The fabrication of free form sculptured surfaces such as those for airfoils, turbine blades, C H A P T E R 1

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1 C H A P T E R 1 Introduction The fabrication of free form sculptured surfaces such as those for airfoils, turbine blades, automotive components, shoe soles, etc. requires a significant effort toward the design and manufacturing of the custom-engineered (special) cutting tools correctly. Development of accurate geometric models of special cutting tools holds a key position to create these surfaces. Traditionally, the geometry of cutting tools, including customized cutters, has been defined using the principles of two-dimensional projected geometry. Such definitions are twodimensional (2D) in nature and 2D modeling is insufficient to support current analysis, prototyping and manufacturing technologies as they lack "information completeness". The growth of curve and surface modeling in the realm of Computer Aided Geometric Design (CAGD) [38, 85, 109] helps a designer to accurately model the complex geometry of customized cutting tool surfaces.

2 Chapter 1. Introduction 2 This chapter develops the background for the present work and discusses the need to take up this work. It presents a review of available relevant literature. Objectives of the present work along with methodology adopted to accomplish them are also discussed here. 1.1 Background With the growth in technology, the expectations from the product have greatly increased and the demand on product s profile has started becoming more and more complex. The need is for differently shaped products to capture the customers expectations. The commercial success of a new product is strongly influenced by the highest possible quality and productivity achieved. This can be achieved only if the product development process can be realized in a relatively small time period with the best precise solution. To realize any surface accurately using conventional subtractive machining process, two most important factors to be properly controlled are: geometry of the cutting tool and the kinematic structure of the machine tool. The cutting tool geometry along with the relative motion between the cutting tool and the work piece generates the profile of the cut. Even the shapes not possible to manufacture earlier are achievable due to increased control of machine tools by CNC controllers [146]. Thus, the stress is towards generating accurate geometry of cutting tools. However, for machining special (complex, free-form) surfaces, the development of special cutting tools, usually occurs through the time consuming trial and error iterations, caused by limited, principles of projected geometry approaches. The current state-of-affairs deals with geometric definition of cutters in terms of 2D based orthographic representations and nomenclature [30, 33, 149]. This 2D based projected geometry approach is tough to visualize and understand particularly for complex objects. Many times, it leads to communication gap. A 2D based model cannot be directly used for any technological application. Precise three-dimensional (3D) geometric models would be immensely beneficial in reducing the number of experiments required for tool design and machinability evaluation. 1.2 Motivation Special revolving cutters are very important cutting tools for many manufacturing industries. Their geometry, dimensional accuracy and performance along with the quality of cutter s cutting surface, directly influence the precision, efficiency and quality of the machined

3 Chapter 1. Introduction 3 products. In machining special (complex, free-form) surfaces, existing technology basically depends on 3-axis / 5-axis CNC machine tools using ball end milling or similar cutters [9, 40, 49, 87, 124, 135]. The existing technology of using ball-end milling cutter to generate varied profiles has its own disadvantages. Custom-engineered special cutting tools are required not only to machine complex surfaces but also as special toolings for mass manufacturing. Replacing a number of tools with just one will generate savings in many aspects as well as lead to quality enhancement, time saving, cost effectiveness, etc. The evolution of customdesigned products and their fabrication through machining has placed stringent demands on customized cutters due to existence of freeform and complex surfaces in its geometric profile. An accurate mathematical model of a customized cutter is important for its geometric design. Cutting tool manufacturers and advanced users also require more appropriate definition of cutting tool geometries. Further, as the three dimensional definition is available it will become a lot easier to design the special cutting tool as per the specified application. A 3D parametric based geometric model if developed in a generic manner can represent a range of similar cutters. To create a comprehensive geometric model that could take into account the wide variety of tool geometry is rather difficult and this may be the primary reason that the researchers have not been attracted towards modeling them and the field remains largely unexplored. At present, the geometry of cutting tools is generally expressed in a mathematical form not suitable for further manipulations. The advancements in the domain of Computer- Aided Geometric Design (CAGD) allow a designer to directly define the three-dimensional (3D) parametric models of the cutting tool surfaces [57, 59]. The proposed 3D models of the customized cutter can further be used for the Finite Element based engineering analysis, stress analysis, simulation of the cutting process, grinding / manufacturing of the cutter, etc. For this reason, studies relating to customized cutters (their unified representation scheme, accurate mathematical 3D model, dedicated cutting tool design software along with downstream technological usage) are both broad in scope and versatile in application. 1.3 Problem Definition This works makes an attempt to develop a novel unified representation scheme that can provide direct 3D generic definitions of custom-engineered (special) cutting tools for (a) their correct design and fabrication and (b) downstream technological applications. In view of the

