A Study of Fixture Layout and Clamping force for a Ti-6Al-4V Disk in a Vertical Turning Lathe Numerically Controlled Machine

Transcription

1 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 Institute Hartford, CT November, 2009 (For Graduation December 2009)

2 Copyright 2009 by Maureen Fang All Rights Reserved ii

3 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 Objectives Background and Significance Literature Review Machining Set-up Vertical Turning Lathe (VTL) process Machine Axis Machine Table Description of Workpiece Geometry of the Disk Material Properties of Ti-6Al-4V Machinability Description of fixture Plate Locators Clamps Machining of Titanium (Ti-6Al-4V) Disk Machining Conditions Cutting Tool Properties iii

4 3.2.1 Cutting Tool Material Cutting Tool Geometry Machining Parameters Feed Rate, h Depth of Cut, b Cutting Speed, v Orthogonal and Oblique Cutting Cutting Forces Orientations Assumptions Calculation Procedure Oblique angle, i, and Chip flow angle, η Normal rake angle, α n Friction angle, β a, and Normal friction angle, β n Chip compression ratio, r c, and Normal shear angle, φ n Cutting Constants Cutting Forces Formulas Matlab Code Calculations Results Verifications of Calculation Results Finite Element Model Analysis Fixture-Disk Model Properties Clamping Candidate Region Clamping Area Clamping Pressure Initial Clamping Force Locating Candidate Region iv

5 4.4 Assumptions Initial Fixture Layout Cutting Forces Applied to Fixture-Disk Model Cutting Forces Locations Represent Complete Cut Cutting Forces Locations Represent Disk Rotation Degree Location DOE to determine the appropriate Fixture Layout Objective Statement Factors Levels The Number of Clamps and Locators The Magnitudes of the Cutting Forces (F) Matrix of Experiments Constraints Solution Procedure Statistical Analyses Main Effects Interaction Effects Results and Recommendations DOE to determine the appropriate magnitude of Clamping Force Objective Statement Clamping Pressure Constraints Screening Stage Recommended Range of Clamping Forces Matrix of Experiments Factors and Levels v

6 6.7 Solution Procedure Statistical Analyses Main Effects Interaction Effects Results and Recommendations Conclusions and Recommendations Conclusions from Machining Ti-6Al-4V Disk and FEM Analysis Conclusions from Design of Experiments Future Studies Appendix: Matlab codes to calculate cutting forces in oblique cutting Matlab codes to calculate cutting forces in orthogonal cutting ANSYS Finite Element Model Results for Chapter ANSYS Finite Element Model Results for Chapter ANSYS Finite Element Model Results for Chapter Reference: vi

7 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]... 6 Table 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] Table 3.2: Actual dimensions of cutting tool. [Donachie, 4] Table 3.3: Cutting speed, feed rate, and depth of cut for chapter Table 3.4: Cutting angles for oblique and orthogonal cutting angles Table 3.5: Cutting Constants for both Oblique and Orthogonal Cutting Table 3.6: Comparisons of the cutting forces Table 4.1: Finite Element Model Properties Table 4.2: Cutting forces are generated by a finish cut Table 5.1: The number of clamps and locators with corresponding total contact surface area Table 5.2: Machining parameters for finish, semi-finish, and rough cut Table 5.3: The cutting forces for finish, semi-finish, and rough cut Table 5.4: Nine experiments with corresponding values of the two factors Table 5.5: Reduction rates for a rough cut Table 6.1: Clamping Pressures with corresponding clamping forces Table 6.2: Six experiments with corresponding values of the two factors Table 6.3: Nine experiments with corresponding values of the two factors vii

8 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 a Radial T Slot [Boothroyd, 13] Figure 2.4: Fixture-disk assembly includes plate, locator and clamp Figure 2.5: The principle of location applied to a rectangular shape workpiece. [Doyle, 16] Figure 2.6: Commercially available fixture clamps. [Wilson, 15] Figure 3.1: Geometry of single-point cutting tool. [Altintas, 18] Figure 3.2: Depth of cut, b, and Feed Direction, Vf, for an outer diameter cut Figure 3.3: Geometries of orthogonal and oblique cutting processes [Altintas, 18] Figure 3.4: Schematic diagram of the lathe turning process of an outer diameter cut with workpiece rotation V, feed direction V f, tangential force, F t, feed force, F f, and radial force F r Figure 3.5: Cutting forces (tangential force, F t, feed force, F f, and radial force F r ) acting on workpiece and feed direction, V f, of cutting tool Figure 3.6: Flow diagram of cutting forces calculations Figure 3.7: Geometry of oblique cutting process. [Altintas, 18] 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 4.8 o for oblique cutting Figure 3.9: Cutting forces results for both oblique and orthogonal cutting Figure 4.1: Disk is divided into 128 equally spaced volumes Figure 4.2: The 360 degrees Clamping/Locating Candidate Region Figure 4.3: Dimensions of a clamp or locator, and one area Figure 4.4: Von Mises stress in the initial fixture layout Figure 4.5: Initial Fixture Layout contains four clamps and locators Figure 4.6: Cutting forces are applied in vertical locations such as top, middle, and bottom to represent a complete cut Figure 4.7: Displacement vector sum represents top, middle, and bottom locations Figure 4.8: Top view of initial fixture layout in ANSYS viii

9 Figure 4.9: Cutting forces applied to seven locations in the initial fixture layout Figure 4.10: Displacement vector sum in seven locations circumferentially Figure 4.11: Displacement components such as x, y, and z in seven locations circumferentially Figure 5.1: Cutting tool travel path in relation to the deflected disk Figure 5.2: Three levels of the number of clamps and locators Figure 5.3: Main Effects Plot for Displacement Vector Sum Figure 5.4: Main Effects for x-component displacement Figure 5.5: Main Effects for y-component displacement Figure 5.6: Main Effects for y-component displacement Figure 5.7: Interaction Plot for Displacement Vector Sum Figure 5.8: Interaction plot for maximum x-component displacement Figure 5.9: Interaction plot for absolute minimum y-component displacement Figure 5.10: Interaction plot for absolute minimum z-component displacement Figure 6.1: The chosen appropriate fixture layout with 16 clamps and locators Figure 6.2: Displacement vector sum for 500N and 3500N clamping forces Figure 6.3: X-component displacement for 500N and 3500N clamping forces Figure 6.4: Y-component displacement for 500N and 3500N clamping forces Figure 6.5: Z-component displacement for 500N and 3500N clamping forces Figure 6.6: Main Effects plot for displacement vector sum Figure 6.7: Main Effects plot for x-component displacement Figure 6.8: Main Effects plot for y-component displacement Figure 6.9: Main Effects plot for z-component displacement Figure 6.10: Interaction plot for displacement vector sum Figure 6.11: Interaction plot for maximum x-component displacement Figure 6.12: Interaction plot for absolute minimum y-component displacement Figure 6.13: Interaction plot for absolute minimum z-component displacement Figure 8.1: Finish Cutting Forces is Applied at Point B (0 o from a Clamp and Locator)73 Figure 8.2: Displacement Vector Sum at Point B (0 o from a Clamp and Locator) Figure 8.3: X-component Displacement at Point B (0 o from a Clamp and Locator) Figure 8.4 Y-component Displacement at Point B (0 o from a Clamp and Locator) ix

