fang thesis final

8/2/2019 Fang Thesis Final

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A Study of Fixture Layout and Clamping force for a Ti-6Al-4V Disk in

a Vertical Turning Lathe Numerically Controlled Machine

by

Maureen Fang

A Thesis Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

MASTER OF SCIENCE

Major Subject: Mechanical Engineering

Approved:

_________________________________________

Ernesto Gutierrez-Miravete, Thesis Adviser

Rensselaer Polytechnic InstituteHartford, CT

November, 2009

(For Graduation December 2009)


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Copyright 2009

by

Maureen Fang

All Rights Reserved


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CONTENTS

A Study of Fixture Layout and Clamping force for a Ti-6Al-4V Disk in a Vertical

Turning Lathe Numerically Controlled Machine ......................................................... i

LIST OF TABLES........................................................................................................... vii

LIST OF FIGURES ........................................................................................................ viii

LIST OF SYMBOLS.......................................................................................................... i

ACKNOWLEDGMENT .................................................................................................. iii

ABSTRACT ..................................................................................................................... iv

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

1.1 Objectives........................................................................................................... 1

1.2 Background and Significance ............................................................................ 1

1.3 Literature Review............................................................................................... 2

2. Machining Set-up......................................................................................................... 3

2.1 Vertical Turning Lathe (VTL) process .............................................................. 3

2.1.1 Machine Axis ......................................................................................... 3

2.1.2 Machine Table........................................................................................ 4

2.2 Description of Workpiece .................................................................................. 5

2.2.1 Geometry of the Disk............................................................................. 5

2.2.2 Material Properties of Ti-6Al-4V........................................................... 5

2.2.3 Machinability ......................................................................................... 6

2.3 Description of fixture ......................................................................................... 8

2.3.1 Plate................................................................................................ 9

2.3.2 Locators .10

2.3.3 Clamps.. ............................................................................................... 11

3. Machining of Titanium (Ti-6Al-4V) Disk................................................................. 13

3.1 Machining Conditions...................................................................................... 13

3.2 Cutting Tool Properties .................................................................................... 13


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4.4 Assumptions..................................................................................................... 36

4.5 Initial Fixture Layout ....................................................................................... 37

4.6 Cutting Forces Applied to Fixture-Disk Model ............................................... 38

4.7 Cutting Forces Locations Represent Complete Cut ......................................... 39

4.8 Cutting Forces Locations Represent Disk Rotation......................................... 41

4.8.1 45 Degree Location.............................................................................. 44

5. DOE to determine the appropriate Fixture Layout .................................................... 45

5.1 Objective Statement ......................................................................................... 45

5.2 Factors.............................................................................................................. 46

5.3 Levels ............................................................................................................... 46

5.3.1 The Number of Clamps and Locators .................................................. 46

5.3.2 The Magnitudes of the Cutting Forces (F)........................................... 47

5.4 Matrix of Experiments ..................................................................................... 48

5.5 Constraints ....................................................................................................... 49

5.6 Solution Procedure........................................................................................... 49

5.7 Statistical Analyses .......................................................................................... 50

5.7.1 Main Effects ......................................................................................... 50

5.7.2 Interaction Effects ................................................................................ 52

5.8 Results and Recommendations ........................................................................ 54

6. DOE to determine the appropriate magnitude of Clamping Force............................ 56

6.1 Objective Statement ......................................................................................... 56

6.2 Clamping Pressure ........................................................................................... 56

6.3 Constraints ....................................................................................................... 56

6.4 Screening Stage................................................................................................ 57

6.4.1 Recommended Range of Clamping Forces.......................................... 58

6.5 Matrix of Experiments ..................................................................................... 60

6.6 Factors and Levels ........................................................................................... 61


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6.7 Solution Procedure........................................................................................... 61

6.8 Statistical Analyses .......................................................................................... 61

6.8.1 Main Effects ......................................................................................... 61

6.8.2 Interaction Effects ................................................................................ 63

6.9 Results and Recommendations ........................................................................ 65

7. Conclusions and Recommendations .......................................................................... 67

7.1 Conclusions from Machining Ti-6Al-4V Disk and FEM Analysis ................. 67

7.2 Conclusions from Design of Experiments ....................................................... 68

7.3 Future Studies .................................................................................................. 69

8. Appendix: .................................................................................................................. 70

8.1 Matlab codes to calculate cutting forces in oblique cutting............................. 70

8.2 Matlab codes to calculate cutting forces in orthogonal cutting........................ 71

8.3 ANSYS Finite Element Model Results for Chapter 4.8 .................................. 72

8.4 ANSYS Finite Element Model Results for Chapter 5 ..................................... 84

8.5 ANSYS Finite Element Model Results for Chapter 6 ..................................... 89

Reference: ........................................................................................................................ 95


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LIST OF TABLES

Table 2.1: Material Properties of Ti-6Al-4V. [Donachie, 4] ............................................. 6

Table 2.2: Machinability comparisons of Ti-6Al-4V with several steel materials.

[Doanchie, 4] ..................................................................................................................... 6Table 2.3: Properties of Ti-6Al-4V compared to a medium carbon steel. [Machado, 14] 7

Table 3.1: Material properties of WC/Co C2 grade cutting tool. [Santhanam, 17]......... 14

Table 3.2: Actual dimensions of cutting tool. [Donachie, 4]........................................... 16

Table 3.3: Cutting speed, feed rate, and depth of cut for chapter 3................................. 17

Table 3.4: Cutting angles for oblique and orthogonal cutting angles.............................. 23

Table 3.5: Cutting Constants for both Oblique and Orthogonal Cutting......................... 28

Table 3.6: Comparisons of the cutting forces. ................................................................. 30

Table 4.1: Finite Element Model Properties.................................................................... 33

Table 4.2: Cutting forces are generated by a finish cut. .................................................. 39

Table 5.1: The number of clamps and locators with corresponding total contact surface

area................................................................................................................................... 47

Table 5.2: Machining parameters for finish, semi-finish, and rough cut. ....................... 48

Table 5.3: The cutting forces for finish, semi-finish, and rough cut. .............................. 48

Table 5.4: Nine experiments with corresponding values of the two factors. .................. 49

Table 5.5: Reduction rates for a rough cut. ..................................................................... 54

Table 6.1: Clamping Pressures with corresponding clamping forces.............................. 56

Table 6.2: Six experiments with corresponding values of the two factors...................... 58

Table 6.3: Nine experiments with corresponding values of the two factors ................... 61


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LIST OF FIGURES

Figure 2.1: Facing on a vertical boring machine [Boothroyd, 13] .................................... 3

Figure 2.2: Amera Seiki Vertical Turning VT2000 Machine............................................ 4

Figure 2.3: A fixture is being clamped onto a vertical-boring machine table through aRadial T Slot [Boothroyd, 13]. .......................................................................................... 5

Figure 2.4: Fixture-disk assembly includes plate, locator and clamp.............................. 10

Figure 2.5: The 3-2-1 principle of location applied to a rectangular shape workpiece.

[Doyle, 16]....................................................................................................................... 11

Figure 2.6: Commercially available fixture clamps. [Wilson, 15] .................................. 12

Figure 3.1: Geometry of single-point cutting tool. [Altintas, 18].................................... 15

Figure 3.2: Depth of cut, b, and Feed Direction, Vf, for an outer diameter cut. ............. 18

Figure 3.3: Geometries of orthogonal and oblique cutting processes [Altintas, 18]. ...... 19

Figure 3.4: Schematic diagram of the lathe turning process of an outer diameter cut with

workpiece rotation V, feed direction Vf, tangential force, Ft, feed force, Ff, and radial

force Fr. ............................................................................................................................ 20

Figure 3.5: Cutting forces (tangential force, Ft, feed force, Ff, and radial force Fr ) acting

on workpiece and feed direction, Vf, of cutting tool. ...................................................... 20

Figure 3.6: Flow diagram of cutting forces calculations. ................................................ 22

Figure 3.7: Geometry of oblique cutting process. [Altintas, 18]..................................... 23

Figure 3.8: The normal Shear angle is determined by the range of chip compression ratio

values from 0.8 to 1.5 and the normal rake angle of 4.8o

for oblique cutting. ................ 26

Figure 3.9: Cutting forces results for both oblique and orthogonal cutting..................... 29

Figure 4.1: Disk is divided into 128 equally spaced volumes. ........................................ 32

Figure 4.2: The 360 degrees Clamping/Locating Candidate Region. ............................. 34