4 Chapter 1. Introduction 4 importance of developing special cutting tools to generate free form complex surfaces and mass manufacturing, we formally state the problems undertaken in this work as follows: (i) The geometry of a generic custom engineered cutting tool is to be defined using geometric modeling approach to develop its three dimensional model. 3D nomenclature that includes 3D rotational angles and other dimensional parameters is to be specified for the geometry of cutting tools. (ii) A cutter design interface is to be developed which may help render the generic definition of custom-engineered cutting tools directly in any CAD modeling environment to validate the methodology and provide convenience in downstream technological applications. (iii) The generic CAD model of custom-engineered cutting tools acts as a core model and the family (a variety) of special cutting tools may be generated by suitable modifications in the parameters of generic cutters. Besides, a few special cutters need to be developed and their geometry is optimized as per the specific application 1.4 Manufacturing Processes and its Classification Manufacturing can be simply defined as value addition processes by which raw materials of low utility and value are converted into high utility and valued products. The process of manufacturing imparts some functional ability with definite dimensions, forms and finish to raw materials of inadequate material properties and poor or irregular size, shape and finish. The core of manufacturing operations is the process responsible for transforming the shape, size and finish of the object [42, 58]. Manufacturing processes can be broadly classified in three major groups, namely, (i) subtractive machining (removal processes), where material is removed from the blank due to relative movement of a cutting tool over a workpiece; (ii) additive manufacturing, that deposits material in an empty volume or layer so as to yield the desired complex configuration and (iii) shaping or forming processes that deform plastically a given volume or sheet of material. Figure 1.1 shows the different classes of manufacturing processes. The purpose of all these manufacturing processes is shape realization.

5 Chapter 1. Introduction 5 Manufacturing Processes Subtractive Machining Additive Manufacturing Forming Processes Conventional Machining Non-traditional Machining Processes (e.g. EDM, USM, ECM, USM, AJM, WJM etc.) Conventional e.g. Welding, Soldering etc. Non Conventional (Rapid Prototyping Processes) Conventional like casting, forging etc. Non conventional like 3D laser forming, laser bending etc. Figure 1.1: Classification of Manufacturing Processes [125] 1.5 Metal Cutting Basically, machining is a semi-finishing or finishing process where the excess material is removed from the preformed blanks in the form of chips so as to impart required or stipulated dimensional and form accuracy as well as surface finish. It is perhaps the most versatile manufacturing process [5, 111]. Besides, it provides a higher degree of geometric complexity to the work. The cutting tool is one of the important elements in realizing the full potential out of any machining operation. It is the relative movement of the cutting tool(s) with respect to the work surface(s) that produces the machined surface. The material to be removed is pressed against the hard edge(s) of the cutting tool and made to flow. The material is removed due to shear deformation over the face of tool [13]. A cutting tool consists of two groups of functional parts. The first group consists of edges and surfaces responsible for actual cutting operation. These are critical elements of a cutting tool and form cutting element(s) or teeth of the cutter. The second group consists of shank, hub, disk, cylinder etc. on which the cutting elements are established. The elements of this group form cutter body and are non-critical as they are meant to complete the geometry. The geometry of a cutting tool consists of face(s) or rake surface(s), flanks, land, cutting