10 Figure 8.5: Z-component Displacement at Point B (0 o from a Clamp and Locator) Figure 8.6: Finish Cutting Forces is Applied at o from a Clamp and Locator Figure 8.7: Displacement Vector Sum at o from a Clamp and Locator Figure 8.8: X-component displacement at o from a Clamp and Locator Figure 8.9: Y-component displacement at o from a Clamp and Locator Figure 8.10: Z-component displacement at o from a Clamp and Locator Figure 8.11: Finish Cutting Forces is Applied at o from a Clamp and Locator Figure 8.12: Displacement Vector Sum at o from a Clamp and Locator Figure 8.13: X-Component Displacement at o from a Clamp and Locator Figure 8.14: Y-Component Displacement at o from a Clamp and Locator Figure 8.15: Z-Component Displacement at o from a Clamp and Locator Figure 8.16: Finish Cutting Forces is Applied at -45 o from a Clamp and Locator Figure 8.17: Displacement Vector Sum at -45 o from a Clamp and Locator Figure 8.18: X-Component Displacement at -45 o from a Clamp and Locator Figure 8.19: Y-Component Displacement at -45 o from a Clamp and Locator Figure 8.20: Z-Component Displacement at -45 o from a Clamp and Locator Figure 8.21: Side View of X Displacement at o from a Clamp and Locator Figure 8.22: Side View of X Displacement at o from a Clamp and Locator Figure 8.23: Side View of X Displacement at -45 o from a Clamp and Locator Figure 8.24: Displacements Contour Plots for Experiment# Figure 8.25: Displacements Contour Plots for Experiment# Figure 8.26: 16 Clamps and Locators for Experiment# 4 to Figure 8.27: Displacements Contours Plots for Experiment# Figure 8.28: Displacements Contours Plots for Experiment# Figure 8.29: Displacements Contours Plots for Experiment# Figure 8.30: 32 Clamps and Locators for Experiment# 7 to Figure 8.31: Displacements Contours Plots for Experiment# Figure 8.32: Displacements Contours Plots for Experiment# Figure 8.33: Displacements Contours Plots for Experiment# Figure 8.34: Displacement Contour Plots of No Cutting Forces Applied Figure 8.35: Displacement Contour Plots for Experiment# x

11 Figure 8.36: Displacement Contour Plots for Experiment# Figure 8.37: Displacement Contour Plots for Experiment# Figure 8.38: Displacement Contour Plots for Experiment# Figure 8.39: Displacement Contour Plots for Experiment# Figure 8.40: Displacement Contour Plots for Experiment# Figure 8.41: Displacement Contour Plots for Experiment# Figure 8.42: Displacement Contour Plots for Experiment# Figure 8.43: Displacement Contour Plots for Experiment# xi

12 LIST OF SYMBOLS Angles Symbol Descriptions Unit i oblique angle degree α f cutting tool side rake angle degree α p cutting tool back rake angle degree ψ r cutting tool side cutting-edge angle degree cl f Side relief angle degree cl p End relief angle degree k r End cutting-edge angle degree α f Side rake angle degree α n normal rake angle degree α o orthogonal rake angle degree α p Back rake angle degree α r orthogonal rake angle degree β a friction angle degree β n normal friction angle degree η chip flow angle degree φ n normal shear angle degree φ n,c orthogonal normal shear angle degree ψ 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 F c Clamping Force N F f Feed force N F r Radial force N F t Tangential force N h feed rate mm/rev K fc Feed cutting constant MPa K fe Average edge force coefficient N/mm

13 K rc Radial cutting constant MPa K tc Tangential cutting constant MPa K te Average edge force coefficient N/mm P Clamping Pressure Pa R Nose radius mm r c Chip compression ratio ~ V Workpiece rotation m/min v Cutting Speed m/min V f Feed direction ~ τ s Shear yield stress MPa ii

14 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 my career at Pratt and Whitney. I am truly appreciated for Scot s 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. iii

15 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 cutting forces 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 360 o 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. iv

16 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 quasi equilibrium 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[wilson 1, 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. 1

17 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 [Ezugwa 2, 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], [Polmer 3, 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 Review A 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 [Walczyk 5, 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, [Walczyk 6, 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. [Deng 7, 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. [Krishnakumar 8, 9, 8,9], [Kaya 10,10] and [Chen 11,11] have extensive discussions on implementations of GA. In addition, fixture layout optimization can be determined by a min-max loading criteria [DeMeter 12, 12]. 2

18 2. Machining Set-up 2.1 Vertical Turning Lathe (VTL) process 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 [Boothroyd 13, 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. 3

19 Tool Head Numerically Controlled Unit Machine Table/ Worktable Figure 2.2: Amera Seiki Vertical Turning VT2000 Machine 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. 4

20 Fixture Clamp Radial T Slot Machine Table 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 Geometry of the Disk The geometry of the workpiece is a symmetric disk. The dimensions of the disk are 0.508m, 0.456m, m, and m as outer diameter, inner diameter, radial thickness, and height, respectively 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 400 o 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, corrosionresistant, good thermal stability, heat treatable, good forge-ability, and good fabricability. 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 5

21 turning and milling processes. Both turning and milling offer the best tolerance requirements at the most economical cost. Material Condition Tensile Strength Yield Strength Ultimate Shear Strength Elongation Modulus of Elasticity Tension Hardness Poisson Ratio MPa MPa MPa % GPa Hv Ti-6Al- 4V Annealed Ti-6Al- 4V solution treated and aged Table 2.1: Material Properties of Ti-6Al-4V. [Donachie, 4] 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 [Machado 14, 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. Alloy Condition (a) Machinability rating (b) B1112 resulfurized steel HR carbon steel CD 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] 6

22 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 Ti-6Al- 4V annealed bar Tensile Strength Yield Strength Elongation Reduction Area Modulus of Elasticity Tension Hardness Density Specific heat at oC Thermal Conductivity MPa MPa % % GPa Hv g/cm 3 J/kg K W/m K Ti-6Al- 4V solution treated and aged bar AISI cold drawn 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 2.3 states 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 7

23 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 [Wilson 15, 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 Young s Modulus of 201 GPa and Poisson Ratio of 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 8

24 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 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. 9

25 Ti-6Al-4V Disk Clamp Locator Radial T-Slot Plate Figure 2.4: Fixture-disk assembly includes plate, locator and clamp Locators There are six requirements for choosing the locating points within a fixture [Doyle 16, 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 360 o 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 method of location [Wilson, 15]. The method is to place and hold a workpiece against three points in 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. 10

26 Figure 2.5: The principle of location applied to a rectangular shape workpiece. [Doyle, 16] 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]. 11

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

28 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. This heat 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 Properties 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 13

29 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 composition Grain size Hardness Density Transverse strength Compressive strength Modulus of elasticity Relative abrasion resistance Coefficient of thermal expansion at 200 C Thermal conductivity Hv g/cm 3 MPa MPa GPa m/m K W/m K 94WC-6Co Medium Table 3.1: Material properties of WC/Co C2 grade cutting tool. [Santhanam 17, 17] 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 singlepoint 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. 14

30 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 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 [Altintas 18, 18]. A graphic representation of the tool feature symbols are shown in Figure 3.1. The cutting tool has back rake angle, α p, and side rake angle, α f, of zero degree and five degrees, respectively, which are suggested by [Donachie, 4] for finishing cut. A positive side 15

31 rake angle will minimize the cutting forces. This may considered to be an optimal machining condition. Tool Feature symbols Tool Feature Names Actual Tool α p Back rake angle 0 α f Side rake angle 5 o cl p End relief angle 5 o End clearance angle cl f Side relief angle 5 o Side clearance angle k r ψ r End cutting-edge angle Side cutting-edge angle 15 o 15 o R Nose radius 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

32 Cutting Speed, v Feed Rate, h Depth of Cut, b m/min 60 mm/rev mm Table 3.3: Cutting speed, feed rate, and depth of cut for chapter 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 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 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. 17

33 Figure 3.2: Depth of cut, b, and Feed Direction, Vf, for an outer diameter cut 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 [Gente 19, 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 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, 18

34 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 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 m and radial thickness of m. The grade C-2 carbide insert has mm nose radius and is part of a single point tool. The cutting tool travels in the feed direction, V f, which is parallel to vertical z-axis as shown in Figure 3.5. This generates a feed force onto the workpiece, F f 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 19