Figure 4.3: Dimensions of a clamp or locator, and one area. .......................................... 35

Figure 4.4: Von Mises stress in the initial fixture layout. ............................................... 37

Figure 4.5: Initial Fixture Layout contains four clamps and locators.............................. 38

Figure 4.6: Cutting forces are applied in vertical locations such as top, middle, and

bottom to represent a complete cut.................................................................................. 40

Figure 4.7: Displacement vector sum represents top, middle, and bottom locations. ..... 40

Figure 4.8: Top view of initial fixture layout in ANSYS................................................ 41


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Figure 4.9: Cutting forces applied to seven locations in the initial fixture layout........... 42

Figure 4.10: Displacement vector sum in seven locations circumferentially.................. 43

Figure 4.11: Displacement components such as x, y, and z in seven locations

circumferentially.............................................................................................................. 44

Figure 5.1: Cutting tool travel path in relation to the deflected disk. .............................. 46

Figure 5.2: Three levels of the number of clamps and locators....................................... 47

Figure 5.3: Main Effects Plot for Displacement Vector Sum.......................................... 50

Figure 5.4: Main Effects for x-component displacement. ............................................... 51

Figure 5.5: Main Effects for y-component displacement. ............................................... 51

Figure 5.6: Main Effects for y-component displacement. ............................................... 52

Figure 5.7: Interaction Plot for Displacement Vector Sum............................................. 52

Figure 5.8: Interaction plot for maximum x-component displacement. .......................... 53

Figure 5.9: Interaction plot for absolute minimum y-component displacement. ............ 53

Figure 5.10: Interaction plot for absolute minimum z-component displacement............ 54

Figure 6.1: The chosen appropriate fixture layout with 16 clamps and locators............. 57

Figure 6.2: Displacement vector sum for 500N and 3500N clamping forces. ................ 58

Figure 6.3: X-component displacement for 500N and 3500N clamping forces.............. 59

Figure 6.4: Y-component displacement for 500N and 3500N clamping forces.............. 59

Figure 6.5: Z-component displacement for 500N and 3500N clamping forces. ............. 60

Figure 6.6: Main Effects plot for displacement vector sum. ........................................... 62

Figure 6.7: Main Effects plot for x-component displacement......................................... 62

Figure 6.8: Main Effects plot for y-component displacement......................................... 63

Figure 6.9: Main Effects plot for z-component displacement. ........................................ 63

Figure 6.10: Interaction plot for displacement vector sum.............................................. 64

Figure 6.11: Interaction plot for maximum x-component displacement. ........................ 64

Figure 6.12: Interaction plot for absolute minimum y-component displacement. .......... 65

Figure 6.13: Interaction plot for absolute minimum z-component displacement............ 65

Figure 8.1: Finish Cutting Forces is Applied at Point B (0o

from a Clamp and Locator)73

Figure 8.2: Displacement Vector Sum at Point B (0o

from a Clamp and Locator) ......... 73

Figure 8.3: X-component Displacement at Point B (0o

from a Clamp and Locator) ...... 74

Figure 8.4 Y-component Displacement at Point B (0o

from a Clamp and Locator) ....... 74


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Figure 8.5: Z-component Displacement at Point B (0o

from a Clamp and Locator)....... 75

Figure 8.6: Finish Cutting Forces is Applied at -11.25o

from a Clamp and Locator....... 75

Figure 8.7: Displacement Vector Sum at -11.25o

from a Clamp and Locator................. 76

Figure 8.8: X-component displacement at -11.25o

from a Clamp and Locator............... 76

Figure 8.9: Y-component displacement at -11.25o

from a Clamp and Locator............... 77

Figure 8.10: Z-component displacement at -11.25o

from a Clamp and Locator ............. 77

Figure 8.11: Finish Cutting Forces is Applied at -22.5o

from a Clamp and Locator....... 78

Figure 8.12: Displacement Vector Sum at -22.5o

from a Clamp and Locator................. 78

Figure 8.13: X-Component Displacement at -22.5o

from a Clamp and Locator............. 79

Figure 8.14: Y-Component Displacement at -22.5o

from a Clamp and Locator............. 79

Figure 8.15: Z-Component Displacement at -22.5o

from a Clamp and Locator ............. 80

Figure 8.16: Finish Cutting Forces is Applied at -45o from a Clamp and Locator.......... 80

Figure 8.17: Displacement Vector Sum at -45o

from a Clamp and Locator.................... 81

Figure 8.18: X-Component Displacement at -45o

from a Clamp and Locator................ 81

Figure 8.19: Y-Component Displacement at -45o

from a Clamp and Locator................ 82

Figure 8.20: Z-Component Displacement at -45o

from a Clamp and Locator ................ 82

Figure 8.21: Side View of X Displacement at -11.25o

from a Clamp and Locator......... 83

Figure 8.22: Side View of X Displacement at -22.5o

from a Clamp and Locator........... 83

Figure 8.23: Side View of X Displacement at -45o

from a Clamp and Locator.............. 84

Figure 8.24: Displacements Contour Plots for Experiment#2......................................... 85

Figure 8.25: Displacements Contour Plots for Experiment#3......................................... 85

Figure 8.26: 16 Clamps and Locators for Experiment# 4 to 6 ........................................ 86

Figure 8.27: Displacements Contours Plots for Experiment# 4 ...................................... 86



Figure 8.30: 32 Clamps and Locators for Experiment# 7 to 9 ........................................ 88


Figure 8.32: Displacements Contours Plots for Experiment#8 ....................................... 89


Figure 8.34: Displacement Contour Plots of No Cutting Forces Applied....................... 90

Figure 8.35: Displacement Contour Plots for Experiment# 1 ......................................... 90


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Figure 8.37: Displacement Contour Plots for Experiment#3 .......................................... 91






Figure 8.43: Displacement Contour Plots for Experiment#9 .......................................... 94


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LIST OF SYMBOLS

Angles

Symbol Descriptions Unit

i oblique angle degree

f cutting tool side rake angle degree

p cutting tool back rake angle degree

r cutting tool side cutting-edge angle degree

clf Side relief angle degree

clp End relief angle degree

kr End cutting-edge angle degree

f Side rake angle degree

n normal rake angle degree

o orthogonal rake angle degree

p Back rake angle degree

r orthogonal rake angle degree

a friction angle degree

n normal friction angle degree

chip flow angle degree

n normal shear angle degree

n,c orthogonal normal shear angle degree

r Side cutting-edge angle degree

Symbol Descriptions Unit

b depth of cut mm

F1 The magnitude of the cutting forces for finish cut N

F2 The magnitude of the cutting forces for semi-finish cut N

F3 The magnitude of the cutting forces for rough cut N

Fc Clamping Force N

Ff Feed force N

Fr Radial force N

Ft Tangential force N

h feed rate mm/rev

Kfc Feed cutting constant MPa

Kfe Average edge force coefficient N/mm


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Krc Radial cutting constant MPa

Ktc Tangential cutting constant MPa

Kte Average edge force coefficient N/mm

P Clamping Pressure Pa

R Nose radius mmrc Chip compression ratio ~

V Workpiece rotation m/min

v Cutting Speed m/min

Vf Feed direction ~

s Shear yield stress MPa


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ACKNOWLEDGMENT

I would like to offer my appreciation to my advisor Prof Ernesto Gutierrez-Miravete for

his support and time. It has been a great learning experience. I would like to offer my

gratitude to Mr. Scot Webb for his mentorship throughout my graduate studies and mycareer at Pratt and Whitney. I am truly appreciated for Scots guidance and reviews of

my thesis. I would like to thank my colleague, Chris Quinn, for helping me in learning to

use ANSYS software and review of my thesis. In addition, my parents and brother,

Leon, have offered me a tremendous amount of support and love. I am truly fortunate

and happy to have such a wonderful support.


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ABSTRACT

Fixtures are the most critical and expensive tool within a machining process such as

turning, milling, and drilling. The reason is that a fixture must be able to support and

hold a workpiece in a precise location and orientation while it is subjected to the cuttingforces during chip formation. The cutting forces cause the workpiece to elastically

deform which in turn jeopardize the machining dimensional accuracy. A properly

designed fixture should be able to minimize the deflections and to enhance dimensional

control within the workpiece.

