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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 8.28: Displacements Contours Plots for Experiment# 5 ...................................... 87
Figure 8.29: Displacements Contours Plots for Experiment# 6 ...................................... 87
Figure 8.30: 32 Clamps and Locators for Experiment# 7 to 9 ........................................ 88
Figure 8.31: Displacements Contours Plots for Experiment# 7 ...................................... 88
Figure 8.32: Displacements Contours Plots for Experiment#8 ....................................... 89
Figure 8.33: Displacements Contours Plots for Experiment# 9 ...................................... 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 8.36: Displacement Contour Plots for Experiment# 2 ......................................... 91
Figure 8.37: Displacement Contour Plots for Experiment#3 .......................................... 91
Figure 8.38: Displacement Contour Plots for Experiment# 4 ......................................... 92
Figure 8.39: Displacement Contour Plots for Experiment# 5 ......................................... 92
Figure 8.40: Displacement Contour Plots for Experiment# 6 ......................................... 93
Figure 8.41: Displacement Contour Plots for Experiment# 7 ......................................... 93
Figure 8.42: Displacement Contour Plots for Experiment# 8 ......................................... 94
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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( )
( ) 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
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