elset, elset=_FREE-S_S4, internal, instance=WORKPIECE-l
•Elset, elset=_FREE-S_Sl, internal, instance=WORKPIECE-l
•Elset, elset=_FREE-S_S2, internal, instance=WORKPIECE-l
* Surface, type=ELEMENT, name=FREE-S
*Elset, elset=_SHANK-l_SNEG, internal, instance=SHANK-l
*Surface, type=ELEMENT, name=SHANK-l
SHANK-1SNEG, SNEG
*Elset, elset=_SHANK-2_SP0S, internal, instance=SHANK-l
*Surface, type=ELEMENT, name=SHANK-2
SHANK-2SPOS, SPOS
•Elset, elset=_TOOLR_S2, internal, instance=TOOL-l
•Elset,
* Elset,
elset=
elset=
TOOLRS1, internal, instance=TOOL-l
TOOLRS4, internal, instance=TOOL-l, generate
* Surface, type=ELEMENT,
*Elset,
* Elset,
elset=
elset=
•Elset, elset=
TOOLRTS2,
TOOLRTS3,
TOOLRTSL
name=TOOLR
, internal, instance1
, internal, instance:
, internal, instance1
=TOOL-l
=TOOL-l,
=TOOL-l
generate
•Elset, elset=_TOOLRT_S4, internal, instance=TOOL-l, generate
122
** Constraint: Rigid-Shank
*Rigid Body, ref node=REF-P, elset=INSERT, tie nset=SHANK
** Constraint: Tie
*Tie, name=Tie, adjust=yes, type=SURFACE TO SURFACE
TOOLRT, SHANK-1
*End Assembly
*P 5JC 5j* *jZ m% *jC 5JC 5fC *[C J|C 5|C 5p 3}£ 5jC »p 5JC *(C *J* 5(C 5|C 3f» • ( • #p 5|C *f» 3f* *JC 7j* *|C *f* *J( 5JC % | \ / | I J I I I I I 1 1 \-i ** *1^ *t* *T* *t* *l* *** ^ M* *?* *(* *i* *P ^ ^ T^ "P ^ T^ T^ ^ ^ ^ ^ ^ ^ ^ ^
* Amplitude, name=RAMP, definition=SMOOTH STEP
0.,0., 1.5e-05, 1.
* *
*********************MATERIAL-MODEL'EXAMPLE **********************
** MATERIALS
**
*Material, name=TOOL
* Conductivity
25.,
*Density
10600.,
*Elastic
5.2e+l 1,0.22
* Expansion
7.2e-06,
* Specific Heat
200.,
123
*Material, name=WP
* Conductivity
42.6,100.
42.2,200.
37.7,400.
33.,600.
*Density
7800.,
^Elastic
2.1e+ll, 0.3
* Expansion
1.22e-05,20.
1.37e-05,250.
1.46e-05,500.
* Inelastic Heat Fraction
0.9,
*Plastic, hardening=JOHNSON COOK
5.98e+08,7.68e+08, 0.2092, 0.807, 1520., 25.
*Rate Dependent, type=JOHNSON COOK
0.0137,0.001
* Specific Heat
473.,200.
519.,350.
561.,550.
**
****************** INTERACTION PROPERTIES: EXAMPLE *****************
** INTERACTION PROPERTIES
** * Surface Interaction, name=FRICTION
124
*Friction
0.23,
*Gap Conductance
le+09, 0.
0., le-08
*Gap Heat Generation
1., 0.632
* Surface Interaction, name=FRICTION-l
* Friction
0.23,
*Gap Conductance
le+09, 0.
0., le-08
*Gap Heat Generation
1., 0.632
**
******************gQjjNi)ARY CONDITIONS' EXAMPLE ******************
** BOUNDARY CONDITIONS
**
** Name: BOTTOM Type: Displacement/Rotation
*Boundary
BOTTOM, 2, 2
** Name: REF-P Type: Displacement/Rotation
* Boundary
REF-P, 1, 1
REF-P, 2, 2
REF-P, 6, 6
**
** PREDEFINED FIELDS
125
** Name: TEMPERATURE-1 Type: Temperature
* Initial Conditions, type=TEMPERATURE
ALLW, 25.
** Name: TEMPERATURE-2 Type: Temperature
* Initial Conditions, type=TEMPERATURE
INSERT, 25.