6 Chapter 1. Introduction 6 edges and the corner(s) or nose [42, 149]. Face is the surface of the cutting tool along which the chip flows out, while flanks are the surfaces facing the workpiece. The land is that part of the back of the tooth adjacent to the cutting edge which is relieved to avoid interference between itself and the surface being machined. The cutting edge is the intersection of the face of the tooth with the leading edge of the land. Based on the geometry of cutting elements, the basic cutting tools are of single-point or multi-point design, although they may differ in appearance and in their methods of application Single-Point Cutting Tools A single-point cutting tool refers to tool for turning, shaping, planing, boring etc., that has one shank (or body) and one cutting element in the form of a cutting edge at one end [88]. This cutting edge is often designed to be at one end of a solid piece of steel, either formed or in the form of an insert, held to the body of the tool by brazing, welding or mechanical means [61]. They are commonly used in lathes, shapers, planers and similar machine tools. During machining a single-point cutting tool is provided translatory motion while the job is rotated or translated Multi-Point Cutting Tools A tool with a series of two or more cutting elements / edges (points) on a common body is known as multi-point cutting tool [88, 111]. These include double (two) point cutters: e.g., drills and multipoint (more than two) cutters: e.g., milling cutters, broaching tools, hobs, gear shaping cutters, etc. The majority of multi-point cutting tools are provided rotary motion for shape realization as shown in Table 1.1 [13]. The common machining operations associated with multi-point tools - milling, drilling - are introduced in the following subsections. Milling Milling is a subtractive shape realization process that removes a predetermined amount of material from the work piece with the cutting tool rotating at a comparatively high speed. The cutting tool used for the purpose has multiple cutting teeth. The characteristic feature of the milling process is that each milling cutter tooth removes its share of the stock in the form of small individual chips during each revolution from the advancing work [30, 33, 149].

7 Chapter 1. Introduction 7 Table 1.1: Relative Motion of various Cutting Operations Operation Motion of Cutting Tool Motion of Workpiece Turning Translation Rotation Shaping Translation Intermittent Translation Planing Intermittent Translation Translation Milling Rotation Translation Drilling Rotation and Translation Fixed Boring Rotation Forward Translation Hobbing Rotation and Translation Rotation Surface Grinding Rotation Translation A wide variety of operations can be performed during milling since both the workpiece and the cutter can be moved relative to one another independently or in combination. Milling consists of two motions: rotation of the cutter about its axis which is primary cutting motion, and a feed motion. In some applications, the feed is given to the workpiece while in other the workpiece is held stationary and the cutter is traversed across at a given feed rate. The feed motion is along a straight line in milling flat and cylindrical surfaces; it is rotary in milling surfaces of revolution and helical in milling helicoidal surfaces. Milling operations are performed on different machines with different type of cutters. Milling cutters are bodies of revolution, rotating about their axes, with equally spaced cutting teeth on their surfaces (Figure 1.2). Applications of milling include the production of flat or contoured surfaces, slots, profile surfaces, grooves, recesses, bodies of revolution, threads, and other configurations. Milling cutters are made in large range of sizes and types for generating regular and irregular shaped surfaces on the workpiece [33]. They may be classified in several different ways, e.g. based upon Construction characteristics: They may be of solid type, with teeth and body integral; or carbide or cast alloy (brazed) tipped solid cutters; or inserted-tooth type, with removable teeth held and rigidly locked in suitable cavities in the body. Inclination of the teeth: The teeth may be straight, parallel to axis of rotation; or helical, at an angle known as helix angle.

8 Chapter 1. Introduction 8 Relief of the teeth: The teeth may be profile-relieved, when the relief surface is comparatively simple flat or helical and the relief is obtained by grinding a narrow land back of the cutting edge, viz. slab or plain milling cutters, side milling cutters, slotting cutters, end milling cutters, face milling cutters, etc; or form-relieved, when the relief surface is curved and the relief is obtained by grinding the faces of the teeth, viz. form cutters, gear milling cutters, spline shaft cutters, thread milling cutters etc. Method of mounting: The milling cutters can be made arbor mounted, with a center hole for mounting on an arbor; or shank type; or spindle mounted, with the back recessed for bolting directly on the spindle nose. Hand of rotation and hand of helix: Milling cutters may be made for either right or left hand of rotation, and with either right or left hand helix. Purpose or use of the cutter: Milling cutters can be of type T-slot cutter, Woodruff key seat cutter, Gear or Thread milling cutter. In the broader perspective, milling cutters may fall into the following two categories: Standard Milling Cutters: These conform to dimensions approved by the international standards bodies (e.g. ISO, ASA, DIN, BS). The dimensional standards, relating chiefly to cutter diameter and width, size of center hole, width and depth of keyway, etc., have been adopted by cutter manufacturers. Special Milling Cutters: These are designed for work on special jobs. They may or may not have standard dimensions, and do not conform to any generally accepted standard. They are normally designed to combine several milling operations in one, and may be used for milling regular or irregular surfaces. Drilling The operation where the tool is rotated and fed along its axis of rotation while the work piece remains stationary is called drilling [33, 88]. The most common type of drilling is the operation with a twist drill to generate a hole. A twist drill with a shank has two (or more) cutting edges, each responsible for removal of work material. The tool used for drilling is the drill bit. The drill bit is a multipoint, end cutting tool. It cuts by applying pressure and rotation to the work piece, which forms chips at the cutting edge. There are a variety of drill styles that each serves a different purpose.