35 workpiece, F t 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, F r, is in the negative x-axis or radial direction of workpiece. All cutting forces F t, F f, and F r act onto the workpiece at the point of contact with the nose radius of the cutting tool. The tangential Force, F t, is the primary cutting force and has the maximum magnitude. The radial force, F r, 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 V f, tangential force, F t, feed force, F f, and radial force F r. Figure 3.5: Cutting forces (tangential force, F t, feed force, F f, and radial force F r ) acting on workpiece and feed direction, V f, of cutting tool. 20

36 3.4.2 Assumptions The shear yield stress, τ s, of Ti-6Al-4V is assumed to be 613 MPa. The average edge force coefficients, Kte and 18]. The coefficients, Kte and K fe represent the rubbing forces per unit width [Altintas, K fe, 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 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 of the 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 20.5 o. 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. 21

37 Tool Geometries Machining Parameters Input Variables Normal rake angle Normal Shear Angle Chip Compression Ratio=1.2 (Oblique Cutting) Cutting Constants Friction Angle = 20.5 degree Formulas and assumptions from literatures Cutting Forces Formulas Matlab Codes Cutting Forces (Fr, Ft, Ff) Figure 3.6: Flow diagram of cutting forces calculations Oblique angle, i, and Chip flow angle, η The oblique angle is calculated to be 1.3 o 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, α f, back rake angle, α p, and side cuttingedge angle, ψ r are summarized in Table 3.4. Figure 3.7 shows the graphical representation of the angles. Where i - oblique angle α p - cutting tool back rake angle ψ r - cutting tool side cutting-edge angle tan i = tanα cosψ + tanα sinψ 3.1 p 22 r f r

38 α f - cutting tool side rake angle Angles Oblique Cutting Orthogonal Cutting Degree Radian Degree Radian α f cutting tool side rake angle α p cutting tool back rake angle ψ r cutting tool side cutting-edge angle i oblique angle η chip flow angle α n normal rake angle β a friction angle β n normal friction angle Φ n normal shear angle Table 3.4: Cutting angles for oblique and orthogonal cutting angles. Rake face Z α n η Cut Surface Y X φ n Tool i h Workpiece b Figure 3.7: Geometry of oblique cutting process. [Altintas, 18] Normal rake angle, α n The orthogonal rake angle, α 0,is 4.8 o, which is determined by cutting tool properties such as side rake angle, α, back rake angle, f α p, and side cutting-edge angle, ψ 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, 1.3 o and 0 o, for oblique and orthogonal cutting, respectively, are used to determine the normal rake 23

39 angles. Since the difference between the two oblique angles for oblique and orthogonal cutting is so small, the values of normal rake angle are 4.8 o. Where α 0 - orthogonal rake angle Where α n - normal rake angle tanα 0 α ψ Friction angle, β a, and Normal friction angle, β n α ψ = tan f cos r tan p sin r 3.2 tanα n = tanα 0 cosi 3.3 The equation to calculate the frictional angle β 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, βa β for orthogonal cutting. The calculated frictional angle, a, is 20.5 o for orthogonal cutting. The normal friction angle, β n, is 20.5 o 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. β = n o a α n ( tan β cosi) β = tan a Chip compression ratio, r c, and Normal shear angle, φ n The chip compression ratio, r c, 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, φ n as indicated in equation 3.6. The value of the normal shear angle affects the values of the cutting constants, K tc, K fc, and K rc, which will affect the values of cutting forces and will be defined in later section in this study. 24

40 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. Where φn - normal shear angle r c cosα n φ = n tan rc sinα n rc - chip compression ratio Both [Gente, 19] and [Cotterell 20, 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 [Li 21, 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 nose radius 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 25

41 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 37.5 o at cutting speed of 60m/min. [Li, 21] conducted oblique baseline cutting tests on a titanium workpiece using two feed rates of and 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 and 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 4.8 o. 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 40 o to 60 o as the chip compression ratio increases from 0.8 to Normal Shear Angle, degree Chip Compression Ratio 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 4.8 o for oblique cutting. 26

42 In this study, the chip compression ratio is chosen to be 1.2 and the normal shear angle, φ n, is 53.1 o 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, φ 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, φ n, c, is 37.2 o for orthogonal cutting. This calculation is based on Merchant s 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 37.5 o in the experiment conducted by [Cotterell, 20] for orthogonal cutting of Ti-6Al-4V with feed rate of 0.1mm/rev Cutting Constants π β a α n φ, = 3.7 n c 4 2 The cutting constants, K tc, K fc, and K rc, for tangential, feed, and radial forces, respectively, are calculated by equation 3.8 to The values of the cutting constants are stated in Table 3.5 for both oblique and orthogonal cutting. Both K tc and K fc have lower values for orthogonal than oblique cutting. The main reason is the different values of the normal shear angle, φ n, which is 53.1 o and 37.2 o for oblique and orthogonal cutting, respectively. The cutting constants are dependent on the values of the normal shear angle, φ n. Therefore, the oblique cutting constants have higher values of cutting constants than orthogonal cutting. In addition, the cutting constant, K rc, is zero for orthogonal cutting due to both oblique angle and chip flow angle is zero. K K tc fc τ cos ( βn α n ) + tani tanη sin βn 2 2 ( φn + βn α n ) tan η sin βn = 3.8 s sin φn 2 + cos sin( βn α n ) 2 2 ( φn + βn α n ) tan η sin βn τ s = 3.9 sin φn sin i 2 cos + 27

43 K rc ( βn α n ) tani tanη sin βn 2 2 ( φn + βn α n ) tan η sin βn τ cos = 3.10 s sin φn 2 cos + Constants Oblique MPa Orthogonal MPa K tc K fc K rc Table 3.5: Cutting Constants for both Oblique and Orthogonal Cutting 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, K te and K fe. 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, K tc, K fc, and K rc 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. Where Ft - tangential force Ff - feed force Fr - radial force b - depth of cut h - feed rate = uncut chip thickness Ft = Ktcbh + Kteb 3.11 F = K fcbh K feb 3.12 f + Kte - average edge force coefficient = 24 N/mm K fe - average edge force coefficient = 43 N/mm Fr = Krcbh

44 Cutting Forces using Feedrate=0.178mm/rev or in/rev Cutting Forces (N) Depth of cut (mm) Ft, Tangential Ff, feed Fr, radial Ft. Tangential_Orthogonal Ff, feed_orthogonal Figure 3.9: Cutting forces results for both oblique and orthogonal cutting 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 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 29

45 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 Verifications of Calculation Results The machining parameters from previous studies [Li, 21 and Molinar 22, 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 Longitudinal Force =1042 N Feed Force = 1115 N Hoffmeister Longitudinal Force =1667 N Feed Force = 1115 N F t, F f, F r are , 51-71, and 14- Li N, respectively - FE Models F t, F f, F r are 137, 47 and F t, F f, F r are , 51-61, and 16-2N, respectively 33N, respectively - Experiments 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 30

46 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. 31

47 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 ANSYS 23 software. The dimensions of the model are 0.254m, m and m; 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 in Figure 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. 32

48 4.2 Clamping Candidate Region Number of elements Number of Nodes Degree of Freedom per Node 3 Type of Elements 3D-Brick Material of Workpiece Ti-6Al-4V Modulus of Elasticity 110 GPa Poisson Ratio 0.34 Table 4.1: Finite Element Model Properties. 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 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. 33

49 360 degrees Clamping/Locating Candidate Region Figure 4.2: The 360 degrees Clamping/Locating Candidate Region 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 o, m, and m; degree, inner radius and outer radius respectively, are shown in Figure 4.3. The area, A, is calculated to be 2.92e-4 m 2 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. 34

50 A=2.92e-4 (m^2) Figure 4.3: Dimensions of a clamp or locator, and one area 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. FC FC 4.1 P = 2 = 2 4 A 2.92e S Where P Clamping pressure per area F c Clamping Force 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 35

51 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 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 m 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. 36

