MODELING AND SIMULATION OF TURNING PROCESS

AND

TOOL RADIUS EFFECT IN MICRO-TURNING

USING FEM SOFTWARE –

A THESIS

submitted by

SUGAN DURAI MURUGAN V

ME09B056

for the award of the degree

of

BACHELOR OF TECHNOLOGY

DEPARTMENT OF MECHANICAL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY MADRAS.

MAY 2013.

THESIS CERTIFICATE

This is to certify that the thesis titled MODELING AND SIMULATION OF TURNING

PROCESS AND TOOL RADIUS EFFECT IN MICRO-TURNING USING FEM

SOFTWARE-DEFORM 3D submitted by Sugan Durai Murugan V (ME09B056), to the Indian

Institute of Technology Madras, Chennai for the award of the degree of Bachelor of Technology, is

a bona fide record of the research work done by him under our supervision. The contents of this

thesis, in full or in parts, have not been submitted to any other Institute or University for the award of

any degree or diploma.

Date: 20th

May 2013

Place : Chennai

Date : 18.05.2013

Dr. G.L Samuel

Project Guide

Dept. of Mechanical Engineering

IIT-Madras, Chennai -600036

Dr. T. Sundararajan

Head

Dept. of Mechanical Engineering

IIT-Madras, Chennai – 600036

i

ACKNOWLEDGEMENTS

I wish to thank and express my deepest gratitude to Dr.G.L Samuel who offered guidance and

support for my project during the whole semester.

I would also like to show my gratitude to all the faculty members of Mechanical engineering

department who were supportive and encouraging throughout the undergraduate course period.

ii

ABSTRACT

Understanding of the basics of metal cutting processes through the experimental studies has many

limitations. Researchers find this investigation through experiments a very time consuming and

expensive work. Using the capabilities of Finite Element Analysis, metal cutting modeling and

simulation provides an alternative and easier way for better understanding of machining process

under different cutting conditions with less number of experiments. Finite element modeling makes it

possible to deal with complicated conditions in metal cutting and to model several factors that are

present during the chip formation including friction at the chip tool interface, while minimizing

machining time and tooling cost.

Turning is one of the widely used metal cutting manufacturing technique in the industry world

and there are lots of studies going on to investigate this complex process. Several models have been

presented in the past with different assumptions. Certain validated models have been used to

simulate turning process conditions. In this paper, application of Finite Element Method is used in

simulating the effect of cutting tool geometry and cutting speed on effective stress, cutting force and

temperature changes.

Miniaturization of parts is becoming an upcoming trend in manufacturing. Investigation in micro-

machining has been a challenging task for researchers, since at micro level the validity of certain

assumptions made for conventional machining processes goes wrong. In this study, the tool radius

effect in micro turning process has been discussed and results show that the ratio of depth of cut and

tool radius pledge a important factor in nature of cutting.

DEFORM 3D is the simulation tool used in this study. DEFORM 3D is a robust simulation tool

that uses the FEM to model turning process in three dimensions. Autodesk INVENTOR is the

modeling tool used to model work piece and tool geometry. AISI 1045 and AISI 4340 stainless steels

have been used as work piece in this study.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