* *
** STEP: STEP
**
*Step, name=STEP
DYNAMIC, TEMP-DISP, EXPLICIT
*Dynamic Temperature-displacement, Explicit
, 0.0006
*Bulk Viscosity
0.06, 1.2
******************************JyT A C§ SCALING***************************
** Mass Scaling: Semi-Automatic
** ABC
*Fixed Mass Scaling, elset=ABC, factor=50.
**
###*******************#**goUNDARY CONDITIONS**********************
* *i* *i* *t* *i* *i* *l# *l« *l* *l* «l# *i» «i» *i» *i* *t* *t* *i* *i* *3+ «l# «j* *l» ^ ^ ^ ^ *^ ^ ^ ^ *l* *i* *^ J # ^» - ^ ^ *^ J* ^ ^ ^ ^ ^ ^ ^ ^ t ^ t *|> *fc ^* *^ * t ^ ^ ^ ^ ^ ^ ^ ^f v|* *fc J ? ^tf *fc ^1; If ^ *fe fc 5[» Jp 5]> 5J» Jp *J* /(* J[* #|* #[* *|* J|C «J* JJ5 5[» SJ» ?J* Sf* *t* ¥f* J|» *p y^ *J» *^ *^ ^ ^ *J* ^ *(* 3J* 5^ 5fl» « > ^ J ^ ^ ^ ^* ^ *^ ^ ^ ^ ^ *^ ^ ^ *|* *^ >^ *J» *^ ^ ^ *^ ^ ^ ^» n* *>* * *i* *l* *i* *T* *T* * *T* ^*
** BOUNDARY CONDITIONS
**
126
** Name: INFLOW Type: Velocity/Angular velocity
*Boundary, amplitude=RAMP, type=VELOCITY
INFLOW, 1, 1,3.33
* Adaptive Mesh Controls, name=ALE, geometric enhancement=YES, mesh constraint
angle=20.
l. ,0.,0.
* Adaptive Mesh, elset=ALLW, controls=ALE, initial mesh sweeps=5, mesh sweeps=5,
op=NEW
**
** ADAPTIVE MESH CONSTRAINTS
**
** Name: OUTFLOW Type: Displacement/Rotation
* Adaptive Mesh Constraint
S-2, 2, 2, 0.0
S-l, 1, 1,0.0
OUTFLOW, 1, 1,0.0
*********************** JNTERACTIONS'EXAMPLE ***********************
** INTERACTIONS
**
** Interaction: FRICTION
* Contact Pair, interaction=FRICTION, mechanical constraint=PENALTY, weight=l.,
cpset=FRICTION
TOOLL, CHIPCONTACT
** Interaction: FRICTION-1
^Contact Pair, interaction=FRICTION-l, mechanical constraint=PENALTY,
cpset=FRICTION-l
RAKE-F, CHIPCONTACTUP
** Interaction: SFILM-1
*Sfilm
127
FREE-S, F, 25., 10.
** Interaction: SFILM-2
•Sfilm
Flank-F, F, 25., 140.
** Interaction: SFILM-3
* Sfilm
OUT-S, F, 25., 10.
**
*******************Qjjypjjp REOUESTS' EXAMPLE ***********************
** OUTPUT REQUESTS
**
* Restart, write, number interval=l, time marks=NO
**
** FIELD OUTPUT: F-Output-1
**
*Output, field, number interval=400
*Node Output
A, NT, RF, RFL, U, V
*Element Output, directions=YES
ER, HFL, LE, PE, PEEQ, S
* Contact Output
CFORCE, CSTRESS, FSLIP, FSLIPR
**
** HISTORY OUTPUT: H-Output-1
**
*Output, history, variable=PRESELECT, time interval=le-05
*End Step
************************************************************************
128
VITAE
Name: Abdulfatah Maftah
EDUCATION
Master of Science in Mechanical Engineering (Jan. 2006 - April. 2008) University of New Brunswick, Fredericton, NB
Thesis: Finite Element Simulation of Orthogonal Metal Cutting Using an ALE Approach
Related Courses: • Flow Induced Vibrations, • Principle of Metal Cutting, • Mechanics of Continua, • Applied of Finite Elements
Bachelor of Science in Mechanical Engineering (Sept. 1993 - Apr. 1998) Seventh April University, Sabratha, Libya
Thesis: Design of Heat Exchangers using Heat Pipes
Conference Paper: A. Maftah, H. Kishawy, and R. Rogers "FINITE ELEMENT SIMULATION OF ORTHOGONAL METAL CUTTING WITH DIFFERENT INITIAL GEOMETRIES", Third Mechanical Engineering Graduate Students Conference University of New Brunswick, November 12, 2007.