The type of machining process, physical characteristics of the workpiece, and the

magnitude of cutting forces govern the specifications for designing a fixture. A

numerically controlled vertical turning lathe is chosen as the type of machining process

in this study. The machining parameters and cutting tool properties are determined to

best represent turning Ti-6Al-4V workpieces in the aerospace industry. The chosen

workpiece is a symmetrical Ti-6Al-4V disk which represents a rotor within an aircraft

engine because the aerospace industry is heavily dependent on machining to make

rotors. The turning process in this study is determined to be oblique cutting. The

formulas and assumptions from published literature are used in the written Matlab codes

for the calculations of cutting forces.

In order to determine the best fixture design, the deflections within the disk are

examined by a finite element (FE) model in ANSYS to represent the fixture-workpiece

system of the entire turning process. The FE model calculates the elastic deflections

within the disk. This study uses Design of Experiments method to determine an

appropriate number of clamps and locators, and magnitude of clamping force by

achieving a tolerable amount of deflection within the disk. The statistical analyses are

performed in Minitab. 16 clamps and locators are chosen as the appropriate fixture

layout which consists of 50% coverage of the clamping/locating candidate regions.

There are no significant additional benefits to use 32 clamps and locators which

represent the 360o

full ring type of configuration as widely being used in the industry.

An appropriate amount of clamping force is determined to be 100N. This is significantly

smaller than the suggested clamping force from the published literature.


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1. Introduction

Fixtures orient and stabilize a workpiece during machining processes such as

turning, drilling, and milling. A typical fixture contains a base plate, locators, and

clamps. The goal of a fixture is to provide the constrained workpiece with a quasiequilibrium environment throughout an entire machining operation which includes setup

and material removal. In the aerospace industry, the rotors within an aircraft engine are

axisymmetrical and are made of titanium or nickel alloys. The industry is heavily

dependent on machining processes to make these products because these products have

very tight tolerances and unique features which impose great challenges upon the

fixture-workpiece environment. In this study, a Ti-6Al-4V disk is chosen as the

workpiece to represent an aircraft engine rotor. A Numerically Controlled (NC) Vertical

Turning Lathe (VTL) process is chosen as the machining process.

1.1 Objectives

There are three objectives in this study. First, determine a specific set of machining

parameters and the corresponding cutting forces to best represent a machining process in

the industry. Second, develop a finite element model for fixture-workpiece system in a

VTL process to calculate the amount of deflections within the disk. Third, perform

Design of Experiments which determines the appropriate fixture layout and clamping

force to achieve the minimum tolerable amount of deflections within the disk.

1.2 Background and Significance

The rigidity provided by a fixture is vital to maintain dimensional accuracy and

surface finish quality in a machining process[Wilson1, 1]. During a machining process,

the cutting forces generated by the cutting tool induce a deflection within the

constrainted workpiece as the cutting tool enters and exits the cutting surface. The

machining dimensional accuracy may be jeopardized by the deflection within the

workpiece. A properly designed fixture is able to minimize the deflections within the

workpiece. It can also provide the control of vibration during a machining process to

ensure the desired surface finish is achieved.


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Titanium alloys are considered to be difficult-to-machine metals in the industry. The

low thermal conductivity, low elastic modulus, high temperature strength, and high

chemical reactivity of titanium alloys induce many challenges in machining processes

[Ezugwa2, 2]. The success in machining titanium alloys depends largely on overcoming

of the principal problems associated with the inherent material properties [Ezugwa, 2].

One critical solution is a rigid support of the workpiece as suggested by [Ezugwa, 2],

[Polmer3, 3] and [Donachie

4, 4] to minimize the deflection of the workpiece and

resultant in reducing machining errors such as dimensional tolerance control and chatter.

Therefore, this study will focus on the proper support from the fixture to ensure the

workpiece is held rigidly during a turning process.

1.3 Literature ReviewA literature search is performed to understand the fixture-workpiece systems. Much

research has been done regarding fixture-workpiece systems. These studies give a great

insight into various fixturing schemes. However, these studies lack the focus on the

turning process. Development of fixture design for sheet metal and composite products

is completely based on CAD models by [Walczyk5, 5]. This method eliminates the need

for datum surfaces and registration features on the CNC machine table. This method

makes fixture fabrication easy and inexpensive while maintaining high geometrical

accuracy [Walczyk, 5]. To enhance the rigidity of the fixture, [Walczyk6, 6] uses a

computer-controlled reconfigurable fixturing device (RFD) concept which is based on a

matrix of individually stoppable pins lowered by a single rigid platen. The fixture is used

in machining process such as drilling, routing, and deburring. [Deng7, 7] focuses on

fixturing stability during a milling process by examining loss of contact and gross

sliding.

There are several studies illustrated the optimization of fixture layout and clamping

forces in a milling process by using the genetic algorithm (GA). The optimization

focuses on minimize the dimensional machining errors induced by elastic deflections of

workpiece within machining processes. [Krishnakumar8,9, 8,9], [Kaya

10,10] and

[Chen11

,11] have extensive discussions on implementations of GA. In addition, fixture

layout optimization can be determined by a min-max loading criteria [DeMeter12

, 12].


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2. Machining Set-up

2.1 Vertical Turning Lathe (VTL) process

2.1.1 Machine Axis

A vertical turning lathe also known as vertical-boring machine uses a vertical axis to

enhance the support for a large diameter workpiece [Boothroyd13

, 13]. It enables an easy

access to load the workpiece onto the horizontal worktable also called machine table.

Figure 2.1 shows a generic schematic of a vertical-boring machine. The bed is the

bottom support of the overall machine weight and motion. The machine rotates the

worktable, fixture, and workpiece about the z-axis in a counterclockwise direction. The

tool travels in the negative x-axis for facing the top surface of the workpiece, and in the

negative z-axis for turning inner or outer diameter of workpiece [Boothroyd, 13].

Figure 2.1: Facing on a vertical boring machine [Boothroyd, 13]

In the industry, vertical lathe machines are controlled by a Numerically Control

(NC) unit as shown in Figure 2.2. The NC unit stores NC programs which contain all the

machining parameters and geometry of the workpiece in G&M machining codes. The

NC programs govern all motions such as machine table rotation and tool travel to

complete an entire machining cycle automatically and come to a stop. Multiple cuts can

be combined into one NC program to generate multiple features within a workpiece.


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Figure 2.2: Amera Seiki Vertical Turning VT2000 Machine

2.1.2 Machine Table

The fixture usually sits on top of the machine table and connects the workpiece onto

the machine table. The fixture is locked onto the machine table by clamping through the

radial T slots of the machine table as shown on Figure 2.3. Ideally, there should be a

minimum amount of gap between the fixture and machine table to have the maximum

amount of rigidity and support from the machine onto the fixture.

Machine Table/

Worktable

Numerically

Controlled

Unit

Tool Head


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Fixture

Radial T Slot

MachineTable

Clamp

Figure 2.3: A fixture is being clamped onto a vertical-boring machine table through a Radial T Slot

[Boothroyd, 13].

2.2 Description of Workpiece

2.2.1 Geometry of the Disk

The geometry of the workpiece is a symmetric disk. The dimensions of the disk

are 0.508m, 0.456m, 0.0254m, and 0.0508m as outer diameter, inner diameter, radial

thickness, and height, respectively.

2.2.2 Material Properties of Ti-6Al-4V

The material of the disk is chosen to be Titanium Ti-6Al-4V. The material

properties of both annealed and solution treated and aged (STA) conditions of Ti-6Al-

4V are shown in Table 2.1. The STA condition has higher tensile and yield strength, and

hardness. The maximum operating temperature is approximately 400o

C [Donachie, 4].

Ti-6Al-4V alloys are light weight metals with excellent material properties such as high

strength-to-weight ratio at elevated temperatures, excellent creep strength, corrosion-

resistant, good thermal stability, heat treatable, good forge-ability, and good fabric-

ability. These material properties offer the performance required by the aerospace

industry which holds the 50% of overall usage of titanium alloys [Donachie, 4]. Engine

manufacturers use titanium alloys to make most of the front section of the engine. Most

of the titanium products within the engine manufacturing industries are produced by


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turning and milling processes. Both turning and milling offer the best tolerance

requirements at the most economical cost.