9 Chapter 1. Introduction 9 Figure 1.2: Canonical View of Milling Cutters [111]

10 Chapter 1. Introduction Custom-Engineered Cutting Tools A customized form tool is a cutting tool having one or more cutting edges with a defined profile or contour that will be reproduced as the desired form on the work surface (Figure 1.3). Basically, the geometry of cutting elements / edges (points) of form tools can be of single point or multipoint design. Besides, form tools may be classified according to type of cross-section, which may be (a) flat form tools, (b) circular tools and (c) end-form tools (Figure 1.4) [13]. Flat or block tools are further classified according to setting of the tool with respect to work piece like radial-fed or tangential-fed type. Further form tools are also classified with respect to orientation of tool axis in relation to work piece axis. 1.6 Need of Geometric Modeling for the Design of Custom- Engineered Cutting Tools Geometric modeling is defined as generation of computer-compatible mathematical definition of geometry / shape of an object [38, 85]. In geometric modeling, we define a shape by a set of mathematical statements and logical relations satisfying a set of axioms. These axioms we interpret as true statements about the model, and the consequent general properties of the model we analyze and evaluate as representative of the modeled object itself. Geometric modeling is the process of creating these statements and relationships. Besides, geometric modeling is the construction or use of geometric models. Geometric models can be built for objects of any dimension in any geometric space. Basically, 2D, 2½D and 3D geometric models are extensively used in computer graphics. 2D models are important in computer typography and technical drawing. 2½D and 3D models are central to computer-aided design and manufacturing, and many applied technical fields such as geology, medical image processing, etc. Computer-aided geometric design (curve and surface modeling) (CAGD) and solid modeling are the branches of geometric modeling. Computer-aided geometric design (CAGD) applies the mathematics of curves and surfaces to modeling, primarily using the parametric equations of differential geometry [109]. Solid modeling allows us to combine simple shapes to create complex solid models. Solid modeling has its mathematical foundations in topology, algebraic geometry and Boolean algebra. Geometric modeling has applications in the fields of

11 Chapter 1. Introduction 11 Figure 1.3: A few Custom-Engineered Special Cutters [ , ]

12 Chapter 1. Introduction 12 Customized From Tools (according to cross-section) Flat or Block (according to setting of cutting edge) Circular (according to orientation of tool axis) End-Form Radial Tangential Parallel Angular (skiving) Figure 1.4: Classification of Customized Form Tools [13] computer animation, computer graphics, computer vision, robotics, CAD/CAM, fluid dynamics, and structural analysis. Design and manufacturing of special cutting tools is a critical segment of any manufacturing system. Traditionally, cutting tools are defined by the specification approach (ISO standards). Such definitions are complicated. Further, they are not unified and cannot be used for computer based manufacturing / grinding and engineering analysis. With recent developments in the area of conjugate geometry and availability of better definitions of curves, surfaces and solids, cutting tools can be designed and manufactured automatically [60], without depending on the expertise of fast vanishing experienced tool designers. Machining of free form sculptured surfaces is possible due to increased control of machine tools by CNC controllers using ball end milling and other related cutters. The existing technology of using ball end milling cutter to generate varied profiles has its own disadvantages. Thus, the stress is towards generating the accurate geometry of special cutting tools. This can be achieved by geometric modeling techniques. In the present times, accurate geometric models of special cutting tools are essential, as increasingly, the design and manufacturing is performed in the virtual world, called virtual prototyping and manufacturing [54, 89, 95] before actual machining is carried out.