52 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 4.4. This stress allows chip formation during machining process. The magnitude of von mises stress decreases rapidly at the area outside of cutting tool contact area. This means there is no plastic deformation outside of the contact area between the disk and cutting tool. Thus, this study will assume all deflections not associated with the actual cutting are elastic. Figure 4.4: Von Mises stress in the initial fixture layout. 4.5 Initial Fixture Layout The chosen initial fixture layout consists of four equally spaced clamps and locators as shown in Figure 4.5. A set of clamp and locator is positioned 90 o away from each other. The clamping force of 1500N is being used. The clamping pressure is 2.56e6 Pa which is applied onto the eight areas onto the top surfaces to represent four clamps. The locators are aligned directly below the clamps and are constrained in all three x, y, and z axis. 37

53 The initial fixture layout configuration will be used to examine the deflection behaviors within the disk when the cutting forces are applied at different locations of the model. The initial fixture layout is chosen because it contains the smallest possible number of clamps and locators because this configuration generates the maximum amount of deflections. The maximum amount of deflection is a critical factor in designing a functional fixture. A properly designed fixture will be able to minimize the amount of deflections within the disk. Figure 4.5: Initial Fixture Layout contains four clamps and locators. 4.6 Cutting Forces Applied to Fixture-Disk Model The cutting forces are added onto the fixture-disk model to represent the material removal in a machining process. The model calculates the deflections within the disk. The cutting forces are applied at a single node on the outer diameter of the disk to represent a snap shot of an entire outer diameter machining process. During a machining process, safety is a very critical factor. In the industry, the machining shops take a tremendous amount of precautions to prevent any accidents and injuries. Therefore, the designs of fixtures must meet the necessary strength specifications to withhold an unexpected impact during the machining processes. In this study, a safety factor of three is chosen. This means that the magnitudes of the cutting forces applied within the finite 38

54 element model are three times the calculated values. The magnitudes of the cutting forces for the finishing cut are shown in Table 4.2 for both the calculated forces and the magnitudes of the cutting forces within the finite element model. The calculated forces are generated by the Matlab Code which is shown in the Appendix by using the machining parameters such as the feed rate of 0.178mm/rev and depth of cut of 0.635mm. The cutting forces within the finite element model are determined by multiplying the calculated forces by three as summarized in Table 4.2. Calculated Forces Forces in FEM Cutting Forces Orientations N N Fr, radial -x 3 10 Ft, Tangential -y Ff, feed -z Table 4.2: Cutting forces are generated by a finish cut. 4.7 Cutting Forces Locations Represent Complete Cut The machining surface is chosen to be the outer diameter of this disk in this study. The cutting tool travels vertically downward from the top to bottom on the outer diameter surface during a diametrical machining process as shown in Figure 4.6. The radial thickness of the disk is being reduced by the depth of cut during the turning process. The ANSYS model calculates the overall deflection and displays the results as the displacement vector sum. The displacement vector sum is examined and the values are summarized in Figure 4.7. The displacement vector sum is largest at the top surface as the cutting tool enters onto the machining surface. When the cutting forces are at the middle of the outer diameter, the maximum amount of material is surrounded the contact point between the cutting tool and disk. The material of the disk is enabling a counteracting force to prevent the deflections induced by the cutting forces, thus, producing the minimum amount of displacement vector sum as indicated in Figure 4.7. As the tool exiting the machining surface at the bottom, the displacement vector sum increases because of the less amount of material within the disk to counteract with the cutting forces. In this study, the top location is chosen to perform the subsequent analysis because the cutting forces applied at the top node generate the maximum amount of deflections within the disk. The fixture is designed to minimize this deflection to provide the most rigid support to the disk. 39

55 Top Middle Bottom Figure 4.6: Cutting forces are applied in vertical locations such as top, middle, and bottom to represent a complete cut. Displacement vector sum 1.90E E-05 Top 1.80E-05 Bottom 1.75E-05 Displacement (m) 1.70E E E E E-05 Middle 1.45E E-05 Location of cutting forces (node position) Figure 4.7: Displacement vector sum represents top, middle, and bottom locations. 40

56 4.8 Cutting Forces Locations Represent Disk Rotation In an actual turning process, the disk is rotating at the cutting speed of 60 m/min in the counterclockwise direction. The distance between the cutting forces and fixture components such as clamps and locators are not fixed. The finite element model in ANSYS is static and can not be rotated. Therefore, the cutting forces are applied at seven locations circumferentially to represent the full rotation of the disk. The locations of the clamps and locators of the initial fixture layout are shown in Figure 4.8 on the top view within ANSYS. The chosen seven locations are illustrated in Figure 4.9. The first location is identified by point A which is negative 45 o away from a set of clamp and locator. When the cutting forces are aligned with a set of clamp and locator, the point is identified to be B. The region between point A and B is identified as the cutting forces are approaching toward the clamp and locator by using a sign convention of negative. As the clamp and locator is moving away from the cutting forces, the region is identified as positive region and ends at point C. The location of point C identified as positive 45 o location. Figure 4.8: Top view of initial fixture layout in ANSYS. 41

57 Figure 4.9: Cutting forces applied to seven locations in the initial fixture layout. The ANSYS model calculates the deflections also known as displacement within the disk. As the cutting forces approaching and moving away from the fixture components such as locators and clamps, the displacements within the disk change. The rotational motion reduces the distance between the cutting forces and the set of clamp and locator. The component displacement such as x, y, and z displacement are generated by the model in ANSYS. The overall deflections are represented by the displacement vector sum. Figure 4.10 shows the displacement vector sum generated by the cutting forces in seven locations circumferentially. The plot shows that both point A and C have identical displacement behaviors. However, the plot is not symmetric about point B which at 0 o position. The displacement vector sum within the disk decreases rapidly when the cutting forces are approaching toward the set of the clamp and locator as of from point A to B. The displacement vector sum is smallest at 0 o position because the clamp and locator are closest to the cutting forces. When the cutting forces are moving away from the clamp and locator are moving from point B to C, the displacement vector sum is 42

58 increasing rapidly at 22.5 o position, and then continues in a slower rate to reach the maximum level at point C. Displacement vector sum 1.40E-05 A 1.20E-05 C D isp lacem en t (m ) 1.00E-05 B 8.00E E Circumferential location of one clamp and locator with respect to cutting forces (degree) Figure 4.10: Displacement vector sum in seven locations circumferentially. The range of the magnitudes of the displacement throughout a full rotation of the disk is very large. The difference between the maximum and minimum displacement is approximately 85%. A common terminology known as potato chip is used in the industry to describe this behavior. A good fixture design should reduce this variation and provide a good amount of support to the disk. The displacement within the model was further examined by generating the displacement components such as x, y, and z; radial, circumferential, and axial respectively. Each displacement component displays an individual behavior as shown in Figure Both the y and z component displacements are negative due to the negative values of the tangential and feed forces. ANSYS considers the large negative values to be the minimum values. The minimum values represent the largest deflections within the disk. Therefore, all minimum values generated by ANSYS are converted into positive values and are named as Absolute minimum y-component displacement and Absolute minimum z-component displacement for analysis in this study. The z-component displacement increases rapidly as the cutting forces move further away from fixture components. The z-component displacement is double the amount of the x-component displacement. The y-component displacement is fairly constant because the tangential 43

59 cutting force is acting in the negative y axis. The y-component displacement is highly dependent on the stiffness of the disk because both clamps and locators contribute only the normal supports to the disk. Y-component = circumferential direction Displacement components 1.00E E-06 Z-component = axial direction 8.00E E-06 Displacement (m) 6.00E E E E E E E+00 X-component = radial direction Circumferential location of one clamp and locator with respect to cutting forces (degree) maximum x-component Displacement Absolute minimum y-component Displacement Absolute minimum z-component Displacement Figure 4.11: Displacement components such as x, y, and z in seven locations circumferentially Degree Location The maximum amount of displacement takes place at point A and C which are 45 o away from a set of clamp and location as shown in Figure Therefore, the circumferential location of the cutting forces is determined to be 45 o for analysis in Design of Experiments in Chapter 5 and 6. The goal is to utilize the worst scenario within a turning process to enable the most robust fixture design. 44