ABSTRACT ii

LIST OF TABLES v

LIST OF FIGURES vi

ABBREVIATIONS vii

1. INTRODUCTION 1

1.1. Metal Cutting process 1

1.2. Orthogonal Metal Cutting 2

1.3. Finite Element Method 3

1.4. Turning Process 4

1.5. Micro Turning process 4

1.6. DEFORM 3D 5

2. TURNING PROCESS MECHANICS 6

2.1. Cutting force model 6

2.2. Shear angle model 7

2.3. Cutting tool geometry 9

3. FINITE ELEMENT MODELING IN DEFORM 3D 11

3.1. About DEFORM 3D 11

3.2. Material Constitutive Laws 11

3.3. Boundary Conditions 16

3.4. Meshing and Simulation Controls 18

iv

4. RESULTS AND DISCUSSION 21

4.1. Deformation zone 21

4.2. Effect of Cutting speed on Effective Stress 22

4.3. Effect of Cutting speed on Temperature 24

4.4. Effect of Cutting speed on Cutting force 25

4.5. Effect of Change in rake angle 26

4.6. Discussions and Conclusion 27

5. TOOL RADIUS EFFECT IN MICRO-TURNING 29

5.1. Art of Micro-turning 29

5.2. Tool radius effect 31

5.3. Simulation using DEFORM 2D 31

5.4. Conclusion 35

6. REFERENCES 36

v

LIST OF TABLES

Table 4.1: Cutting speed vs. Average effective stress 23

Table 4.2: Cutting speed vs. Average temperature 24

Table 4.3: Rake angle vs. Maximum temperature vs. Average cutting force 27

vi

LIST OF FIGURES

1.1. Orthogonal cutting 2

1.2. Basics of turning 4

2.1. Merchant‟s orthogonal cutting model 6

2.2. Thin shear zone model 8

2.3. Thick shear zone model 8

2.4. Variables used in shear angle relationships 8

2.5. Basic tool angles of a single point cutting tool 9

2.6.a) 3D cutting tool model 10

2.6.b) 2D cutting tool model 10

3.1. Stress strain curve vs. temperature 11

3.2. Stress strain curve vs. strain rate 11

3.3. Deformation zones in orthogonal cutting 14

3.4. Frictional stress distribution on the rake face of the tool 17

3.5.a) Mesh of tool and work piece 19

3.5.b) Mesh showing formation of chip 19

4.1. Primary and Secondary deformation zones 21

4.2. Effective stress vs. Time 22

4.3. Average effective stress vs. Cutting speed 23

4.4. Temperature vs. Time 24

4.5. Average Temperature vs. Cutting speed 25

4.6. Cutting force vs. Time 25

4.7.a) Cutting tool with rake angle (+50) 26

4.7.b) Cutting tool with rake angle (00) 26

4.7.c) Cutting tool with rake angle (-50) 26

4.8. Temperature vs. Time for different rake angles 27

5.1. Mesh of Work piece and tool geometry in 2D 32

5.2. Initial mesh distortion for different tool radii 32

5.3. Von-Mises Effective stress distribution for various tool radii 33

5.4. Formation of negative rake angle at the rounded tool edge 34

5.5. Thrust force vs. time for tools with different edge radius 34

5.6. Cutting force vs. time for tools with different edge radius 34

vii

ABBREVIATIONS

FEM Finite Element Model

FEA Finite Element Analysis

ALE Arbitrary Lagrangian Eulerian

1

1.INTRODUCTION

1.1. METAL CUTTING PROCESS

Metal cutting operations still represent the largest class of manufacturing operations widely used

to remove unwanted material and achieve dimensional accuracy and desired surface finish of

engineering components. In metal cutting processes, the unwanted material is removed by the shear

cutting tool, which is significantly harder than the work piece.

The conditions in metal cutting are extreme than most of other deformation processes. The

distinguishing features of the metal cutting process are the following:

1) It is a plastic-flow process with exceptionally large strains. There is a high compressive stress

acting on the plastic zone and this prevents rupture from occurring until the strain is well above the

rupture value measured in tensile test

2) The deformation is localized to an extremely small plastic zone. Thus the strain rate is

unusually high.

Metal cutting involves shear deformation of work material by a rigid tool to form a chip. Lathe

machine is most generally used for these cutting operations. The cutting tool used could be either a

single point cutting tool or a multi point cutting tool. There are two basic types of metal cutting by a

single point cutting tool namely orthogonal and oblique metal cutting. If the cutting face of the tool is

at 90○

to the direction of the tool travel then the cutting action is called as orthogonal cutting. If the

cutting face of the tool is inclined at less than 90○ to the path of the tool then the cutting action is

called as oblique cutting. In this study, Orthogonal metal cutting is preferred over oblique cutting for

simplicity. Processes such as turning, milling, boring and drilling are among others the most

important process for discrete part manufacturing. Researchers have been studying these processes

for more than a century to gain better understanding and develop more advanced manufacturing

technology.

2

1.2. ORTHOGONAL METAL CUTTING

Orthogonal metal cutting is the simplest machining process and rarely used in industrial practice.

The plane-strain orthogonal metal cutting process, in which the direction of relative movement of

wedge-shaped cutting tool is perpendicular to its straight cutting edge as shown in Figure 1.1.

Figure 1.1: Orthogonal Cutting

The significance of orthogonal cutting is serving as an ideally simple cutting process model in

theoretical and experimental work, therefore it has been extensively studied for a reasonable good

modeling of the chip formation. In orthogonal cutting, effects of independent variables have been

eliminated as much as possible so that influences of basic parameter can be studied more accurately.

The assumptions Shaw et al [2] on which orthogonal cutting is based to achieve simplicity include as

follows,

1) The tool is perfectly sharp and there is no contact along the clearance face.

2) The shear surface is a plane extending upward from the cutting edge.

3) The cutting edge is a straight line extending perpendicular to the direction of the cutting

velocity and generates a plane-machined surface.

4) The chip does not flow to either side.

5) The depth of cut is constant.

6) The width of cut is constant.

7) The work piece moves relative to the tool with uniform velocity.

3

8) A continuous chip is produced with no build-up edge.

9) The shear and normal stresses along shear plane and tool are uniform.

1.3. FINITE ELEMENT METHOD

Finite Element Method (FEM) technique was first introduced in 1960s and has been widely used

to analyze in designing tools and forming processes. Based on the success of FEM simulations for

bulk forming processes, many researchers developed their own FEM codes to analyze metal cutting

processes. This advanced tool allows engineers to

1) Reduce the need for costly shop floor trials and redesign of tooling and processes

2) Improve tool and die design to reduce production and material costs

3) Shorten lead time in bringing a new product to market

Finite Element Method (FEM) based modeling and simulation of metal cutting process is

continuously attracting researchers for better understanding the chip formation mechanisms, heat

generation in cutting zones, tool-chip interfacial frictional characteristics and integrity on the

machined surfaces. Predictions of the physical parameters such as temperature and stress

distributions accurately play a vital role for predictive process engineering of machining processes.

Development of accurate and reliable continuum-based FEM models allow engineers to study the

stress and strain distributions, tool edge geometry, tool wear mechanisms and analyze the cutting

conditions.

Recently, the application of finite element method(FEM) in metal cutting process was a great help

for researchers in study of metal cutting and chip formation. Especially there are numerous studies

on finite element analysis of orthogonal metal cutting which provides information about plane strain

analysis where chip cut thickness is greater then critical uncut chip thickness.

4

1.4. TURNING PROCESS

Turning is the machining operation that produces cylindrical parts. In its basic form, it can be

defined as the machining of an external surface as with the work piece rotating, with a single-point

cutting tool, and with the cutting tool feeding parallel to the axis of the work piece and at a distance

that will remove the outer surface of the work. The three primary factors in any basic turning

operation are speed, feed, and depth of cut as shown in Figure 1.2.

Figure 1.2: Basics of Turning.

The cutting speed is the speed of the work as it rotates past the cutting tool. The feed rate is the

rate at which the tool advances into the work. The depth of cut is the amount of material removed as

the work revolved on its axis. Other factors include the type and geometry of the cutting tool, the

angle of the tool, and the overall material removal rate.

1.5. MICRO TURNING PROCESS

Micro turning is one type of micro machining process which uses a solid tool and its material

removal process is almost similar to conventional turning process. Micro turning is generally used to

define the practice of material removal for the production of parts having dimensions that lies

between 1 and 999 In recent years, researchers have explored a number of ways to improve the

micro turning process performance by analyzing the different factors that affect the quality

characteristics.