Material ConditionTensile

Strength

Yield

Strength

Ultimate

Shear

Strength

Elongation

Modulus

of

Elasticity

Tension

HardnessPoisson

Ratio

MPa MPa MPa % GPa Hv

Ti-6Al-

4VAnnealed 900-993 830-924 529 14 110 310-350 0.34

Ti-6Al-4V

solution treatedand aged

1172 1103 676 10 - 350-400 0.34

Table 2.1: Material Properties of Ti-6Al-4V. [Donachie, 4]

2.2.3 Machinability

Titanium Ti-6Al-4V alloys have machinability rating of 18 and 22 for annealed(A)

and solution treated and aged (STA) conditions, respectively, as stated in Table 2.2

[Donachie, 4]. The rating is based on 100 for B1112 steel material which is assumed to

have the best machining conditions by having the lowest production costs. Ti-6Al-4V

alloys have two ratings due to the different material properties are produced by two

different alloying conditions. The different material properties between annealed and

solution treated and aged conditions of a Ti-6Al-4V bar are shown in Table 2.3

[Machado14, 14]. The solution treated and aged alloys have higher mechanical properties

than the annealed alloys especially the hardness. This contributes to the difference for

the machinability ratings among Ti-6Al-4V alloys.

AlloyCondition

(a)

Machinability

rating (b)

B1112 resulfurized steel HR 100

1020 carbon steel CD 70

302 stainless steel A 35

Ti-6Al-4V A 22

Ti-6Al-4V STA 18

(a): HR=hot rolled, CD=cold drawn, A=annealed, and STA=solution treated

and aged

(b): Based on a rating of 100 for B1112 steel

Table 2.2: Machinability comparisons of Ti-6Al-4V with several steel materials. [Doanchie, 4]


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In addition, the material properties are very different between Ti-6Al-4V alloys and

steel as stated in Table 2.3. Ti-6Al-4V alloys are stronger and have double the amount of

hardness. Ti-6Al-4V has very low thermal conductivity, whereas, steel has very good

thermal conductivity which enables the ability to dissipate heat generated by machining.

The cutting tool life is much higher for machining steel than titanium alloys. Therefore,

steel is able to achieve a very good machinability rating.

Material

Tensile

Strength

Yield

StrengthElongation

Reduction

Area

Modulusof

Elasticity

Tension

Hardness Density

Specificheat at

20-

100oC

Thermal

Conductivity

MPa MPa % % GPa Hv g/cm3 J/kg K W/m K

Ti-6Al-

4V

annealedbar

895 825 10 20 110 340 4.43 580 7.3

Ti-6Al-4V

solution

treated

and aged

bar

1035 965 8 20 - 360 - - 7.5

AISI-1045

cold

drawn

625 530 12 35 207 179 7.84 486 50.7

Table 2.3: Properties of Ti-6Al-4V compared to a medium carbon steel. [Machado, 14]

The two major characteristics of titanium alloys are low thermal conductivity and

low elastic modulus that induce many challenges during machining processes. Table 2.3states that the thermal conductivity for Ti-6Al-4V alloys is less than steel by

approximately seven times. The modulus of elasticity for Ti-6Al-4V is half the amount

for steel. Under normal conditions, the cutting forces may be predicted to be only

slightly higher than those required for steels of the equivalent hardness [Polmear, 3]. In

real practice, the cutting forces in machining Ti-6Al-4V are increased by factor of

several times due to the fracture of the cutting edge in the cutting tools [Polmear, 3]. The

cutting tools tend to fracture due to the high temperature which is generated at a small

contact surface area between chip and tool [Polmear, 3]. This high temperature is caused

by low thermal dissipation of heat within titanium because of the low thermal

conductivity.

In addition, the increased magnitudes of the cutting forces can easily deflect the

workpiece because titanium has low elastic modulus which makes titanium very


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sensitive to external forces [Polmear, 3]. The deflections within the workpiece cause

machining errors such as poor surface finishes, chatter problems, and reduced

dimensional tolerances. Therefore, the machinability rating is very low for titanium

alloys.

2.3 Description of fixture

The term workholder embraces all devices that hold, grip, or chuck a workpiece in a

prescribed manner of firmness and location within a manufacturing operation [Wilson15

,

15]. During a material removal process, the workholder is identified as a machining

fixture or simply called fixture in this study. The specific functions of a fixture within a

machining process are discussed within this section. A fixture must support a workpiece

in a precise location and orientation while the workpiece is subjected to the cutting

forces during material removal. The physical characteristics of a workpiece such as

material properties, size, shape, and weight govern the overall structural integrity of a

fixture. A fixture must be able to provide tool path clearance to enable tool access into

the machining surfaces. A fixture should allow access in loading and unloading of the

workpiece efficiently. This is very critical for a high production volume environment.

The fixture provides the safety to all users by containing all components from being

dislocated during a machining process. In additional, the costs of a fixture should be

economical.

There are many generic fixtures available for purchase in the industry. The chucks,

pump-jigs, vises, and V-blocks are common examples. Chucks are heavily used in

horizontal and vertical turning process for round shaped workpieces. Due to the specific

machining parameters and specific physical properties of the chosen workpiece, a chuck

is not adequate to be used in this study. The commonly used material properties of

fixture components are hardened steel with Youngs Modulus of 201 GPa and Poisson

Ratio of 0.296.

The two methods of designing a machining fixture are cut-and-try and analytical

approach [Wilson, 15]. The cut-and-try method involves building a fixture and trying out

the proposed machining operation. The analytical approach involves determining the

magnitudes and directions of the cutting forces, and then following a step-by-step


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determination of designing a fixture can withstand the cutting forces. The analytical

approach is not widely used in the industry due to the extensive time required. The

analytical approach might not be practical because the calculation results might require

having fasteners of different diameter at each attachment point to match the anticipated

load [Wilson, 15]. This creates difficulties for installation and maintenance. Tool

designers usually apply the analytical approach mentally without any mathematical

computations [Wilson, 15]. However, the analytical approach must always predominate

to ensure proper structural integrity of a fixture [Wilson, 15]. This study will use

analytical approach to determine the best fixture scheme for the chosen machining

parameters.

2.3.1 Plate

A plate of a fixture is being clamped onto the VTL machine table through the radial

T slots as shown in Figure 2.4. It orients and holds both the locators and clamps in

proper locations. It contains the most weight and has the highest strength among the

fixture components. The bottom surface of the plate usually has very fine flatness

requirement to reduce the possibility of gaps between fixture and machine table. This

surface can be maintained within flatness requirement by grinding process. In this study,

a plate is chosen because of the good contact surfaces between the fixture and machine

table. A fixture can easily be removed from the machine table by unclamping the bolt

and nut from the T slots within the plate. This type of fixture will enable the flexibility

of using multiple fixtures in the same machine. The geometry of a plate is governed by

the machine table size and location of the radial T slots, the size and location of locators

and clamps, and the physical size of workpiece. The thickness of the plate is suggested

to be at least 10cm.


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Clamp

Plate

Locator

Radial

T-Slot

Ti-6Al-4V

Disk

Figure 2.4: Fixture-disk assembly includes plate, locator and clamp.

2.3.2 Locators

There are six requirements for choosing the locating points within a fixture

[Doyle16

, 16]. Each point of contact between the locators of a fixture and workpiece

should eliminate one degree of freedom up to six points for total of six degree of

freedom. This will determine the proper placement of locating points. The conditions of

the locating surface should be considered. A finished surface of a workpiece may be

acceptable to have a full 360o

locating surface as shown in Figure 2.4. When the surface

of a workpiece is a non-finished surface, more than three points in a plane do not

improve locating purposes, but may promote stability and give extra support [Doyle, 16].

The shape of a workpiece affects both the shape and location of locators. The location of

the machining surface governs the locating points within a fixture. The locating supports

should be as close to the machining surface as possible for maximum support.

When a workpiece is positively located by means of six pins which collectively

restrict the workpiece in six degrees of freedom, this is known as the 3-2-1 method of

location [Wilson, 15]. The method is to place and hold a workpiece against three pointsin a base plane, two points are in a vertical plane, and one point is in a plane

perpendicular to the other two planes as shown in Figure 2.5. This method works very

well for a rectangular shaped workpiece.


