(Sticking Sliding Region ) Finite Element Simulation of Orthogonal Metal

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


6-3-3 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


6-5 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


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


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 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


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


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


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


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


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


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


9 0 - ( a - ^ )

a ••Îs

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


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


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


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


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


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


/ \

(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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


transition 0 for e<0lr

0 = \{0- Vraôn )/(#„„/, " ^™„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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


(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


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


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


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


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


Figure 6.7 Percentage error of the contact length

69


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


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 'CTyîidw^.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


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


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^^^û^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


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


• |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


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


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


(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



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


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


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


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 ûuu 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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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



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


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


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


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


—*— 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


-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


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


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


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


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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I l l

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114

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[36] M. N. A. Nasr, E. G. Ng and M. A. Elbestawi "Modeling the effects of tool edge

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[38] Y. B. Guo, C. R. Liu, "3D FEA Modeling of Hard Turning", Journal of

Manufacturing Science and Engineering, Vol. 124, pp. 189-199, 2002.

[39] Nihad Balihodzic, "A numerical investigation of orthogonal machining", M.Sc.Eng.

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[40] V. Grolleau, « Approche de la validation experimentale des simulations numeriques

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116

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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.,

Êlastic

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.


•Sfilm

Flank-F, F, 25., 140.


* 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.

Documents

(Sticking Sliding Region ) Finite Element Simulation of Orthogonal Metal