5

But unlike conventional macro machining process, micro turning process displays a different

set of characteristics due to its significant size reduction. Size effect comes into play in such

cases. Size effect is defined as the effect due to the small ratio of depth of cut to tool radius. The

main differences that arise apart from size effect from macro machining are tool deflection, non-

homogeneity, different crystallographic orientation, critical minimum chip thickness. Tool radius

plays a major role with respect to depth of cut in micro turning characteristics. This study

demonstrates using Finite Element Method, the effect of tool radius in micro turning process.

1.6. DEFORM 3D, 2D

DEFORM is a Finite Element Method (FEM) based process simulation system designed to

analyze various forming processes used by metal forming applications. It is available in both

Lagrangian (Transient) and arbitrary Lagrangian and the Eulerian (ALE Steady-State) modeling.

Additional, the software is currently capability of Steady-State function and it is required of running

a transient simulation previous to steady state cutting simulation.

Unlike general purpose FEM codes, DEFORM is tailored for deformation modeling. A user

friendly graphical user interface provides easy data preparation and analysis so engineers can focus

on forming. A key component of this is a fully automatic, optimized remeshing system made

especially for large deformation problems.

The DEFORM system consists of three major components:

1) A pre-processor for creating, assembling, or modifying the data required to analyze the

simulation, and for generating the required database file.

2) A simulation engine for performing the numerical calculations required to analyze the

process, and writing the results to the database file. The simulation engine reads the

database file, performs the actual solution calculation, and appends the appropriate

solution data to the database file.

3) A post-processor for reading the database file from the simulation engine and displaying

the results graphically and for extracting numerical data.

Using this FEM software; the goal is to build a computational working model that will closely

predict deformation, stress, plastic strain distribution, and instantaneous strain rate in work piece and

load on the tool under parameter variations including the cutting depth, cutting angle, cutting speed

of the turning process.

6

2. TURNING PROCESS MECHANICS

2.1. CUTTING FORCE MODEL

Since 1930, many researchers have tried to understand the turning process under plasticity theory.

Their main goal was to know about the cutting force, stresses and temperatures involved in the

process. Various methods were proposed based on fundamentals of mechanical cutting process, in

those simplified analytical approaches of orthogonal cutting were first considered by Merchant [9],

who introduced the concept of shear plane angle.

Merchant‟s analysis is based on the two-dimensional process geometry as shown in Figure 2.1.

An orthogonal cutting is defined by cutting velocity V, uncut chip thickness tu, chip thickness tc,

shear angle Ø, rake angle α, and width of cut w. The width of cut w is measured parallel to the

cutting edge and normal to the cutting velocity.

Figure 2.1: Merchant‟s Orthogonal Cutting model

The work piece material moves at the cutting velocity while cutting tool remains still. A chip is

thus formed and is assumed to behave as a rigid body held in equilibrium by the action of forces

7

transmitted across the chip-tool interface and across the shear plane. The resultant force Fr is

transmitted across the chip-tool interface. No force acts on the tool edge or flank. Fr can be further

resolved into components on shear plane, rake face, on cutting direction depending upon research

interest. Components on shear plane are Fs in the plane and Ns normal to shear plane. Cutting force

Fp is in the cutting direction and a trust force Fq normal to the work piece surface. On the rake face,

the friction force is in the direction of chip flow and the normal force Nc is normal to the rake face.

The relationships between those components and resultant force can be defined by the following

equations (1), (2), (3),

[ ] *

+ [ ] (1)

[ ] *

+ [ ] (2)

(

) (3)

The concept of orthogonal cutting and all of the simplifying assumptions helped to build the

fundamental cutting force analysis and left space for improvement in succeeding studies. Most force

models incorporated in Finite Element Analysis follow this shear plane theory.

2.2. SHEAR ANGLE MODEL

In the last thirty years many papers on the basic mechanics of turning process have been written.

Several models have tried describe the process with nature of deformation zone formed at the shear

plane. There is a conflicting evidence about the nature of the deformation zone in metal cutting. This

has led to two basic approaches in the analysis. Many workers, such as Merchant[9], Kobayashi and

Thomsen[20], have favored the thin-zone shear model, as shown in Figure 2.2. Others such as

Palmer and Oxley[8], and Okushima and Hitomi[9], have suggested the thick-zone shear model as

shown in Figure 2.3

8

Figure 2.2: Thin zone shear model Figure 2.3: Thick zone shear model

Available experimental evidence indicates that the thick-zone model may describe the cutting

process at very low speeds, but at higher speeds most evidence indicates that a thin-zone model is

approached. Thus, for our model the thin-zone model is used, which is likely the most realistic for

practical cutting conditions.

In case of the thin zone shear model, shear angle can be defined. Shear angle is actually a measure

of the plastic deformation in cutting and is an essential quantity for predicting the forces in cutting.

Shear angle depends on both rake angle and friction angle, as shown in Figure 2.4.

Figure 2.4: Variables used in shear angle relationships.

Merchant‟s relationship [7] suggests that material will choose to shear at angle that minimizes the

required energy. The relationship is given in equation (4),

( ) (4)

9

2.2.1. Chip formation

When the metal cutting is in progress, the chip presses heavily on the top face of the tool and

continuous shearing takes place across the shear plane, resulting in chip formation. Chip formation is

a plastic-flow process due to shear. Merchant‟s cutting model claimed that the chip is formed by

simple shear on a plane running from the tool tip to a point on the free surface work piece. No plastic

flow takes place on either side of this shear plane.