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Figure 2.5: The 3-2-1 principle of location applied to a rectangular shape workpiece. [Doyle, 16]

2.3.3 Clamps

The purpose of clamping is to firmly hold a workpiece against the locating points or

surfaces and to secure a workpiece against all cutting forces[Doyle, 16]. A clamp must

direct and maintain a force onto the workpiece. There are four main considerations of

choosing clamps [Doyle, 16]. The size of the clamping force is affected by the type and

positions of the locators, the availability of clamping surfaces, the conditions of

clamping surfaces, and the directions and magnitude of cutting forces. The clamping

forces applied against the workpiece must counteract the cutting forces [Wilson, 15].The clamping pressure should not be large enough to change the dimension of a

workpiee. The source and size of the force which is available for actuating the clamp

will determine the type and size of a clamp. In the industry, the clamps as shown in

Figure 2.6 can be tightened manually using a torque wrench. These clamps are widely

available for purchase. The economy of clamping involves a choice of best clamping in

terms of the advantages of a complicated and quick acting device for a high production

volume environment as compared to a simpler and slower device for low production

volume environment [Doyle, 16].


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Figure 2.6: Commercially available fixture clamps. [Wilson, 15]


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3. Machining of Titanium (Ti-6Al-4V) Disk

3.1 Machining Conditions

Titanium alloys are well known for the very low machinability due to the specific

material properties. The material properties of titanium alloys are high temperature

strength, very low thermal conductivity, relatively low modulus of elasticity and high

chemical reactivity. These material properties induce high cutting temperature and high

stresses at the cutting edge during the machining processes [Ezugwu, 2]. Therefore,

machining titanium alloys requires very unique machining parameters. There are six

main guidelines provided by [Donachie, 4] for machining titanium alloys. Titanium

alloys are very sensitive to the heat generated by cutting tools because titanium has low

heat conductivity. This will create a tremendous amount of heat during machining. Thisheat causes a significant temperature buildup within the contact surface between the

workpiece and cutting tool. Thus, a low cutting speed is highly recommended. A

sufficient amount of cutting fluid should be applied during machining. The cutting fluid

reduces the amount of heat which enters into both the cutting tool and workpiece. In

addition, the geometry of the cutting tool is very critical in terms of heat dissipation

during machining. Thus, the cutting tool should have a sharp cutting edge. In ideal

conditions, the cutting edge of the tool is constant and has no tool wear. Tool wear

would result in built-up edge for turning titanium alloys. The built-up edge causes poor

surface finishes, and increases the magnitudes of the cutting forces. The increased

cutting forces can cause deflection within the workpiece. In this study, the cutting tool is

assumed to be in good condition and no built-up edge. In addition, the feed rate will be

continuous and steady state. There is no rapid stopping during the entire machining

process.

3.2 Cutting Tool Properties3.2.1 Cutting Tool Material

The turning of titanium alloys requires unique cutting tool properties. There are five

specific requirements suggested by [Ezugwu, 2]. First, the cutting tool should have high

hardness to resist the high stresses developed during machining. Second, the cutting tool


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should have good thermal conductivity to minimize thermal gradients and thermal

shock. Third, the cutting tool should have good chemical inertness to depress the

tendency to react with titanium. Fourth, the cutting tool should have toughness and

fatigue resistance to withstand the chip segmentation process. Fifth, the cutting tool

should have high compressive, tensile, and shear strength. Based on previous studies, the

straight tungsten carbide-cobalt (WC/Co) is the best suitable tool materials for

machining titanium alloys as suggested by [Ezugwu, 2] and [Donachie, 4]. The C-2 also

known as ISO K20 is the best carbide grade which is low cost and is widely used in the

industry. The material properties of the cutting tool are stated in Table 3.1. The straight

tungsten carbide-cobalt alloys have excellent resistance to simple abrasive wear. For

example, the aerospace industry intensively uses straight carbide tools for machining

titanium engine and airframe products. Thus, the C-2 grade is chosen for this study.

Nominal

compositionGrain

size Hardness Density

Transverse

strength

Compressive

strength

Modulusof

elasticity

Relativeabrasion

resistance

Coefficient of

thermalexpansion at

200 C

Thermal

conductivit

Hv g/cm3 MPa MPa GPa m/m K W/m K

94WC-6Co Medium 91.7-92.2 15 2000 5450 648 58 4.3 100

Table 3.1: Material properties of WC/Co C2 grade cutting tool. [Santhanam17, 17]

3.2.2 Cutting Tool Geometry

A single-point tool is chosen for this study because it is commonly used in turning

processes. A single-point tool is shown in Figure 3.1 which has one major cutting edge

which comes in contact with the chip. It has one shank. In industry, an insert is

assembled onto a single-point tool and provides the major cutting edge for the single-

point tool. The insert can be replaced once a single cut is completed. This method

maintains the sharpness requirement of the cutting edge for all cuts. The replacement of

an insert has lower cost than the replacement of a single point tool. An insert can also

provide index-able cutting edges. This means that an insert can be rotated and to provide

new cutting edges for multiple cuts.


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Figure 3.1: Geometry of single-point cutting tool. [Altintas, 18]

The actual tool geometry is tabulated in Table 3.2 based on given values from

[Donachie, 4]. The most important feature is the nose radius which is given to be 0.762

mm in this study. The nose radius is suggested by [Donachie, 4] to be used for finishing

cuts. The nose radius is assumed to be constant because no built-up edge cutting

condition is assumed. Additional care must be implemented to ensure the tool life to be

maintained. A large range in size of the cutting tool nose radius is being used in the

industry to machine various engineering materials. The cutting tool nose radius affects

the amount of cutting forces exerted onto the workpiece. The temperature at the contact

area between the workpiece and cutting tool is highly dependent on the nose radius. A

large nose radius has a large surface area to dissipate heat. Whereas, a small nose radius

is able to reduce the amount of cutting forces acting onto the workpiece. However, the

amount of heat generated would be significant, thus, the tool life would be drastically

reduced. This is the main reason that industry uses a large nose radius tool for titanium

alloys due to the low heat specific coefficient within the materials.

Table 3.2 contains tool feature symbols which are used in calculation of cutting

forces. These tool feature symbols are taken from [Altintas18

, 18]. A graphic

representation of the tool feature symbols are shown in Figure 3.1. The cutting tool has

back rake angle, p , and side rake angle, f , of zero degree and five degrees,

respectively, which are suggested by [Donachie, 4] for finishing cut. A positive side


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rake angle will minimize the cutting forces. This may considered to be an optimal

machining condition.

Tool Feature symbols Tool Feature Names Actual Tool

p Back rake angle 0

f Side rake angle 5o

clp End relief angle 5o

End clearance angle

clf Side relief angle 5o

Side clearance angle

kr End cutting-edge angle15

o

r Side cutting-edge angle15

o

R Nose radius 0.762 mm

Table 3.2: Actual dimensions of cutting tool. [Donachie, 4]

3.3 Machining Parameters

The machining parameters are critical input parameters for this study. They are

chosen to best represent an actual turning process. It is impossible to utilize the actual

machining parameters from industry due to most companies guarding their specific

machining parameters as Intellectual Properties. However, the chosen machining

parameters which are gathered from published information are considered to be a

generic representation of an actual machining process. [Donachie, 4] has defined the

typical parameters for machining gas turbine components which are made of Ti-6Al-4V

alloys. The three major machining parameters are feed rate, cutting speed, and depth of

cut. For a turning operation, there are three types of cuts which are defined as rough,

semi-finish and finish cut. Each type of cut has individual unique machining parameters.

A specific set of machining parameter is chosen for this chapter and summarize in Table

3.3.


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Cutting Speed, v Feed Rate, h Depth of Cut, b

m/min mm/rev mm

0.127

0.254

0.3810.508

60 0.178

0.635

Table 3.3: Cutting speed, feed rate, and depth of cut for chapter 3

3.3.1 Feed Rate, h

The feed rate, h, is defined as the uncut chip thickness per revolution of workpiece

rotation during a turning process. This study uses the feed rate, h, of 0.127 mm/rev

within this chapter. This is an average value which represents the generic machining

parameters from [Donachie, 4] for a typical finishing cut of aerospace type of Ti-6Al-4V

alloys. The direction of feed rate is in the negative z-axis which is shown in Figure 3.2.

3.3.2 Depth of Cut, b

The range of depth of cut, b, is determined to be from 0.127mm to 0.635mm as

shown in Table 3.3. The depth of cut is smaller than the cutting tool corner radius which

is 0.762mm. The main reason is that semi-orthogonal cutting mechanics may be applied

[Altintas, 18]. This will simplify calculations. Therefore, orthogonal calculations will be

used for verification purposes. In real machining processes within industries such as

automotive and aerospace, the values of the depth of cut are extensively different. It is

largely dependent on the material properties of the workpiece, cutting tool geometry and

production volume requirement. Figure 3.2 illustrates the depth of cut which pertains to

the outer diameter of the workpiece. This means that each cut reduces the outer diameter

of the workpiece, thus, the thickness of the workpiece is being reduced.