13 Chapter 1. Introduction 13 Recent developments in the area of CAGD have led to various mathematical definitions of analytic and synthetic uniparametric curves and biparametric surfaces [39, 85, 109, 157]. These biparametric surfaces can correctly model any free formed sculptured surface. This has led to tremendous growth in the development of CAD models of complex shaped objects. However, the area of application is still mainly confined to automobile and aerospace sectors and any work that is undertaken in the direction of developments of CAD models of cutting tools is not known. The need of geometric modeling of the customengineered (special) cutting tools can be further stressed due to (i) Cutting tool surfaces are complex, hence their proper definitions are required. (ii) Cutting tool standards need upgradation as they depend on 2D definitions. (iii) Tool and cutter grinders are having a focused shift from manual to computer controlled. (iv) Cutting tools are increasingly manufactured and sharpened by CNC machine tools and in CNC machines, programming is crucial, particularly of free form surfaces. Convenience and accuracy of CNC programming improves with the CAD definition of the object. (v) Though there exist many powerful CAD softwares today, but a dedicated cutting tool CAD software is yet to be designed. (vi) None of the existing CAD softwares contain any cutting tool design module. (vii) Geometric modeling enables the designer to generate centralized and integrated database. Such a database for special cutting tools can convey design information for a range of downstream engineering and manufacturing applications. (viii) A generic CAD model of the available custom-engineered cutting tools acts as a core model and new special cutting tools can be generated by modifying its parameters and activities like rendering, simulation, analysis, manufacturing etc. can be performed using this core model. 1.7 Review of Literature The prediction of cutting forces in machining along with mechanics and dynamics of cutting tools are the areas that have captured major attention of researchers in the field of manufacturing. Even in these areas also, the stress is towards milling processes and milling

14 Chapter 1. Introduction 14 cutters due to their wide spread usage. With more and more components having sculptured surfaces, CNC machining is in greater demand. These surfaces are normally generated on CNC machines by ball end mills and this has made the researchers' focus on developing cutting force models for end milling. These models approximate the geometry of cutting tools by presenting them in two-dimensional space. The end geometry of the ball and flat end mills is modeled by dividing cutting edges into infinitesimal elements is proposed by Abrari and Elbestawi [1], Zheng et al. [161], Li et al. [72], Zhang et al. [160], Wang et al. [142]. Wan and Zhang [138] have done a systematic study on cutting force modeling methods in peripheral end milling in the presence of cutter runout. The analytical representation of helical flute geometry is proposed by Lee and Altintas [68], Gradisek et al. [41], Yucesan and Altintas [156], while cutting force prediction model is combined with models for cutter deflection and machining accuracy to study surface errors for end milling by Liu et al. [78-79], Ratchev et al. [106] and Xu et al. [152]. In all these approaches, mechanistic or analytical models for predicting cutting forces are developed based on the input data of work piece material properties, tool geometry and cutting conditions. They have shown that the instantaneous cutting force model has better prediction ability than the model with constant cutting force coefficients. The work in the area of modeling the mechanics and dynamics of milling cutters is to predict factors like chip thickness, cutting force, vibration, torque, power, surface finish etc. Smith and Tlusty [120] have reviewed frequently used models of force and deflection computation for milling process and highlighted their validity, applications and limitations while mechanics and dynamics of general milling cutters, especially helical end mills and inserted cutters has been reported by Engin & Altintas [36-37]. Here, the end mill geometry is modeled by helical flutes wrapped around a parametric envelope and the chip thickness at each cutting point on helical flute is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and work piece. Chiou et al. [25] has demonstrated an instantaneous shear plane based computational model to predict the cutting force components for end milling. A comprehensive integrated static and dynamic cutting model for ball end milling processes has been presented by Altintas and Lee [2-3]. Lee et al. [69] have designed a face milling cutter and developed a cutting model to improve its dynamic characteristics. Chang [18] has also presented a new predictive force model and proposed high efficiency face milling tools. Besides this, a simplified and efficient calibration