2.3. CUTTING TOOL

The geometry of a cutting tool is defined by certain basic tool angles, faces and edges. The cutting

tool angles are described by means of taking appropriate projections of the cutting tool surfaces. A

system of tool angles is shown in Figure 2.5

Figure 2.5: Basic tool angles of a Single point cutting tool.

The components of the cutting tool are defined as follows:

1) Rake face is the surface over which the chip, formed in the cutting process, slides.

2) Flank face is the surface over which the surface, produces on the work piece, passes.

3) Cutting edge is a theoretical line of intersection of the rake and the flank surfaces.

4) Cutting wedge is the tool body enclosed between the rake and the flank faces.

5) Shank is the part of the tool by which it is held.

10

Rake angle:

Rake angle is the angle between the top face of the tool and the normal to the work surface at the

cutting edge. In general, the larger the rake angle, the smaller the cutting force on the tool. The

reason is that the shear plane decreases as rake angle increases for a given depth of cut. A large rake

angle will improve cutting action, but eventually lead to early tool failure, since the tool wedge

angle is relatively weak. A compromise must therefore be made between adequate strength and good

cutting action.

Clearance Angle:

Clearance angle is the angle between the front face of the tool and a tangent to the work surface

originating at the cutting edge. All cutting tools must have clearance to allow cutting to take place.

Excessive clearance angle will not improve cutting efficiency and it will merely weaken the tool.

2.3.1. Modeling in Autodesk Inventor

AUTODESK Inventor is a solid modeling tool, it unites the 3D parametric features with 2D

tools, but also addresses every design through manufacturing process. The model of a 3D single

point cutting tool is quite simple as shown in Figure 2.6.a). The cutting tool is modeled in 2D will

have only two angles, rake angle and clearance angle. The 2D section of the cutting tool is drawn in

sketcher and the part is extruded in 3D to obtain the cutting tool model as shown in Figure 2.6.b).

The part is then exported as STL files into DEFORM 3D .

Figure 2.6.a) 3D cutting tool model. Figure 2.6.b) 2D cutting tool model.

1

3. FINITE ELEMENT MODELING IN DEFORM 3D

3.1. ABOUT DEFORM 3D

This project is being done to study the turning process using computational Finite Element

Method in DEFORM software. This software is used to simulate the turning process from the initial

transient state to steady state of cutting forces. Simulating deformation by those cutting forces in a

three-dimensional environment makes it possible to study the process and make more accurate

predictions that are well represented by orthogonal cutting.

To build a continuum based FEM model for turning, the essential and desired attributes of the

model are

1) The work material model should satisfactorily represent elastic-plastic and thermo-

mechanical behavior of the work material deformations.

2) FEM model requires a chip separation criteria for physical process simulation of chip

formation around the tool cutting edge during machining.

3) Interfacial friction characteristics on the tool-chip and tool-work contacts to account for

additional heat generation and stress developments due friction.

Thus the simulation model in DEFORM is build with thermal and mechanical properties,

boundary conditions, contact conditions between tool and the work piece. The cutting process model

is simulated as a dynamic event causes large deformations in a few numbers of increments resulting

in massive mesh distortion and an adaptive remeshing technique with intensity for maintaining a

successful mesh throughout the turning process.

3.2. CONSTITUTIVE MATERIAL LAWS

In DEFORM , a thermo-mechanically coupled Lagrangian incremental simulation is done with

elastic-plastic material work piece and a rigid material tool. AISI 1045 is used as the work piece

material in this study, because it has been the focus of many recent modeling and as well as

machinability. Tungsten Carbide with no coating is being used as tool material.

12

3.2.1. Stress strain curve vs. Temperature:

With all other factors equal, increasing the temperature decreases the stress required for an

increment of deformation. In other words when temperature increases, the stress-strain curve flattens

along the Y-axis and the material gets yielded easily as shown in Figure 3.1.

Figure 3.1: Stress strain curve vs. Temperature

3.2.2. Stress strain curve vs. Strain rate:

With all other factors equal, increasing the rate of deformation increases the stress required for an

increment of deformation. The material gets stiffer as the strain rate increases, therefore at higher

strain rate the elastic part becomes more elastic and plastic part becomes more plastic in nature as

shown in Figure 3.2.

Figure 3.2: Stress strain curve vs. Strain rate

3.2.3. Flow Stress Curves:

In DEFORM , the concept of flow stress is used. The flow stress models are used extensively in

the simulations of deformation processes occurring at high strains, strain rates and temperature. The

idea of flow stress is important in the case of incremental plasticity. As a material is deformed

plastically, the amount of stress required to incur an incremental amount of deformation is given by

13

the flow stress curve. Actually the flow stress curve is an extended and focused region of plasticity in

the true stress-strain curve.

Flow stress is strongly dependent on several state variables, among these are accumulated strain,

instantaneous strain rate and temperature[18]. As seen in the Figure 3.1 and 3.2 the flow stress

curves can vary strongly with these state variables. Therefore for determining the material behavior

accurately, the flow stress data is important.

Numerous empirical and semi-empirical flow stress models are used in the computational

plasticity. The models that are currently in use are

1) The Johnson-Cook model

2) The Steinberg-Cochran-Guinan-Lund model

3) The Zerilli-Armstrong model

4) The Mechanical threshold model

5) The Preston-Tonks-Wallace model

3.2.4. The Johnson-Cook model:

The Johnson-Cook model [17] is purely empirical and widely used to represent the strength

behavior of the materials, typically metals , subjected to large strains, high strain rates and high

temperature. This model exhibits an unrealistically small strain-rate dependence at high

temperatures. Johnson-cook model gives the following equation (5) for the flow stress

( ) [ ( ) ][

][ ( ) ] (5)

Where is the equivalent plastic strain, is the plastic strain-rate, and A, B, C, n, and m are

material constants. The strain-rate and temperature are normalized for simplicity in representing the

model. The normalized strain-rate and temperature in equation (5) are defined as

,

( )

( ) (6)

Where is the effective plastic strain-rate of the quasi-static test. is a reference temperature,

and is a reference melt temperature.