60 5. DOE to determine the appropriate Fixture Layout A Design of Experiments (DOE) is used to determine the appropriate fixture layout which will consist of the optimal number of clamps and locators. The appropriate fixture layout is determined using the initial clamping force of 1500N as discussed in Chapter 4. The appropriate magnitude of clamping force will be determined once the appropriate fixture layout is determined. In a turning process, the disk and fixture components such as clamps and locators are rotating 360 o at a cutting speed. The distance between the fixture components and the point of contact of the disk and the cutting tool is not fixed. Therefore, the distance between the cutting forces and fixture components varies throughout the entire turning process. The contact surface areas between the fixture components and disk are the critical design variable which can be determined to minimize the deflections within the disk. The number of clamps and locators are the corresponding to the contact surface areas between the disk and fixture components. By increasing the number of clamps and locators, the contact surface areas will be increased and the amount of support provided to the workpiece increases. The Design of Experiments will determine the appropriate amount of contact surface areas required to the tolerable amount of deflection within the disk. 5.1 Objective Statement All deformations within the disk are determined to be elastic. The cutting tool is traveling in a predefined path which is governed within the NC program. The cutting forces inherently generate deflections within the disk during chip formation. The deflections within the disk would distort the material removal volume within the entire cut. Figure 5.1 shows the cutting tool is traveling in a predefined path and removing materials from a deflected disk. In this case, the top section of outer diameter is being removed in an excessive amount of material due to the bending shape of the disk. Whereas, the lower section of the outer diameter would not have removed the proper amount of material. Therefore, a dimensional error will exist during this cut. The cutting forces are required within a machining process to remove materials from the workpiece. Therefore, the cutting forces cannot be removed nor reduced due to chip formation required. One solution is to design a fixture which is able to provide a sufficient amount 45

61 of support to the workpiece to minimize the machining dimensional errors. In this study, the DOE will determine the appropriate number of clamps and locators to achieve the tolerable amount of deflections within the disk. The objective of the DOE is to achieve the tolerable amount of deflections within the disk by selecting the appropriate number of clamps and locators which represents the appropriate fixture layout. Cutting Tool Travel Path Figure 5.1: Cutting tool travel path in relation to the deflected disk. 5.2 Factors Two factors are chosen for the Design of Experiments to determine the appropriate fixture layout. The factors are the number of clamps and locators, and the magnitudes of the cutting forces (F).The number of clamps and locators represent the contact surface areas between the fixture components and disk. As the number of clamps and locators increases, the contact surface areas increases and provides a larger amount of support to the disk. The cutting forces are generated by the machining parameters such as feed rate and depth of cut. 5.3 Levels The levels within the Design of Experiments are defined as the chosen range of values for an individual factor. [Willcox 24, 24] The Number of Clamps and Locators The three levels of the number of clamps and locators are chosen to be 4, 16, and 32. Figure 5.2 shows the three configurations in ANSYS. The four clamps and locators 46

62 is the initial fixture layout which was defined in the previous chapter. This fixture layout is considered to have the smallest amount of the total contact surface area which is 2.34e-3 m 2. The Table 5.1 lists the total contact surface area for all three fixture layouts. The 32 clamps and locators have the maximum amount of total surface area between the fixture components and disk. The 360 o full ring configuration is represented by 32 clamps and locators as shown in Figure 5.2. This fixture layout is expected to be able to provide the maximum amount of support. 4 Clamps and Locators 16 Clamps and Locators 32 Clamps and Locators Figure 5.2: Three levels of the number of clamps and locators. Number of clamps and locators Total Contact Surface Area m E E E-02 Table 5.1: The number of clamps and locators with corresponding total contact surface area The Magnitudes of the Cutting Forces (F) The magnitudes of the cutting forces (F) are generated by the machining parameters such as feed rates and depth of cuts. Three different types of cuts are finish, semi-finish, and rough cuts are chosen to represent the three levels of the magnitudes of the cutting forces in this Design of Experiments. The machining parameters are listed in Table 5.2. The cutting speed is 60m/min for all three types of cuts. The feed rate and depth of cut are significantly larger for rough than finish cut as indicated in Table 5.2. In the industry, rough cuts represent the preliminary machining processes to remove excessive amount of materials in the forgings. The dimensional tolerance can be very large because the machined surfaces are not part of the finished products which can be delivered to customers. The subsequent type of cut such as finish is used to remove the remaining 47

63 material. A finish cut is mostly a fine cut which removes a small amount of material. The dimensional tolerances of the features produced by the finish cuts are very small. The manufacturers use different resources such as machines and tools for different type of cuts such as finish, semi-finish, and rough cuts. Type of Cut Cutting Speed, v Feed Rate, h Depth of Cut, b m/min mm/rev mm Finish Semi-Finish Rough Table 5.2: Machining parameters for finish, semi-finish, and rough cut. The three levels of the magnitudes of the cutting forces are represented by F1, F2, and F3 as of finish, semi-finish, and rough cut, respectively. The magnitudes of the cutting forces are calculated using the Matlab codes which discussed previously and stated in the Appendix. The calculated cutting forces were multiplied by the safety factor of three. The safety factor is to prevent any accidents due to an unforeseeable magnitude of the cutting forces being generated in the actual machining. The results are summarized in Table 5.3. The magnitude of cutting forces increases rapidly from finish to rough cuts due the large amount of depth of cut and feed rate being used. All cutting forces are applied at the node which is located at the top of the outer diameter as determined in Chapter 4. Type of cuttings Finish=F1 Semi-Finish=F2 Rough=F3 Cutting Forces Orientations N N N Fr, radial -x Ft, Tangential -y Ff, feed -z Table 5.3: The cutting forces for finish, semi-finish, and rough cut. 5.4 Matrix of Experiments A full factorial design is chosen for this Design of Experiments. The number of experiments is determined to be nine using the formula of level factor [Montgomery 25, 25]. The matrix of experiments is shown in Table 5.4. The two factors such as the number of clamps and locators, and cutting forces are listed in columns. Each row of the matrix corresponds to one experiment. An individual experiment has a combination of two factors and its corresponding level. For example, the first experiment has a combination 48

64 of 4 clamps and locators, and F1 cutting forces which represent a finish cut. All the experiments are performed by the finite element model in ANSYS. The finite element model calculates deflections within the disk. 5.5 Constraints Experiment No Number of clamps and locators 49 Cutting Forces 1 4 F1 2 4 F2 3 4 F F F F F F F3 Table 5.4: Nine experiments with corresponding values of the two factors. The constraints of Design of Experiments are factors which can not be changed [Montgomery, 25]. The constraints are the size of an individual clamp and locator, the locations of clamps and locators, the clamping force, and the displacement constraints of the locators. The size of an individual clamp and locator is identical. This means each locator and clamp occupies two surface areas within the finite element model as stated in Chapter 4. Each surface has the area of 2.92e-4 m. The locations of the clamps and locators are restricted within the identified candidate region which discussed in the previous chapter. The clamps and locators must be aligned vertical to eliminate any bending moment might have induced to the disk. This will prevent the disk from slipping during the machining process. The clamp force is determined to be 1500N [Krishnakumar, 8] as discussed in the previous chapter. The clamping pressure per area of 2.56e6 Pa is applied in the ANSYS finite element model. The locators are constrained in x, y, and z-axis. 5.6 Solution Procedure The analyses of all nine experiments are performed using the finite element model in ANSYS. The deflections also known as the displacements within the disk are gathered from the finite element model. The analysis results are displacement vector sum, x-