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Figure 3.2: Depth of cut, b, and Feed Direction, Vf, for an outer diameter cut.

3.3.3 Cutting Speed, v

The cutting speed, v, for this study is assumed to be 60m/min which is given by

[Donachie, 4]. The previous study by [Gente19

, 19] shows that the cutting speed does not

affect the magnitudes of cutting forces obtained from turning Ti-6Al-4V alloys. In

addition, [Altintas, 18] illustrated that there is no significant change to the magnitude of

cutting forces when the cutting speed changes from 4.61m/min to 47.3m/min in

orthogonal cutting. Thus, this study will not examine the effects of the cutting speed

upon the magnitudes of the cutting forces, although this would be a good topic for future

studies. This study will focus on the impact of the depth of cut upon the magnitude of

cutting forces in this chapter.

3.3.4 Orthogonal and Oblique Cutting

Orthogonal cutting is defined as the cutting edge of the cutting tool is perpendicular

to the machined surface. Orthogonal cutting generates two-components cutting forces

such as tangential and feed force. The oblique cutting defined as the cutting edge of

cutting tool known as rake face and machine surface in an angle known as oblique angle,


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i . Oblique cutting generates the third-component cutting force known as radial force.

The magnitudes of cutting forces are higher for oblique than orthogonal cutting. Figure

3.3 shows the geometries of both orthogonal and oblique cutting.

Orthogonal Cutting

Geometry

Oblique Cutting

Geometry

Figure 3.3: Geometries of orthogonal and oblique cutting processes [Altintas, 18].

3.4 Cutting Forces

3.4.1 Orientations

A finishing cut of the outer diameter of the workpiece will be examined in this

chapter. Figure 3.4 illustrates the workpiece, cutting tool, cutting forces and feed

direction of the cutting tool. The workpiece is a Ti-6Al-4V alloy disk. It has outer

diameter of 0.508 m and radial thickness of 0.0254 m. The grade C-2 carbide insert has

0.762 mm nose radius and is part of a single point tool. The cutting tool travels in the

feed direction, Vf, which is parallel to vertical z-axis as shown in Figure 3.5. This

generates a feed force onto the workpiece, Ff which is acting vertically down onto the

workpiece from the cutting tool nose radius. The workpiece rotation, V, rotates about the

vertical z-axis in the counterclockwise direction. This generates a tangential force onto


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workpiece, Ft which is tangent to the outer diameter of the workpiece and is in the

negative y-axis direction as shown in Figure 3.5. In oblique cutting, the radial force onto

the workpiece, Fr, is in the negative x-axis or radial direction of workpiece. All cutting

forces Ft, Ff, and Fract onto the workpiece at the point of contact with the nose radius of

the cutting tool. The tangential Force, Ft, is the primary cutting force and has the

maximum magnitude. The radial force, Fr, has the smallest magnitude and has zero

magnitude in orthogonal cutting.

Figure 3.4: Schematic diagram of the lathe turning process of an outer diameter cut with workpiece

rotation V, feed direction Vf, tangential force, Ft, feed force, Ff, and radial force Fr.

Figure 3.5: Cutting forces (tangential force, Ft, feed force, Ff, and radial force Fr ) acting on

workpiece and feed direction, Vf, of cutting tool.


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3.4.2 Assumptions

The shear yield stress, s , of Ti-6Al-4V is assumed to be 613 MPa. The average

edge force coefficients, teK and feK represent the rubbing forces per unit width [Altintas,

18]. The coefficients, teK and feK , are 24 N/mm and 43 N/mm, respectively. All three

assumptions are based the empirical data collected by [Altintas, 18] on orthogonal

cutting experiment machining Ti-6Al-4V alloy.

3.4.3 Calculation Procedure

In this study, the calculation of the cutting forces the equations and assumptions

which are given by Manufacturing Automation by [Altintas, 18]. The flow diagram of

the calculation of the cutting forces is shown in Figure 3.6 which gives the overview ofthe calculation procedure of the cutting forces. The input variables are the tool

geometries and machining parameters which are determined to best represent the

machining processes in the industry. The normal shear angle is calculated based on the

chip compression ratio is determined to 1.2 and the friction angle is 20.5o. Then, the

cutting constants are calculated using the formulas gathered from [Altintas, 18]. The

cutting forces are calculated using Matlab Codes which are included in the Appendix.


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Figure 3.6: Flow diagram of cutting forces calculations.

3.4.4 Oblique angle, i , and Chip flow angle,

The oblique angle is calculated to be 1.3o for oblique cutting. The oblique angle is

zero degree for orthogonal cutting because the orthogonal cutting defines the cutting

edge of the tool is perpendicular to the machined surface. The oblique angle is calculated

using equation 3.1 which is given by [Altintas, 18]. The oblique angle depends on the

cutting tool properties such as side rake angle, f , back rake angle, p , and side cutting-

edge angle, r are summarized in Table 3.4. Figure 3.7 shows the graphical

representation of the angles.

rfrpi sintancostantan += 3.1

Where

i - oblique angle

p - cutting tool back rake angle

r - cutting tool side cutting-edge angle

Tool

Geometries

Machining

Parameters

Input

Variables

Normal Shear

Angle

Cutting

Constants

Cutting Forces

Formulas

Cutting Forces

(Fr, Ft, Ff)

Formulas and

assumptions from

literatures

Chip

Compression

Ratio=1.2

(Oblique

Cutting)

Friction Angle =

20.5 degree

Normal rake

angle

Matlab Codes


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f - cutting tool side rake angle

Oblique CuttingOrthogonal

CuttingAngles

Degree Radian Degree Radian

f cutting tool side rake angle 5.0 0.087 5.0 0.087

p cutting tool back rake angle 0.0 0.000 0.0 0.000

r cutting tool side cutting-edge angle 15.0 0.262 15.0 0.262

i oblique angle 1.3 0.023 0.0 0.000

chip flow angle 1.3 0.023 0.0 0.000

n normal rake angle 4.8 0.084 4.8 0.084

a friction angle 20.5 0.358 20.5 0.358

n normal friction angle 20.5 0.358 20.5 0.358

n normal shear angle 53.1 0.9261 37.2 0.649

Table 3.4: Cutting angles for oblique and orthogonal cutting angles.

i

n

n

Tool

Cut Surface

Rake face

X

Y

Z

b

h Workpiece

Figure 3.7: Geometry of oblique cutting process. [Altintas, 18]

3.4.5 Normal rake angle, n

The orthogonal rake angle, 0 ,is 4.8o, which is determined by cutting tool properties

such as side rake angle, f , back rake angle, p , and side cutting-edge angle, r using

equation 3.2. The orthogonal rake angle is input into equation 3.3 to calculate the normal

rake angle for both orthogonal and oblique cutting. The oblique angles, 1.3o

and 0o, for

oblique and orthogonal cutting, respectively, are used to determine the normal rake


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angles. Since the difference between the two oblique angles for oblique and orthogonal

cutting is so small, the values of normal rake angle are 4.8o.

rprf sintancostantan 0 += 3.2

Where 0 - orthogonal rake angle

in costantan 0 = 3.3

Where n - normal rake angle

3.4.6 Friction angle, a , and Normal friction angle, n

The equation to calculate the frictional angle a

was determined by using the

empirical data collected by [Altintas, 18] on an orthogonal cutting experiment. The

experiment was performed on Ti-6Al-4V alloys with different cutting tool rake angles at

different feed rates and cutting speeds with the material of cutting tool of tungsten

carbide. A force dynamometer was used to measure the cutting forces. The equation 3.4

was generated from the data collected from this experiment to determine the friction

angle, a

for orthogonal cutting. The calculated frictional angle, a

, is 20.5o

for

orthogonal cutting. The normal friction angle, n

, is 20.5o

which is calculated using the

equation 3.5. The normal friction angle is same for both of orthogonal and oblique

cutting because the difference between the oblique angles for both cutting conditions is

negligible.

na 29.01.19 +=o 3.4

( )ian costantan1 = 3.5

3.4.7 Chip compression ratio, rc, and Normal shear angle, n

The chip compression ratio, rc, is defined as the ratio of uncut chip thickness, also

known as feed rate, over actual chip thickness [Altintas, 18]. The chip compression ratio

affects the values of normal shear angle, n as indicated in equation 3.6. The value of

the normal shear angle affects the values of the cutting constants, Ktc, Kfc, and Krc, which

will affect the values of cutting forces and will be defined in later section in this study.