Properties such as Young‟s modulus and Poisson‟s ratio are implicitly used in flow stress

equations, and these properties are temperature dependent. Thus temperature dependent property

data has to be given.

14

3.2.5. Oxley’s Equation – Cutting model:

Oxley and coworkers developed a model [4] to predict cutting forces, average temperatures and

stresses in primary and secondary deformation zones by using Johnson-Cook‟s Flow stress model

[17], thermal properties, tool geometry and cutting conditions.

A simplified illustration of the plastic deformation for the formation of a continuous chip when

machining a ductile material is given in Figure 3.3.

Figure 3.3 Deformation zones in Orthogonal cutting

. Where V is the cutting speed, is the rake angle, VS is the shear velocity, is the shear angle,

is the length of AB, is the undeformed thickness, is the chip thickness.

There are two deformation zones in this simplified model – a primary zone and a secondary zone.

The primary plastic deformation takes place in a finitely sized shear zone. The work material begins

to deform when it enters the primary zone from lower boundary CD, and it continues to deform until

it reaches the upper boundary EF. Even after exiting from the primary deformation zone, some

material experiences further plastic deformation in the secondary deformation zone only on a smaller

scale. Assumption is being made that the primary deformation zone is a parallel-sided shear zone and

secondary deformation zone is triangular shape and the maximum thickness is proportional to the

chip thickness.

15

The average value for shear strain rate along AB is,

(7)

The velocity along the shear plane is,

( ) (8)

The shear angle is expressed as,

[

] (9)

The average shear strain in the primary deformation zone is given by

( ) (10)

3.2.6. Thermal model

In a thermo-mechanically coupled model, a huge amount of heat energy will be generated due to

large deformations and temperature of the model will increase during the process. Heat is mainly

generated due to two reasons:

1) Due to the heavy plastic work done at the shear zone. It is assumed that, 90% of all plastic

work is converted into heat.

2) Due to friction at the interface of tool and chip. Most of this generated heat is given to chip

and tool.

The rate of specific volumetric flux due to plastic work is given by the following equation,

(11)

Where, f is the fraction of plastic work converted into heat, and is the rate of plastic work.

Heat generated due to friction is given by the equation,

(12)

Where, Ffr is the friction force, Vr is the relative sliding velocity between tool and chip.

16

Due to the change in temperature, thermal material laws are needed to be defined to adapt the

elastic-plastic model to the new temperature conditions. The following processes are defined within

the thermal model.

1) Heat Transfer:

Heat generated due to plastic work will dissipate to other parts of the work piece via conduction

and then to environment by convection and radiation. Heat transfer coefficients for tool-work piece

interface are given to dissipate the heat generated. The heat transfer coefficients can be approximated

to be constant over a wide range of temperature since amount heat lost by this means is insignificant

compared to the amount of heat generated.

2) Thermal Expansion:

When temperature of a material changes, the material tends to expand or contract. Defined by a

thermal expansion coefficient to represent the change in material volume. The coefficient again

depends on existing temperature.

3) Heat Capacity:

The heat capacity for a given material is the measure of the change in internal energy per degree of

temperature change. It is also a temperature dependent property

3.3. BOUNDARY CONDITIONS

3.3.1 Friction between tool and work piece

A resistive force acts tangentially when two objects slip, is called friction force. At normal loads

and conditions the friction force is proportional to the normal force, the proportionality constant is

called coefficient of friction. But these laws of friction have been invalid for metal cutting conditions

where plastic deformation is occurring close to the sliding interface, i.e. under the condition of very

high normal load. In this situation the real area of contact approaches to the apparent area. Hence the

proportionality between the real area of contact and applied normal load is constant and equal to the

apparent area. Under these conditions the friction force is independent of normal load [19]. as shown

in Figure 3.4.

17

Figure 3.4: Frictional shear stress distribution on the rake face of the tool

The dependence of friction parameter on the cutting conditions can be explained by considering

the distribution of frictional shear stress on the rake face of the tool. Over the length h1, the normal

stress is very high and the metal adheres to the rake face, plastic flow occurs in the work material . In

this region the friction stress is independent of the normal load and generally equal to the shear yield

stress of the material. This region is called sticking region. On the length h2, smaller normal stresses

exist and the usual condition of sliding friction applies. This region is called sliding region.

Based on this, two types of friction models were developed called Coulomb type and Shear type.

Shih et al.[10] introduced a model that consists of the sticking region for which the frictional force is

Shear type, and the sliding region for which the friction force is Coulomb type.

The shear friction model is given by

(13)

Where m is the shear friction factor needs to be estimated and given as input, is the

shear flow stress of the chip at the primary zone and is the frictional stress.

The coulomb friction model is given by

(14)

Where is the coulomb friction factor needs to be estimated and given as input, is the normal

stress at the shear plane.

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3.3.2. Heat Transfer properties

The work piece and tool temperature and heat transfer coefficient at tool-work piece has to be

given. Both the tool and work piece is allowed to heat transfer with the environment.

3.3.4. Self Contact

The chip formed from the work piece will contact the work piece after a curl, therefore a

constraint is deployed to avoid contact between work piece and its chip.

3.3.3. Movement

In actual turning process, the work piece is rotated at a specific rpm, and the tool is moved along

the axis of the work piece at a constant feed rate. In Simulation, work piece is fixed and tool is

moved along the surface of the work piece. The tool is being driven at respective cutting velocity

along the surface of the work piece.

3.4. MESHING AND SIMULATION

Meshing is forming a grid to the finite element model, consisting of nodes. Mesh generation is the

process of dividing the analysis model into a number of finite elements. This generated mesh is

programmed on how the model will respond to the machining conditions. These mesh elements act

like a spider web, from each node of a mesh element, it exchanges data to each of the adjacent nodes

by means of inbuilt shape functions.