65 component, y-component, and z-component displacement. These results are entered into Minitab 26 software which performs statistical analyses to generate the Interaction and Main Effect plots. 5.7 Statistical Analyses Main Effects The four Main Effect plots are shown Figure 5.3, Figure 5.4, Figure 5.5, and Figure 5.6 for displacement vector sum, x-component, y-component, and z-component displacement, respectively. The main effect plots illustrate the relations between the two factors and displacement within the disk. A negative correlation relationship exists between the number of clamps and locators and displacement within the disk. This means as the number of clamps and locators increases, the displacement decreases. The three types of cutting forces are represented by 1, 2, and 3 as of the finish, semi-finish, and rough cut, respectively. A large positive slope exists within the four graphs for the cutting forces and indicates that the displacement increases as the type of cut changes from the finish to rough cut. Main Effects Plot for Displacement Vector Sum Data Means Number of Clamps and Locators Type of Cutting Forces Mean Figure 5.3: Main Effects Plot for Displacement Vector Sum. 50

66 Main Effects Plot for Maximum x-component displacement Data Means Number of Clamps and Locators Type of Cutting Forces Mean Figure 5.4: Main Effects for x-component displacement. Main Effects Plot for Absolute minimum y-component displacement Data Means Number of Clamps and Locators Type of Cutting Forces Mean Figure 5.5: Main Effects for y-component displacement. 51

67 Main Effects Plot for Absolute minimum z-component displacement Data Means Number of Clamps and Locators Type of Cutting Forces Mean Figure 5.6: Main Effects for y-component displacement Interaction Effects The four Interactions plots are shown in Figure 5.7, Figure 5.8, Figure 5.9, and Figure 5.10 for displacement vector sum, x-component, y-component, and z-component displacement, respectively. The Interaction plot is the displacement plotted against the magnitudes of three types of cutting forces which are represented by 1, 2, and 3 as of finish, semi-finish, and rough cut. Each plot contains three graphs which represent the three different fixture layout configurations. The deflection within disk is very small for a finish cut when compared with a rough cut Interaction Plot for Displacement Vector Sum Data Means Number of Clamps and Locators Mean Type of Cutting Forces 3 Figure 5.7: Interaction Plot for Displacement Vector Sum. 52

68 Interaction Plot for Maximum x-component displacement Data Means Number of Clamps and Locators Mean Type of Cutting Forces 3 Figure 5.8: Interaction plot for maximum x-component displacement. Interaction Plot for Absolute minimum y-component displacement Data Means Number of Clamps and Locators Mean Type of Cutting Forces 3 Figure 5.9: Interaction plot for absolute minimum y-component displacement. 53

69 Interaction Plot for Absolute minimum z-component displacement Data Means Number of Clamps and Locators Mean Type of Cutting Forces 3 Figure 5.10: Interaction plot for absolute minimum z-component displacement. Overall, as the number of clamps and locators increase, the amount of displacement decreases. The 32 clamps and locators have the smallest amount of displacement because the fixture layout has the maximum amount of the total contact surfaces areas by having a 360 o full ring configuration. Table 5.5 summarized the reduction rate of displacements for a rough cut. When the fixture layout changes from 4 to 16 clamps and locators, the displacement vector sum is decreased by 31%, while the z-component displacement decreases by 51%. There is no significant reduction even though the number of clamps and locators can be reached to 32. This is very similar to the theory of the diminishing of return. Once a certain number has reached, there is no significant additional change. Reduction Rate of Displacement Fixture Layouts (%) Vector Sum x-component y-component z-component From 4 to 16 clamps and locators 31% 40% 11% 51% From 16 to 32 clamps and locators 8% 25% 4% 16% 5.8 Results and Recommendations Table 5.5: Reduction rates for a rough cut. 16 clamps and locators fixture layout configuration is chosen to be 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 360 o full ring type of configuration widely used in the industry. A smaller 54

70 number of clamps and locators will reduce the amount of set-up time and the overall cost of the fixture. The operating costs associated with the fixture would be more economical because of the fewer numbers of components to be repaired and maintained. Thus, the chosen fixture layout offers many advantages. 55

71 6. DOE to determine the appropriate magnitude of Clamping Force 6.1 Objective Statement The initial magnitude of the clamping force is determined be to 1500N as stated in Chapter 4. A Design of Experiments (DOE) is used to determine the best magnitude of the clamping force for 16 clamps and locators fixture layout which is determined to the appropriate fixture layout in Chapter 5. The objective of the DOE is to minimize the deflections within the disk by selecting the appropriate magnitude of the clamping force and confirm the frictional force assumption in Chapter 4. In this study, the frictional force was assumed to be sufficient, thus, no relative motion such as slipping of the disk in relation to fixture will exist. 6.2 Clamping Pressure As stated in Chapter 4, the clamping pressure is calculated based in the magnitude of clamping force. The clamping pressure is required when applying the clamping constraints in the finite element model. The clamping forces and corresponding clamping pressures are summarized in Table 6.1. These values will be used in the Screening Stage and Design of Experiments. Cases Clamping Force Clamping Pressure per area Screening Stage Design of Experiments N Pa E E E E E+05 Table 6.1: Clamping Pressures with corresponding clamping forces. 6.3 Constraints The constraints are identical for the experiments performed in both the Screening Stage and the Design of Experiments. Chapter 5 determines the appropriate fixture layout which has 16 clamps and locators. The location of clamps and locators are shown in Figure 6.1. All locators are constrained in x, y, and z axis. All clamps and locators are 56

72 vertically aligned to prevent any bending moments being induced onto the disk by fixture components. All clamps will have the same magnitude of force. In this study, no slipping is assumed. All cutting forces are applied at the top surface as determined in Chapter 4. Figure 6.1: The chosen appropriate fixture layout with 16 clamps and locators. 6.4 Screening Stage A screening stage determines a valid range of clamping force to be used in the Design of Experiments. A large range of clamping force is determined to explore the design space. The clamping force is chosen to be 500N and 3500N. All three types of cutting forces such as finish, semi-finish, and rough will be used. The Screening Stage composes of six experiments. The corresponding values of the clamping force and the magnitude of the cutting forces for each experiment are summarized in Table 6.2. The magnitudes of the cutting forces F1, F2, and F3 which represent finish, semi-finish, and rough cuts are determined in Chapter 5 and summarized in Table

73 Experiment No. Clamping Forces Cutting Forces N N F F F F F F3 Table 6.2: Six experiments with corresponding values of the two factors Recommended Range of Clamping Forces The parameters for the six experiments are input into the FE model to calculate the displacement within the disk. The results from FE analysis are displacement vector sum, x-component, y-component, and z-component displacement as shown in Figure 6.2, Figure 6.3, Figure 6.4, and Figure 6.5, respectively. Overall, the displacements are very similar for both clamping force of 500N and 3500N. This means that the magnitudes of the clamping force do not affect the deflections within the disk for all three types of cuts. Therefore, a small clamping force is suggested to be used in the Design of Experiments. The chosen values of the clamping forces are 100, 200, and 300N. Displacement Vector Sum 7.00E E E-05 Rough Displacement (m) 4.00E E E-05 Semi-Finish 1.00E-05 Finish 0.00E+00 Type of cutting forces Clamping Force=500N Clamping Force=3500N Figure 6.2: Displacement vector sum for 500N and 3500N clamping forces. 58

74 Maximum x-component displacement 1.80E E E-05 Rough 1.20E-05 Displacement(m) 1.00E E E-06 Semi-Finish 4.00E E E+00 Finish Type of Cutting Forces Clamping Force=500N Clamping Force=3500N Figure 6.3: X-component displacement for 500N and 3500N clamping forces. Absolute minimum y-component displacement Rough Displacement (m) Semi-Finish Finish 0 Type of cutting Forces Clamping Force=500N Clamping Force=3500N Figure 6.4: Y-component displacement for 500N and 3500N clamping forces. 59