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The flow diagram in Figure 3.6 shows the connections among these parameters. A large

chip compression ratio will produce a large shear angle. A large shear angle will increase

the values of cutting constants. Therefore, the cutting forces will be at the maximum

level. This will require the fixture to have the most rigid support for the workpiece.

=

nc

ncn

r

r

sin1

costan 1

3.6

Where

n - normal shear angle

cr - chip compression ratio

Both [Gente, 19] and [Cotterell20

, 20], stated there are two methods to calculate

the normal shear angle. One method is that the shear angle can be calculated by using the

chip compression ratio. This method assumes that the chip is a steady-state continuous

chip. As for machining titanium, the chip is segmented. Other method is that the normal

shear angle is obtained from the actual measurements of the longitudinal cross section of

the segmented chips as indicated by [Gente,19] and [Cotterell, 20] experiments. In their

experiments, both authors concluded the calculated and measured normal shear angles

are correlated well. Therefore, the calculated normal shear angles will be used for both

oblique and orthogonal cutting in this study.

The most important variable in calculating the normal shear angles is the chip

compression ratio. The measurement data of the actual chip thickness from previous

studies by [Li21

, 21] and [Cotterell, 20] gives a good indication of actual chip

compression ratios. Unfortunately, these studies did not use the same machining

parameters as stated in this study. Therefore, a range of values from 0.8 to 1.5 is chosen

to determine the best representative value of the chip compression ratio. The chosen

minimum value of 0.8 is smaller than the chip compression ratio of one which was

chosen by [Altintas, 18]. [Altintas, 18] stated that if the depth of cut is less than noseradius of cutting tool, the chip thickness is constant and equal to feed rate. This

assumption is valid for a continuous chip condition.

However, the titanium alloys usually produce segmented chips. Both [Li, 21] and

[Cotterell, 20] considered the effects of segmented chips during machining of titanium

alloys. The chosen maximum value of 1.5 is the calculated average value from the


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experiments performed by [Li, 21] and [Cotterell, 20]. In addition, [Cotterell, 20]

conducted orthogonal cutting tests on a flat Ti-6Al-4V disk using feed rate of 0.1mm/rev

and measured the local normal shear angles. The chip compression ratio was calculated

to be 1.38 by using the measured shear angle of 37.5o

at cutting speed of 60m/min. [Li,

21] conducted oblique baseline cutting tests on a titanium workpiece using two feed

rates of 0.254 and 0.381 mm/rev at 1.02 mm depth of cut. [Li, 21] measured the actual

deformed chip thicknesses. At cutting speed of 60 m/min, the calculated chip

compression ratios are 1.5 and 1.7 at 0.254 and 0.381 mm/rev, respectively.

The normal shear angle is calculated using the range of chip compression ratios

from 0.8 to 1.5 and the normal rake angle of 4.8o. The normal shear angle is plotted as a

function of the chip compression ratios is shown in Figure 3.8 which shows that the

correlation between the normal shear angle and the chip compression ratio is linear. The

normal shear angle increases from 40o

to 60o

as the chip compression ratio increases

from 0.8 to 1.5.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Chip Compression Ratio

NormalShearAngle,

degree

Figure 3.8: The normal Shear angle is determined by the range of chip compression ratio values

from 0.8 to 1.5 and the normal rake angle of 4.8o for oblique cutting.


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In this study, the chip compression ratio is chosen to be 1.2 and the normal shear

angle, n , is 53.1o

for oblique cutting. The main reason is that the chip compression ratio

should be close to the maximum level because a large value of the normal shear angle,

n , is expected. A large shear angle is able to produce the large value of the cutting

forces. These cutting forces require the fixture to provide the maximum amount of

support to workpiece. Thus, a rigid setup will be needed for this machining process.

For comparisons and verifications purposes, the normal shear angle, cn, , is 37.2o for

orthogonal cutting. This calculation is based on Merchants Minimum Energy Principle

in equation 3.7 by [Altintas, 18]. The normal shear angle corresponds to the

determination by [Gente, 19]. In addition, the measured shear angle is 37.5o in the

experiment conducted by [Cotterell, 20] for orthogonal cutting of Ti-6Al-4V with feedrate of 0.1mm/rev.

=

24,

na

cn

3.7

3.4.8 Cutting Constants

The cutting constants, Ktc, Kfc, and Krc, for tangential, feed, and radial forces,

respectively, are calculated by equation 3.8 to 3.10. The values of the cutting constants

are stated in Table 3.5 for both oblique and orthogonal cutting. Both Ktc and Kfc have

lower values for orthogonal than oblique cutting. The main reason is the different values

of the normal shear angle, n , which is 53.1o

and 37.2o

for oblique and orthogonal

cutting, respectively. The cutting constants are dependent on the values of the normal

shear angle, n . Therefore, the oblique cutting constants have higher values of cutting

constants than orthogonal cutting. In addition, the cutting constant, Krc, is zero for

orthogonal cutting due to both oblique angle and chip flow angle is zero.

( )( ) nnnn

nnn

n

stc

iK

222 sintancos

sintantancos

sin ++

+= 3.8

( )

( )nnnn

nn

n

sfc

iK

222 sintancos

sin

sinsin ++

= 3.9


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28

( )

( ) nnnn

nnn

n

src

iK

222 sintancos

sintantancos

sin ++

= 3.10

Oblique Orthogonal

Constants MPa MPa

Ktc 2035.5 1617.3

Kfc 570.9 453.7

Krc 29.3 0

Table 3.5: Cutting Constants for both Oblique and Orthogonal Cutting.

3.4.9 Cutting Forces Formulas

The cutting forces formulas are stated in equation 3.11 to 3.13 which are given by

[Altintas, 18]. Both the tangential and feed forces are calculated using published value of

the average edge force coefficients, Kte and Kfe. The machining parameters of the depth

of cut, b, and feed rate, h, are given at Table 3.3 as input variables. As previously

discussed, the values of the cutting constants, Ktc, Kfc, and Krc are higher for oblique

than orthogonal cutting. Thus, the values of the cutting forces are expected to be higher

for oblique than orthogonal cutting as shown in Figure 3.9.

bKbhKFtetct

+= 3.11

bKbhKF fefcf += 3.12

bhKF rcr = 3.13

Where

tF- tangential force

fF - feed force

rF - radial force

b - depth of cut

h - feed rate = uncut chip thickness

teK - average edge force coefficient = 24 N/mm

feK - average edge force coefficient = 43 N/mm


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Cutting Forces using Feedrate=0.178mm/rev or 0.007 in/rev

0.0

50.0

100.0

150.0

200.0

250.0

300.0

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700

Depth of cut (mm)

CuttingForces(N)

Ft, Tangential Ff, feed Fr, radial Ft. Tangential_Orthogonal Ff, feed_Orthogonal

Figure 3.9: Cutting forces results for both oblique and orthogonal cutting.

3.4.10 Matlab Code Calculations

A Matlab code was generated to perform the calculations of the cutting forces by

utilizing the previously stated formulas and assumptions. The values of the input

variables are tool geometries and machining parameters which are entered into the

Matlab codes which are included in the Appendix for both oblique and orthogonal

cutting.

3.4.11 Results

The cutting forces are calculated using the chosen tool geometry properties and

machining parameters. This study will use both mechanics of orthogonal and oblique

cutting to calculate the cutting forces. As discussed previously, the procedure of

calculating cutting forces in mechanics of oblique cutting is based on the formulas and

assumptions given by Manufacturing Automation by [Altintas, 18]. The calculation

results are generated by the Matlab Code. The calculated cutting forces as a function of

depth of cut are shown in Figure 3.9. The tangential cutting force is the primary cutting


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force component. It has the highest magnitude which ranges from 50N to 245N. The

feed force ranges from 18N to 92N. This is means the feed force is less than the half of

amount of the tangential force. Moreover, the radial force component is very small; close

to zero.

The cutting forces are calculated using orthogonal cutting and used to verify the

calculated results from oblique cutting. Figure 3.9 shows that the magnitudes of

tangential and feed cutting forces are very similar between oblique and orthogonal

cutting. The main difference between orthogonal and oblique cutting is the shear angle.

The different values of shear angles result in the different magnitudes of the cutting

forces. However, it does not significantly impact the overall results. Moreover, the

orthogonal cutting does not have the radial force because the oblique angle is zero

degrees for orthogonal cutting.