Nodes are assigned at a certain density throughout the model. Generally, important regions have

higher nodal density for more accurate results. Eventually, as the no of nodes increases; the

processing time for solving a problem also increases. Therefore, a compromise between accuracy of

the results and the available time for solving a FEM problem is usually made.

In DEFORM software; meshing can be either relative or absolute. In relative meshing, total no of

elements and size ratio has to be decided wherein absolute meshing, size ratio and minimum element

size or maximum element size is needed. Size ratio is the ratio of largest element size to smallest

element size. Weighting factors are also available on different parameters such as Surface curvature,

Temperature distribution, Strain distribution, and Strain rate distribution. A region with rapid change

in any of the weighting factors will receive more elements than a region with uniform distribution.

Mesh window allows to form secondary meshing details to a specific window chosen. Finally a solid

mesh must be made to represent the work piece and tool as Finite Element models as shown in

Figure 3.5.a) and b).

19

Figure 3.5.a) Mesh of tool and work piece Figure 3.5.b) Mesh showing formation of chip

3.4.1. Simulation controls

The DEFORM system can solve time dependent non-linear problems by generating a series of

FEM solutions at discrete time increments. At each time increment, the key variables of each node in

the finite element mesh are determined based on boundary conditions, thermo mechanical properties

of the work piece materials and possible solutions at previous steps. Other state variables are derived

from these key values, and updated for each time increment.

To define a step, the following must be defined

1) Number of Simulation steps

2) Step increment to save

3) Solution step definition

3.4.2. Remeshing Criteria

Automatic remeshing is the most convenient way to handle the remeshing of objects undergoing

large plastic deformation. When the remeshing criteria has been fulfilled, the object will be

remeshed. Interference depth is referred for triggering remeshing, when the element edge of work

piece has been penetrated by the tool by the master object by a specified amount. This penetration

distance can be absolute or relative.

20

3.4.3. Iteration and Convergence Controls

The iteration controls specify the criteria that FEM solver uses to find a solution at each step of

the problem simulation. DEFORM software has Conjugate-gradient solver and Sparse solver for both

deformation and temperature variables. These iterative solvers improve the overall solving time with

minimum memory requirements, especially in case of large deformation problems like machining

process. There are two types of iteration methods incorporated in the software namely Newton-

Raphson method and direct method. The Newton-Raphson method converges in fewer iterations, but

more likely to fail. The direct method is more likely to converge than Newton-Raphson but it

requires more iterations to converge. The convergence depends on the convergence error limit

provided.

1

4. RESULTS AND DISCUSSION

All the results that have been obtained have certain parameters constant throughout the

simulation.

1) Depth of cut (d) – 0.5 mm

2) Feed rate (f) – 0.3 mm

3) Environment Temperature – 20

4) Shear friction factor – 0.6

5) Heat transfer coefficient at tool-work piece interface – 0.2 N/s/mm/ .

4.1. DEFORMATION ZONE

The largest deformation occurs on the primary deformation zone, followed by the secondary

deformation zone. This result as shown in Figure 4.1, is agreeable with Shih [11], where the major

deformation during cutting process was concentrated in two regions, one near to the cutting tool

edge(yellow region) where primary deformation occurs, and other in the sticking region and sliding

region(green and cyan region) where secondary deformation occurs.

Figure 4.1: Primary and Secondary Deformation zones

22

4.2. EFFECT OF CUTTING SPEED ON EFFECTIVE STRESS

Cutting speed of the tool is an important parameter to study the turning process characteristics.

With all other parameters kept constant, cutting speed is varied to analyze the change in stress

distribution and temperature. When the cutting speed increases the generated temperature on chip

also increases, due to increase of required energy at high cutting speed. More heat will be generated

as cutting speed increases, consequently the maximum temperature on the tool and work piece

surface increase at higher cutting speed, as from the theory and findings from Serenity et al [7].

When the cutting speed increases the strain rate on the primary deformation zone also increases.

Increase in strain rate will increase the effective stress; on the other hand increase in temperature will

decrease the effective stress. In such cases, the temperature effect dominates the strain rate effect at

low cutting speeds. Therefore the effective stress should decrease as cutting speed increase.

Figure 4.2. shows maximum effective stress vs. time for different cutting speeds. The fluctuations

in the effective stress are due to mesh distortion and remeshing during the cutting process. As the

cutting speed increases from 100m/min to 150 m/min the effective stress level drops due to rise in

temperature, but when cutting speed reaches 250 m/min, the stresses increases due to a significant

change in strain rate.

Figure 4.2: Effective stress vs. Time

To find an average effective stress value over varying cutting speed, a constant stroke length is

taken as a reference. A stroke length of 0.35 mm is taken to average the stress values. The cutting

time to reach this stroke length is also noted. Figure 4.2 shows the average Effective stress values

over different cutting speed.

23

Table 4.1

Figure 4.3: Average effective stress vs. Cutting Speed

Cutting

Speed (m/min)

Average Effective Stress

(Mpa)

Cutting time

( e-5 sec)

100 1432.12 20.6

150 1346.57 13.7

250 1404.84 8.0

24

4.3. EFFECT OF CUTTING SPEED ON TEMPERATURE

Figure 4.4. Showing Maximum temperature vs. time for different cutting speeds. As the cutting

speed increases, the temperature rises rapidly in the initial conditions, and keeps increasing gradually

and stabilizes in a small temperature region when steady state is reached. Therefore, coolant flow

rate must also be increased to maintain the temperature constant.

Figure 4.4: Temperature vs. Time

To find an average temperature values over varying cutting speed a small time interval of 2.0e-4

sec to 3.5e-4 sec is taken so that the initial gradient in the transient state will not be accounted for

calculations. Stroke length covered in each cutting speed is also noted. Figure 4.5 showing average

temperature vs. cutting speed.