75 Absolute minimum z-component displacement Rough Displacement (m) Semi-Finish Finish 0 Type of cutting forces Clamping Force=500N Clamping Force=3500 Figure 6.5: Z-component displacement for 500N and 3500N clamping forces. 6.5 Matrix of Experiments A full factorial design is chosen for this Design of Experiments. The number of experiments is determined to be nine using the formula of level factor [Montgomery, 25]. The matrix of experiments is shown in Table 6.3. The two factors such as the number of clamping force, and cutting forces are listed in columns. Each row of the matrix corresponds to one experiment. An individual experiment has a combination of two factors and its corresponding level. For example, experiment number one has the combinations of the clamping force of 300N and the magnitudes of the cutting forces for a finish cut as of F1 which represent a finish cut. All the experiments are performed by the finite element model in ANSYS. The finite element model calculates deflections within the disk. 60

76 Experiment No Clamping Forces Cutting Forces N N F F F F F F F F F3 Table 6.3: Nine experiments with corresponding values of the two factors 6.6 Factors and Levels The two factors are the magnitudes of the cutting forces and clamping forces. The cutting forces, F1, F2, and F3, represent the finish, semi-finish and rough type of cuts. The magnitudes of the cutting forces are determined in Chapter 5 and summarized in Table 5.3. The three levels of the clamping forces per clamp are 100N, 200N, and 300N as stated in Table 6.3. The corresponding clamping pressures are summarized in Table Solution Procedure The analyses of all nine experiments are performed using the ANSYS finite element model in ANSYS. The deflections also known as the displacements within the disk are generated from the finite element model. The finite element model s post-processing results are displacement vector sum, x-component, y-component, and z-component displacement. These results are entered into Minitab software which performs the statistical analyses to generate the Interaction and Main Effect plots. 6.8 Statistical Analyses Main Effects The four Main Effect plots are shown Figure 6.6, Figure 6.7, Figure 6.8, and Figure 6.9, for displacement vector sum, x-component, y-component, and z-component displacement, respectively. A positive correlation relationship exists between the 61

77 displacements and cutting forces. As the cutting forces goes from finish to rough cuts, the displacements increase. This is due to the magnitude of the cutting forces increase from a finish which is represented by F1 or 1 to a rough cut which is represented by F3 or 3. On the other hand, the three different clamping forces do not have any effect on the displacement in the disk. Main Effects Plot for Displacement Vector Sum Data Means Clamping Forces Types of cutting forces Mean Figure 6.6: Main Effects plot for displacement vector sum. Main Effects Plot for maximum x-component displacement Data Means Clamping Forces Types of cutting forces Mean Figure 6.7: Main Effects plot for x-component displacement. 62

78 Main Effects Plot for Absolute minimum y-component displacement Data Means Clamping Forces Types of cutting forces Mean Figure 6.8: Main Effects plot for y-component displacement. Main Effects Plot for Absolute minimum z-component Di Data Means Clamping Forces Types of cutting forces Mean Figure 6.9: Main Effects plot for z-component displacement Interaction Effects The four Interactions plots are shown in Figure 6.10, Figure 6.11, Figure 6.12, and Figure 6.13 for displacement vector sum, x-component, y-component, and z-component displacement, respectively. The displacements within the disk have no significant change among the three different clamping forces among all three types of cutting forces. All displacements are very similar. Surprisingly, the magnitude of the z- 63

79 component displacement is the smallest at the clamping force of 100N as shown in Figure Interaction Plot for Displacement Vector Sum Data Means Clamping Forces Mean Types of cutting forces 3 Figure 6.10: Interaction plot for displacement vector sum Interaction Plot for maximum x-component displacement Data Means Clamping Forces Mean Types of cutting forces 3 Figure 6.11: Interaction plot for maximum x-component displacement. 64

80 Interaction Plot for Absolute minimum y-component displacement Data Means Clamping Forces Mean Types of cutting forces 3 Figure 6.12: Interaction plot for absolute minimum y-component displacement. Interaction Plot for Absolute minimum z-component displacement Data Means Clamping Forces Mean Types of cutting forces 3 Figure 6.13: Interaction plot for absolute minimum z-component displacement. 6.9 Results and Recommendations The 100N is chosen to be the appropriate magnitude clamping force for all three types of cuts. The analyses from Design of Experiments illustrated that there is no significant changes between 100N and 300N clamping force. The results might have suggested a smaller magnitude of clamping force than the industry recommended value. Based on industry experience, the clamping forces should not be smaller than 100N. In 65

81 an actual machining process, there are many unexpected variables such as broken cutting tool, lack of machining coolants, and machine failure might cause the magnitudes of the cutting forces to increase. This might cause unexpected injuries and accidents. Thus, the clamping force is not recommended to be lower than 100N. 66

82 7. Conclusions and Recommendations 7.1 Conclusions from Machining Ti-6Al-4V Disk and FEM Analysis The chip compression ratio is determined to be 1.2 for oblique cutting of the chosen Ti-6Al-4V disk. Using the chosen cutting tool geometry, the normal shear angles, φ n, are calculated to be 53.1 o and 37.2 o for oblique and orthogonal cutting, respectively. The frictional angle is 20.5 o for both oblique and orthogonal cutting. The input variables for calculating the cutting forces are the tool geometries such as nose radius, rake angles, and cutting-edge angles, and the machining parameters such as feed rate and depth of cut. The input variables are entered into the written Matlab codes based on the oblique cutting theory empirical data for calculations of cutting forces. The tangential cutting force is the primary cutting force component for both oblique and orthogonal cutting because it has the highest magnitudes among the three cutting force components such as tangential force, F t, feed force, F f, and radial force F r. This is consistent with previous published findings. The ANSYS FE model calculates the displacements within the disk. As the locations of the cutting forces change circumferentially in relation to the fixture components such as clamps and locators, the displacements within the disk change in a non-symmetrical manner. The difference between the maximum and minimum displacement is approximately 85%. A term potato chip is used in the industry to describe this behavior. The results generated by the finite element model in ANSYS provide an understanding of the behavior of the disk during a turning process. Turning is a dynamic process. Both the disk and fixture are rotating in a speed known as cutting speed which is 60 m/min in this study. The finite element model in ANSYS is static analysis of a dynamic process. Therefore, key locations are identified within the finite element model to represent snap shots of the overall machining process. These snap shots illustrated the behaviors of the 67

83 dynamic machining process and enable readers to make reasonable conclusions and predictions. The deflections in the disk due to the rotational body force are negligible compared to those due to the cutting force. The inertia angular velocity of 1000 rad/sec is applied to the FE 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. Therefore, the inertia angular velocity is chosen to be zero for analysis. The x, y, and z displacement components represent radial, circumferential, and axial, respectively. The maximum x-component displacement has an average displacement of 2.4e-6m for the chosen finish cuts. The maximum amount of z-component displacement is double the maximum amount of the x-component displacement. The y-component displacement is fairly constant and is approximately fives times higher than x-component. When the machining surface is the outer diameter of a disk, the displacement vector sum has the largest magnitude at the top surface where the cutting tool enters into the machining surface of the disk. 7.2 Conclusions from Design of Experiments A full factorial design is chosen for Design of Experiments to determine the appropriate fixture layout. The Screening Stage and the Design of Experiments are used to explore the design space for the magnitudes of the clamping force. The analyses of all experiments are performed using the finite element model in ANSYS. The displacements within the disk are calculated. The statistical analyses in Minitab generate the Interaction and Main Effect plots for DOE. 16 clamps and locators are chosen to be the appropriate fixture layout which consists of 50% coverage of the clamping/locating candidate regions by achieving 31% displacement reduction. There are no significant additional benefits to use 32 clamps and locators which represent the 360 o full ring type of configuration being widely used in the industry. The 360 o full ring type of 68