15 Chapter 1. Introduction 15 of a mechanistic cutting force model for ball-end milling is developed for a wide range of cutting conditions by Azeem et al. [8], for sculptured surfaces by Sun et al. [124] while a novel cutting force modeling method based on instantaneous cutting force and instantaneous uncut chip thickness measurement for cylindrical end mill is proposed by Wan et al. [139]. A review of the above literatures shows the calibration procedure of instantaneous cutting force coefficients during end milling from both the theoretical analysis and the numerical simulation. Also, it is essential to further improve the prediction accuracy of cutting forces and algorithms to concrete implementations for sculptured surface machining. Another domain of interest in manufacturing research is the design of milling cutters. Vickers and Quan [135] have presented a comparison of insert-based flat end mills and solid ball-end mills in machining low curvature surfaces. Chen and Lin [20] have developed design and manufacturing models for ball-end cutters based on envelope theory while Kim and Ko [62] has discussed the design and manufacturing technology for end mills. Chen et al. [21-22] has presented manufacturing models to produce concave cone end milling cutters. Work on cutters other than end mills include geometric modeling of single point cutting tools by Rajpathak [103], design of cutters to manufacture helicoidal surfaces by Karunakaran and Dhande [59], design of hob cutters for generating the multi-cutting angles (radial rake angle, relief angle, and clearance angle) of helical cutting tools is proposed by Liu and Chang [77] and design and manufacturing of hob for machining of precision involute gear by Radzevich [99, 101]. A universal hypoid generator mathematical model for face hobbing spiral bevel and hypoid gears has been developed by Shih et al. [119]. Vasilis et al. [133] has proposed simulation of gear hobbing through three-dimensional kinematics modeling. Author has described an effective and factual simulation of gear hobbing, based on virtual kinematics of solid models representing the cutting tool and the work gear. CAD-based simulation of the hobbing process for the manufacturing of spur and helical gears is done by Dimitriou and Antoniadis [32]. Carlsson and Stjernsoft [15] have calculated the geometrical shape of toolwork interface for rotary tools. Very recently, Shi and Liu [117] have discussed the actual geometry of the cutting tool involved in machining based on their three-dimensional geometric models. The above researchers have emphasized more on manufacturing models, understanding the machining mechanism based on the three-dimensional geometry of the cutting tool. The resulting 3D data allows the effective utilization for further research such as

16 Chapter 1. Introduction 16 prediction of the cutting forces, tool stresses, and wear development as well as the optimization of the cutting tool design process. Simulation of milling processes is also a major area of research in manufacturing. The problem of defining the geometry of a machined surface is essentially a problem of defining the boundary of the swept volume of the cutter. Spence and Altintas [122] have discussed a constructive solid geometry (CSG) based system to simulate the milling process and assist in online monitoring and control tasks. Mounayri [86] have modeled part as boundary representation (B-rep) model and tool cutting edges as cubic Bezier curves to evaluate cutter swept volume, material removed and tool-part immersion geometry. An approach to integrate solid modeling with milling process simulation and its applications in machining is shown by Spence et al. [123]. Imani and Elbestawi [50] have developed precise B-rep model of the cutter swept volume to update part being machined for each NC block, evaluate instantaneous chip geometry and model feed marks and scallops on the machined surface. 5-axis sculptured surface machining is simulated using discrete geometric models of the tool and work piece to determine the tool contact area and a discrete mechanistic model to estimate the cutting forces is presented by Fussell et al. [40]. Simulation of flank milling processes has been discussed by Bedi et al. [11] as well as Larue and Altintas [67]. Also, Li et al. [70] has suggested an easier way to design the surface for flank milling, especially when the guiding curves are nonrational B-spline curves (NUBS). A solid model-based milling process simulation and optimization system integrated with CAD/CAM is developed for 3-axis end milling by Li et al. [73] while modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces is presented by Rao and Rao [105]. These researches contribute towards various surface design methods used to design the surface for flank milling effectively Geometry of the twist drills has been studied by Armarego and Kang [6], Ehmann [34], Ekambaram and Malkin [35], Kaldor et al., [56-57], Sheth and Malkin [115], Ko [63], Shatla and Altan [113], Zhang et al. [159], Lacalle et al. [65]. However, the work is not in the direction of development of generalized CAD (Surface/Solid) model for the twist drills. These works are to evaluate the shape of drill profile for a given milling cutter (or grinding wheel) or identification of geometry of a milling cutter (or grinding wheel) used to generate a given twist drill. The resulting data and information have to be fed to an experienced tool engineer to manufacture or ground the twist drill. Other work on drills includes drill analyses to modify its designs by Bhattacharyya et al. [14], Shi et al. [116], Lin et al. [74], Ren and Ni [108], Paul