Table 4.2

Cutting

Speed (m/min)

Average Temperature

( ) Stroke Length (mm)

100 734.36 0.277

150 750.25 0.376

250 771.50 0.605

25

Figure 4.5: Average Temperature vs. Cutting Speed

4.5 EFFECT OF CUTTING SPEED VS CUTTING FORCE

Figure 4.6. showing Force in cutting direction vs. time for different cutting speeds.

.Figure 4.6: Cutting force vs. Time

26

4.6. EFFECT OF CHANGE IN RAKE ANGLE

To understand the effect of rake angle on machining characteristics, three tools with different rake

angles have been modeled and simulated on similar turning conditions. Figure 4.7 shows the tool

geometry with three different rake angles.

Figure 4.7.c) Cutting tool with Rake angle (00)

According to Gunay et al [6] when rake angle decreases to negative values, high cutting

forces act on the material and therefore high heat will be generated. Figure 4.7. shows temperature

vs. cutting time for different rake angles. Table shows maximum cutting force along the cutting

direction and maximum temperature reached for different rake angles. The results are agreeable with

findings from Gunay et al [6].

Figure 4.7.a) Cutting tool with Rake angle (+50) Figure 4.7.b) Cutting tool with Rake angle (-5

0)

27

Rake angle( ), Clearance

angle( )

Maximum Temperature

(0C)

Maximum Cutting force

(kN)

50 , 7

0 585 0.925

00, 7

0 514 1.178

-50, 7

0 724 1.462

Table 4.3:

Figure 4.8. Temperature vs. Time for different rake angles.

4.5. DISCUSSION

In this study, using Explicit arbitary Lagrangian Eulerian method a FEM simulation model for

turning process of AISI 1045 steel using Tungten Carbide cutting tool. Johnson-cook‟s flow stress

model and Oxley‟s equation is being used as constitutive material laws to model the metal cutting

process. The simulation of the chip formation, temperature distributions and stress distributions in

chip and on the machined surface are succesfully achieved. This study establishes a framework to

further study the turning process conditions and optimization of cutting parameters.

From the results obtained from Simulation, the following can be concluded:

1) As cutting speed increases, the effective stress on the chip formed decreases momentarily and

then increases, indicating i.e a cutting speed for which the effective stress attains a minimum value.

28

2) The temperature of the chip formed in turning of AISI 1045 increases with increase in cutting

speed. Therefore higher the cutting speed, larger the coolant flow to maintain the temperature

constant.

3) Machining with negative rake angle results in higher cutting force and temperature than

positive rake angle. Negative rake angle causes more friction due to which heat generated increases

and in turn temperature increases.

29

5. TOOL RADIUS EFFECT IN MICRO-TURNING PROCESS

5.1. ART OF MICRO TURNING

Unlike conventional macro-machining processes, micro-machining displays different

characteristics due to its significant size reduction. Therefore size effect is defined as the effect due

to the small ratio of the depth of cut to the tool edge radius[22]. Often, the edge radius of the tools is

relatively larger than the chip thickness to prevent plastic deformations or breakage of the micro-

tools. In contrast to the conventional sharp-edge cutting model, chip shear in micro-machining

occurs along the rounded tool edge. As a result, cutting has a large negative rake angle, which affects

the magnitude of the ploughing and shearing forces. Therefore, a relatively large volume of material

has to become fully plastic for a relatively small amount of material to be removed, resulting in a

significant increase in specific energy.

Further, when the chip thickness is below a critical chip thickness, chips may bot be

generated during the cutting process. But the work piece will elastically deform. This is due to

critical minimum chip thickness hm. When the uncut chip thickness, h, is less than a critical

minimum chip thickness, hm, elastic deformation occurs and the cutter does not remove any work

piece material. As the uncut chip thickness approaches the minimum chip thickness, chips are

formed by shearing of the work piece, with some elastic deformation still occurring. As a result, the

removed depth of the work piece is less than the desired depth. However, when the uncut chip

thickness increases beyond the minimum chip thickness, the elastic deformation phenomena

decreases significantly and the entire depth of cut is removed as a chip, the relationship between the

tool radius and minimum chip thickness depends on the cutting edge radius and the material of the

work piece.

As the depth of cut is sometimes less than the grain size of the work piece material. The

assumption of homogeneity in work piece material properties is no longer valid. Because micro-grain

structure size is often of the same order of magnitude as the cutter radius of curvature, the grain

structures will affect the overall cutting properties. This is a distinct difference between micro and

macro mechanical machining. The changing crystallography during the cutting process also causes

vibration. This vibration is difficult to eliminate by changing the machine tool design or process

conditions, because it originates from the work piece.

The major drawback of micro turning process is that the machining force which influences

machining accuracy and also limit the machinable size[23]. The thrust force tends to deflect the work

30

piece. However, the work piece can vibrate in the tangential direction of the tool-work piece contact

region because the vibration along the normal direction is blocked by the cutting tool. As the

diameter of the work piece reduces the rigidity of the work piece decreases. Therefore, controlling

the reacting force during cutting is one of the important factors in improvement of machining

accuracy.

1. Surface roughness:

It is observed that the surface roughness in micro-turning decreases with feed, reaches a

minimum, and then increases with further reduction in feed and also the bigger the tool nose radius is

used, the surface roughness improves with higher depth of cut, high speed and high feed rate[24].

2. Cutting tools:

It is recommended to use smaller tools which have decreases thermal expansion relative to

their size, increased static stiffness from their short structure, increased dynamic stability from their

higher natural frequency, and potential for decreased cost due to smaller quantities of material.