84 configuration obtains 8% of displacement reduction while double the amount of fixture components. The amount of displacement reduction is not significant compared to the number of fixture components being added. 100N is chosen to be the appropriate clamping force for all three types of cuts. The results from the DOE illustrate that the displacement within the disk are approximately identical for 100N, 200N and 300N clamping forces. This study recommends using a smaller magnitude of clamping force because of savings in costs and the amount of set-up time required. 7.3 Future Studies The following key elements are suggested for future studies. The feed rate was assumed to be constant for the calculation of the cutting forces in Chapter 3. It would be highly beneficial to examine the effects of various feed rates. The cutting forces are calculated using formulas and assumptions from published materials. An actual machining verification of the calculated cutting forces would be valuable and significant. The residual stresses within a forged Ti-6Al-4V impact the machining process. A finite element model analysis incorporated residual stress is suggested to explore the effects of residual stresses within the surfaces of a forged material workpiece. Implementation of a real optimization process is suggested to determine the optimal surface contact areas between the workpiece and fixture components such as locators and clamps. The current FE model can be modified to perform an optimization process. The frictional force between workpiece and fixture components such as locators and clamps should be studied for the effects such as the true magnitudes of clamping force required. 69

85 8. Appendix: 8.1 Matlab codes to calculate cutting forces in oblique cutting. %clc %Tool Geometry - Need to convert to Radian angle unit alpha_f=5*(pi/180); %side rake angle of tool alpha_p=0*(pi/180); %back rake angle of tool psi_r=15*(pi/180); %side cutting edge angle of tool % Analyzing the mechanics of oblique cutting Eq 2.63 at P29. With exception % to B_a_degree, all angles are in radian unit. tan_alpha_o=tan(alpha_f)*cos(psi_r)+tan(alpha_p)*sin(psi_r); tan_i=tan(alpha_p)*cos(psi_r)+tan(alpha_f)*sin(psi_r); i=atan(tan_i); n=i; tan_alpha_n=tan_alpha_o*cos(i); alpha_n=atan(tan_alpha_n); rc=1.2; fe_n=atan(rc*cos(alpha_n)/(1-rc*sin(alpha_n))); B_a_degree= *(alpha_n*(180/pi)); %degree B_a_rad=B_a_degree*(pi/180); B_n=atan(tan(B_a_rad)*cos(i)); %rad % Calculations of Oblique Cutting Constants Eq 2.62 at P25 Den=sqrt((cos(fe_n+B_n-alpha_n))^2+(tan(n))^2*(sin(B_n))^2); Ts=613; %613MPa = 613N/mm^2 which will be used. (from Table 2.1 on P13) Ktc=(Ts/sin(fe_n))*((cos(B_n-alpha_n)+tan(i)*tan(n)*sin(B_n))/Den); Kfc=(Ts/(sin(fe_n)*cos(i)))*(sin(B_n-alpha_n)/Den); Krc=(Ts/sin(fe_n))*((cos(B_n-alpha_n)*tan(i)-tan(n)*sin(B_n))/Den); %Cutting Forces %INPUT Cutting Parameters h=0.178; %feedrate [mm/rev] b=0.635 %radial depth of cut [mm] 70

86 %Constant from Table 2.1 Kte=24; %N/mm Kfe=43; %N/mm Kre=0; %N/mm. This assumption is based on orthogonal cutting measurement results. % Calculations of cutting forces from Eq 2.59 on P24 Ft=Ktc*b*h+Kte*b Ff=Kfc*b*h+Kfe*b Fr=Krc*b*h 8.2 Matlab codes to calculate cutting forces in orthogonal cutting. %clc %Tool Geometry - Need to convert to Radian angle unit alpha_f=5*(pi/180); %side rake angle of tool alpha_p=0*(pi/180); %back rake angle of tool psi_r=15*(pi/180); %side cutting edge angle of tool % Analyzing the mechanics of oblique cutting Eq 2.63 at P29. With exception % to B_a_degree, all angles are in radian unit. tan_alpha_o=tan(alpha_f)*cos(psi_r)+tan(alpha_p)*sin(psi_r); tan_i=tan(alpha_p)*cos(psi_r)+tan(alpha_f)*sin(psi_r); %i=atan(tan_i); i=0; %oblique angle is 0 for orthogonal cutting. n=i; tan_alpha_n=tan_alpha_o*cos(i); alpha_n=atan(tan_alpha_n); B_a_degree= *(alpha_n*(180/pi)); %degree B_a_rad=B_a_degree*(pi/180); B_n=atan(tan(B_a_rad)*cos(i)); %rad fe_n=pi/4-((b_a_rad-alpha_n)/2); %Orthogonal Shear angle use Merchant's theory. % Calculations of Oblique Cutting Constants Eq 2.62 at P25 71

87 Den=sqrt((cos(fe_n+B_n-alpha_n))^2+(tan(n))^2*(sin(B_n))^2); Ts=613; %613MPa = 613N/mm^2 which will be used. (from Table 2.1 on P13) Ktc=(Ts/sin(fe_n))*((cos(B_n-alpha_n)+tan(i)*tan(n)*sin(B_n))/Den); Kfc=(Ts/(sin(fe_n)*cos(i)))*(sin(B_n-alpha_n)/Den); Krc=(Ts/sin(fe_n))*((cos(B_n-alpha_n)*tan(i)-tan(n)*sin(B_n))/Den); %Cutting Forces %INPUT Cutting Parameters h=0.178; %feedrate [mm/rev] b=0.127 %radial depth of cut [mm] %Constant from Table 2.1 Kte=24; %N/mm Kfe=43; %N/mm Kre=0; %N/mm. This assumption is based on orthogonal cutting measurement results. % Calculations of cutting forces from Eq 2.59 on P24 Ft=Ktc*b*h+Kte*b Ff=Kfc*b*h+Kfe*b Fr=Krc*b*h 8.3 ANSYS Finite Element Model Results for Chapter 4.8 Cutting Forces generated from finish type of cuts and 1500N Clamping Force are applied to initial fixture layout which consists of 4 equally spaced clamps and locators. 72

88 Figure 8.1: Finish Cutting Forces is Applied at Point B (0 o from a Clamp and Locator) Figure 8.2: Displacement Vector Sum at Point B (0 o from a Clamp and Locator) 73

89 Figure 8.3: X-component Displacement at Point B (0 o from a Clamp and Locator) Figure 8.4: Y-component Displacement at Point B (0 o from a Clamp and Locator) 74

90 Figure 8.5: Z-component Displacement at Point B (0 o from a Clamp and Locator) Figure 8.6: Finish Cutting Forces is Applied at o from a Clamp and Locator 75

91 Figure 8.7: Displacement Vector Sum at o from a Clamp and Locator Figure 8.8: X-component displacement at o from a Clamp and Locator 76

92 Figure 8.9: Y-component displacement at o from a Clamp and Locator Figure 8.10: Z-component displacement at o from a Clamp and Locator 77

93 Figure 8.11: Finish Cutting Forces is Applied at o from a Clamp and Locator Figure 8.12: Displacement Vector Sum at o from a Clamp and Locator 78

94 Figure 8.13: X-Component Displacement at o from a Clamp and Locator Figure 8.14: Y-Component Displacement at o from a Clamp and Locator 79

95 Figure 8.15: Z-Component Displacement at o from a Clamp and Locator Figure 8.16: Finish Cutting Forces is Applied at -45 o from a Clamp and Locator 80

96 Figure 8.17: Displacement Vector Sum at -45 o from a Clamp and Locator Figure 8.18: X-Component Displacement at -45 o from a Clamp and Locator 81

97 Figure 8.19: Y-Component Displacement at -45 o from a Clamp and Locator Figure 8.20: Z-Component Displacement at -45 o from a Clamp and Locator 82

98 Figure 8.21: Side View of X Displacement at o from a Clamp and Locator Figure 8.22: Side View of X Displacement at o from a Clamp and Locator 83

99 Figure 8.23: Side View of X Displacement at -45 o from a Clamp and Locator 8.4 ANSYS Finite Element Model Results for Chapter 5 The ANSYS finite elements results were plotted for Chapter 5 when nine experiments were performed for the Design of Experiments. The experiment number one was performed in Chapter 4. Thus, the following figures represent experiment number two to nine. 84