17 Chapter 1. Introduction 17 et al. [92], Zhang et al. [158], Vijayaraghavan and Dornfeld [136] and mathematical modeling for multiflute drill designs by Wang et al. [140], Hsieh and Lin [43], Hsieh [44]. Optimizing the design of the milling cutter based on finite element based engineering analysis is done by Jha and Hornik [52], Shih [118], Tawfiq and Shahab [130]. Also, simulation of metal cutting process using finite element method has been studied by Shet and Deng [114], Ozel and Altan [90], Lo [81], Ozel and Zeren [91]. To improve the accuracy of the model of milling operations, three-dimensional finite element modeling is performed by Pittala and Monno [94] for the insert based face milling and by Soo et al. [121] for ball nose end milling. Considerable work has been done by the researchers to study the conventional single point [45, 127, 134] and multi-point cutting tools. For producing the sculptured complex surfaces, we are heavily dependent on CNC machine tools using ball end cutters. Basically, generation of sculptured free form surfaces using NC / CNC machines has been worked by Hwang and Chang [49], Warkentin et al. [144], Choy and Chan [27], Wei and Lin [146], Naserian et al. [87], Ren et al. [107]. Recently, Yau and Tsou [153] has presented the use of adaptive voxel data structure in conjunction with the modeling of a universal cutter for the development of an efficient and reliable multi-axis simulation procedure. Very few customengineered cutting tools have drawn the attention of the research fraternity although they are good candidates for manufacturing free form special surfaces as well as for mass manufacturing. The reasons for this could be possibilities of various designs of customized cutters, their complex geometries and difficulties in defining these complex, free form surfaces mathematically. To create a comprehensive geometric model that could take into account this wide variety of complex tool geometry is rather difficult and this could be primary reason that the researchers have not been attracted towards modeling them and the field remains largely unexplored. In fact, Mendoza et al. [83] has developed a new milling cutter for Aluminium honeycomb structures used in the air space industries. Kuo and Wu [64] have presented a work in the direction of geometric solution for the roller nest mill cutter. Manufacturing models of various customized end milling cutters has been discussed by Wang et al. [143], Chen et al. [19], Chen et al. [23], Hsieh [48], Pham and Ko [93]. Hsieh and Tsai [47] have presented the geometric modeling and grinder design for toroid-cone shaped cutters. Radzevich [98-100] has suggested a novel method for mathematical modeling of an optimized form-cutting tool for machining a given sculptured surface based on R-mapping. The work in

18 Chapter 1. Introduction 18 the direction of development of geometry design of a form milling cutter for precisely obtaining the complex freeform surfaces is done by Wang et al. [141]. Also, work related to the design of a plunge shaving cutter is presented by Radzevich [102] and Liu et al. [76] while a novel hob cutter design is developed by Hsieh et al. [46] for the manufacture of spur-typed cutters. If 3D geometric definitions of customized cutting tools are available then it will be of immense benefit to the manufacturing world due to ease in simulation of a machining process before actual machining, as well as numerous direct applications. Recent developments in the field of geometric modeling now provide designers an elegant and precise approach of specifying the geometry of complex shaped objects [85], Choi [26], Farin [38], Rogers and Adams [109], Zeid [157]. A method for computer-aided design for machining of sculptured surfaces taking the complex machined surface as the nonuniform rational B-spline (NURBS) surface has been discussed by Barari et al. [9], while Tandon et al. [ ] have discussed the modeling of side mills and twist drills in terms of biparametric surface patches. It is found that the conjugate geometry approach can be extended to machining and together with computational models and symbolic algorithms, it can conveniently model different manufacturing processes (Dhande et al. [31], Voruganti et al. [137]). Some recent work in the associated areas that motivated the present work includes, the work by Barone [10], where B-spline curve fitting and sweep surface generation are used for the geometric design of involute gears; an approach to optimize macro-level tool geometry in machining by Kaldor and Venuvinod [55]; about orthogonal parameterization of part and tool surface for transformation of coordinate systems by Radzevich and Goodman [97]; parametric surface rendering mentioning the advantages offered by parametric surface for object modeling by Li [71]; the use of computer-aided design tools in the conception and realization of geometrical sculptures as described by Sequin [112]; task automation for modelling solids with Catia V5 by Cidoncha et al. [28]; computer simulation methodology of modelling tooth flanks of cylindrical gears by Michalski and Skoczylas [84] and the methodology proposed by Pu and Liu [96] for the geometric modeling of cylindrical helix end mill with NURBS solid model which is different from the traditional three-dimensional model. The above mentioned research work shows a way to effectively describe complicated geometric shapes of cutter flanks utilizing computer-aided geometric design approaches. Research in the area of feature modeling of sculptured objects has addressed the need of unified geometric models (Au and Yuen [7], Cavendish [16-17], Kagan et al. [53], Roller