Diamond tools are often used for ultra-precision machining, but have a limited ability to machine

ferrous materials. In all other cases Tungsten Carbide tools are used widely. Since cutting is mostly

restricted to nose portion of the tool, the cutting edge radius plays a significant role on tool

performance[24].

3. Cutting force:

Cutting force mainly depends on the work piece hardness. More the hardness more the

required cutting force. With the increase of feed rate and depth of cut, cutting force increases. Unlike

from macro turning, in micro turning much fluctuations happen in cutting forces. This periodicity in

fluctuations is due to the crystallographic orientations of material and frictional condition on grain

structure during cutting.

Cutting force also determines the tool deflection and bending stress that limits the feed rate.

Basically there are two components to cutting forces namely, shearing and plowing forces. Since the

chip thickness in micromachining applications can be comparable in size to the edge radius of the

tool, the conventional sharp-edged theorem cannot be applied in micromachining operations due to

their large negative rake angle. In addition, the elastic-plastic deformation of the work piece also

changes the cutting forces in micro-machining operations. Specifically the elastic recovery of the

work piece along the clearance face of the tool and the plowing effect by the tool edge radius forced

vibration of the tool contribute to the magnitude of the cutting force.

31

5.2. TOOL RADIUS EFFECT

Tool edge radius is an important paramter for surface quality in micro turning process [21].

Under certain machining practices, cutting tip of the tool is strengthened with an edge radius for

higher tool life. Production of tools with perfect sharpness is practically impossible due to

technological limitations. However, this tool geometry is usually neglected in the modeling of the

conventional macromachining process such as merchant‟s shear plane model. Such assumption is

acceptable in the modeling of conventional machining as the undeformed chip thickness „a‟ is at

least larger than the tool edge radius „r‟ by three orders of magnitude. Therefore, it is not appropriate

for micro turning where „a‟ approaches „r‟ in microscale. In this regard, the differences between

conventional machining and micro machining are originated from the great size differences between

„a‟ and „r‟.

5.3. SIMULATION USING DEFORM 2D

In this study, the analysis of micro-turning with FEM is performed under plane strain

condition using the explicity dynamic algorithm and the Arbitary Lagrangian Eulerian formulation as

the solution method similar to that macro turning process we have done already. The work piece

used here is AISI 4340 and tool is Tungsten Carbide.

All the results that have been obtained have certain parameters constant throughout the

simulation.

1) Depth of cut (d) – 2

2) Cutting speed (v) – 1666.67 mm/s

3) Environment Temperature – 20

4) Shear friction factor – 0.6

5) Heat transfer coefficient at tool-work piece interface – 0.2 N/s/mm/ ..

The work piece is modeled as 50 x 10 rectangular block as shown in Figure 5.1, and tool with

rake angle 0 and clearance angle 5 . Tool radius varies from 1 to illustrate the tool edge

radius effect.

32

Figure 5.1: Mesh of Work piece and tool geometry in 2D.

1. CHIP FORMATION

Figure 5.2 shows the mesh distortion initially when tool starts to deform the work piece for different

tool radius. For radius r = 0,1 chip is formed directly on the rake face of the tool. As the radius

increases material begins to flow around the tool edge more gradually. At r = , material takes

the shape of the tool edge and begins to shear much later than for r = .

Figure 5.2: Initial mesh distortion for different tool radii.

a) R= 0μ

d) R= 3μ e) R= 4μ

b) R= 1μ c) R= 2μ

f) R= 5μ

33

2. VON MISES EFFECTIVE STRESS DISTRIBUTION

Plastic deformation behavior of the work at different tool radius is reflected from the Von Mises

flow stress as shown in figure 5.3. For radius r =1,2 plastic deformation is intense at the chip root

and extending towards the turning point of the chip free boundary, which is known as the primary

deformation zone in the conventional turning model. But as the radius increases the deformation

zone gets larger, and material in the vicinity of the rounded tool edge undergoes severe plastic

deformation. The increase in size and thickness of the plastic zone is due to the merger of the

primary and secondary deformation zone. Critically at r =5 , the deformation zone is highly

localized in front of the rounded tool edge which could lead to the changes in chip formation

behavior.

Figure 5.3: Von-Mises Effective stress distribution for various tool radii.

3. CUTTING FORCES

As the radius of the tool edge increases, the effective rake angle deviates from the tool rake angle

because the chip growth doesn‟t happen under rake face, it happens in front of the rounded tool edge

due to the changes in the chip formation. This leads to a effective negative rake angle eff in micro-

turning as shown in Figure 5.4 .Due to this increase in negative rake angle, the cutting forces

increases as the tool radius increases. Figures 5.5 and 5.6 showing cutting forces and thrust forces for

tool radii r =1,3,5

a) R= 0𝜇𝑚

d) R= 3𝜇𝑚

e) R= 4𝜇𝑚

b) R= 1𝜇𝑚

c) R= 2𝜇𝑚

f) R= 5𝜇𝑚

34

Figure 5.4: Formation of negative rake angle at the rounded tool edge.

Figure 5.5: Thrust force vs. time for tools with different edge radius.

Figure 5.6: Cutting force vs. time for tools with different edge radius.

35

4. CONCLUSION

As the tool edge radius „r‟ approaches the depth of cut „a‟, the chip formation behavior and the

associated stress states are greatly affected by rounded tool edge. This study has shown that the

assumption of perfect tool sharpness is invalid in micromachining.

1) The ratio of undeformed chip thickness to tool edge radius is a deciding parameter in micro

machining in which chip formation, material deformation and stress distribution are greatly

influenced.

2) When tool radius becomes more than depth of cut primary and secondary deformation zone

merges together, and a single concentrated shear zone arises at the tool edge.

3) Beyond certain radius size for a given depth of cut, effective rake angle is no longer the tool

rake angle and it becomes negative influencing in cutting forces and surface roughness.

36

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