3.4.12 Verifications of Calculation Results

The machining parameters from previous studies [Li, 21 and Molinar22

, 22] are used

to verify cutting forces calculations stated in Table 3.6. The Cutting forces are calculated

by inputting these given machining parameters into the Matlab code. The feed force is

closer to the longitudinal force from [Molinar, 22] than [Hoffneister, 22]. In addition, all

cutting forces are compared with the findings from [Li, 21]. Both the calculated

tangential and feed forces correspond to [Li, 21] findings. However, the calculated radial

force is much smaller.

Previous Feed

Depth of

Cut

Studies mm/rev mm Previous Studies Results Calculation Results

Molinari 0.120 10.000 Longitudinal Force =1042 N Feed Force = 1115 N

Hoffmeister 0.120 10.000 Longitudinal Force =1667 N Feed Force = 1115 N

Ft, Ff, Fr are 114-140, 51-71, and 14-

30N, respectively - FE ModelsLi 0.254 0.254

Ft, Ff, Fr are 116-130, 51-61, and 16-

33N, respectively - Experiments

Ft, F

f, F

rare 137, 47 and

2N, respectively

Table 3.6: Comparisons of the cutting forces.

In addition, there are many ways to verify the magnitude of cutting forces. The two

well known methods are finite element models and experiments. Actual experiments will


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not be used in this study, although it might be a good topic for future studies. Three

finite element models were created using Thirdwave Advantage software to determine

the cutting forces in orthogonal cutting. The models use the machining parameters and

tool properties stated in this study with three different depth of cuts, 0.127, 0.381, and

0.638mm, respectively, for individual FE model. The maximum amount of cutting force

is calculated to be 1000 N for tangential cutting force at depth of cut in 0.638mm. This

discrepancy of the magnitude of cutting force between the FE models and calculation is

caused by the fact that the machining process described in this study is not orthogonal

which was used in the FE models. Therefore, the magnitude of cutting forces is highly

dependent the chosen mechanics of cutting when both calculations and finite elements

are being used.

In this study, the calculated cutting forces are not 100% accurate. They are

approximations which are considered a good representation of a turning process of Ti-

6Al-4V in the industry. These values will be used in subsequent simulation models to

examine the deflections within the disk.


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4. Finite Element Model Analysis

4.1 Fixture-Disk Model Properties

A finite element model (FEM) is developed to represent the assembly of the fixture

and disk during the machining setup and material removal in ANSYS23 software. The

dimensions of the model are 0.254m, 0.2286m and 0.0508m; outer radius, inner radius

and height respectively. As shown in Figure 4.1, the z-axis is in the vertical direction.

The x-y axis forms a plane which the model sits on. Although the model was created in

Cartesian coordinate system, all nodes and results are rotated into ANSYS Global

Cylindrical Coordinate System known as csys1. The origin of both coordinate systems is

located at the center of the disk. To simplify the selections of the proper regions for the

clamps and locators, the model is divided into 128 equally spaced volumes as shown inFigure 4.1. The boundary conditions such as loads and constraints which represent the

clamps and locators are applied onto the top and bottom surfaces of the volumes. By

using Mapped meshing function within ANSYS, the model contains the uniform size of

hexahedral solid. The element type being used is Solid45 which represents 3D-Brick.

Table 4.1 contains the properties within the model. The large amount of elements and

nodes will enable the model to more accurately perform calculations such as deflections

and stresses. The workpiece material properties such as modulus of elasticity and

poisson ratio represent the chosen Ti-6Al-4V disk.

Figure 4.1: Disk is divided into 128 equally spaced volumes.


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Number of elements 32000

Number of Nodes 38720

Degree of Freedom per Node 3

Type of Elements 3D-Brick

Material of Workpiece Ti-6Al-4VModulus of Elasticity 110 GPa

Poisson Ratio 0.34

Table 4.1: Finite Element Model Properties.

4.2 Clamping Candidate Region

The clamping candidate region is identified within the top surface of the model and

confined within the 360 degrees Clamping/Locating Candidate Region as shown Figure

4.2. The 360 degrees Clamping/Locating Candidate is within the radius of 0.2413 m to

ensure the proper cutting tool travel path clearance is provided. Due to tool path

clearance requirement, only the inner volumes are qualified to be the candidate region

for clamping and locating surface. This method prevents the cutting tool from crashing

onto the clamps and locators. The number of clamps is identical to the number of

locators. The locations of clamps are directly above the locators. This method will

minimize the bending moments might be induced by the clamps and locators being off

location vertically. Also, it increases the possibility that the disk to be properly

constrained during the entire machining process.


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360 degreesClamping/LocatingCandidate Region

Figure 4.2: The 360 degrees Clamping/Locating Candidate Region.

4.2.1 Clamping Area

The clamping candidate region is divided into 64 areas shown in Figure 4.2. Each

clamp occupies two areas on the top surface, thus, the maximum number of clamps is

32. When 32 clamps are applied, the model is constrained in 360 degrees on the top

surface within the clamping candidate region. The dimensions of one clamp or locator

consist of 11.250o, 0.2286m, and 0.2413m; degree, inner radius and outer radius

respectively, are shown in Figure 4.3. The area, A, is calculated to be 2.92e-4 m2

which

will be used to calculate the clamping pressure per area, P. The size of each clamp is

assumed to be identical in this study. This is consistent with the actual practices in the

industry. It would be a good topic for future study to examine the effects of various sizes

of the clamps.


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A=2.92e-4 (m^2)

Figure 4.3: Dimensions of a clamp or locator, and one area.

4.2.2 Clamping Pressure

The clamping pressure per area, P, is calculated using equation 4.1. The clamping

force is divided by two because there are two areas within one clamp. The positive

normal pressure is applied against the top surface within the ANSYS model representing

the vertical downward compressive clamping pressure of an actual machining process.

The clamping pressure is distributed uniformly onto each node within the surface area.

492.2

22

==e

F

A

F

P

C

S

C

4.1

Where

P Clamping pressure per area

Fc Clamping Force

4.2.3 Initial Clamping Force

The initial clamping force is determined to 1500N. This means the initial clamping

pressure per area, P, is 2.56e6 Pa. The magnitude of clamping force was gathered from

published literature by [Krishnakumar, 8]. For simplification purpose, the 1500N is used


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in the initial fixture layout model instead of 1779N as chosen by [Krishnakumar, 8]. The

initial clamping force will be extensively used in both the investigation of deflections

within the Ti-6Al-4V disk and Design of Experiments which determines the best fixture

layout configuration in chapter 5.

4.3 Locating Candidate Region

The clamping candidate region is identified within the bottom surface of the model

and confined within the 360 degrees Clamping/Locating Candidate Region as shown

Figure 4.2. The 360 degrees Clamping/Locating Candidate is within the radius of

0.2413m to ensure the proper cutting tool travel path clearance for the same reasons as

of the clamps. This radial dimensional constraint is to prevent cutting tool from

interfering with the locators. The locating surface is assumed to be within flatness

requirements. No gap between the locators and disk is assumed in this study. The

locators can occupy the whole bottom surface in 360 degrees circumferentially. All

locators have equal size. The locators have the identical size as the clamps. Both locators

and clamps are vertically aligned. This study assumes the locators are firmly supporting

the disk in all three axes. The three axes such as x, y, z displacement constraints are

applied on the identified individual locators in the finite element model.

4.4 Assumptions

The friction is assumed to be sufficient at the contact points between the disk and all

fixture components such as clamps and locators. This frictional force is able to prevent

any relative motion such as slipping of the workpiece relative to the clamps and locators.

This assumption will be further discussed in Chapter 6. The Ti-6Al-4V disk is forged

into a workable shape prior to any machining process. The residual stress from the

forging process is assumed to be removed at previous machining operations in this

study. This means the previous machining operations have been performed and

eliminated all residual stress from the forging process. Future study is suggested to

examine the residual stress effects from the forging process upon the machining process

by modifying the current finite element model.


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The cutting speed of 60 m/min is chosen in this study as discussed in Chapter 3. The

rotational speed is low. However, the inertia angular velocity of 1000 rad/sec is applied

to the model to examine the effect of centrifugal forces during a turning process. There

is no change to analysis results such as displacements and von mises stress. In addition,

the von mises stresses are examined to determine whether any plastic deformations exist.

A large amount of the von mises stress exists at the contact point between the cutting

tool and disk as shown Figure

fang thesis final

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