19 Chapter 1. Introduction 19 [110], Tonshoff [132], Ye et al. [154], Liu [80], Yeh and Su [155], Langerak and Vergeest [66]). Modeling and simulation of machining process is an approach to realize high quality machined parts. The shape of the cutting tool is one of the key factors to affect the machining accuracy and dynamic stability. It is difficult to model the exact three-dimensional shape of a special cutting tool since the cutter geometry is very complicated. For modeling any custommade cutting tools, there are no unified representation schemes that can provide direct 3D models for downstream technological applications. In general, the cutting tools are represented by a simplified model [36-37, 86]. These mathematical models are hardly more than a visual and complete model. The proposed approach of modeling surface patches provides unified models of a range of custom-engineered (special) cutting tools. We aim at producing a system of equations in their parametric form to develop an accurate 3D surface based model of customized cutters. 1.8 Objectives and Scope of the Present Work The primary goals of this work are (a) To develop three-dimensional definitions of the existing custom-engineered cutting tools (form, milling, special purpose, etc.) for machining free form / special surfaces as well as for mass manufacturing, and to define in detail its geometric modeling and (b) To design and manufacture new custom-engineered cutting tools for some special applications (where the surface profile to be generated is already known). Besides, we would also like to (i) Develop surface based geometric models of custom-engineered cutting tools in terms of their surface patches using the evolved 3D rotational angles and other dimensional parameters. (ii) Establish a set of 3D nomenclature for specifying the geometry of the special cutting tools. (iii) Interface properly the new generic definition of custom-engineered cutting tools with advanced modeling software for customized applications. (iv) Verify the surface model based definition of the cutting tools using point cloud data (reverse engineering methodology) for the existing tools.

20 Chapter 1. Introduction 20 (v) (vi) (vii) Perform detailed finite element analysis of the model and if need be, modify the design of the cutting tool. Establish relationship between proposed three-dimensional nomenclatures and traditional two-dimensional projected geometry based nomenclatures (if available). Establish generic definition and to develop a unified definition of custom-engineered special cutting tool that may be used for numerous downstream engineering and manufacturing applications. (i) (ii) (iii) (iv) The scope of the present work includes: Establishment of generic CAD model (mathematical definition) of cutting tool surfaces. Establishment of a new CAGD based 3D nomenclature to define the geometry of customized cutting tools. Development of a Cutter design module that acts as an interface for modeling complex tools as well as mechanical components in existing commercial CAD packages. Demonstration of the effectiveness of the new definition. 1.9 Flow of Work The approach adopted to accomplish the present work is by (i) (ii) (iii) (iv) (v) Critically reviewing and classifying the custom-engineered (special) cutting tools on the basis of their geometric complexity and application. Selecting particular application areas like engineering industry, leather industry, plastic industry, wood carving / shaping industry, etc. and designing the customengineered cutting tool for their engineering applications Identifying critical or functional and non-critical elements of the cutting tool. Developing appropriate mathematical biparametric definitions for unbounded functional surfaces of the cutting tool. Defining the parameterized geometry of bounded curved surfaces by establishing the limits of parameters of the unbounded surfaces, understanding the topology of cutter and ensuring continuity conditions.

21 Chapter 1. Introduction 21 (vi) Specifying the cutting tool geometry in terms of 3D nomenclature (3D rotational angles i, i and i ) and various other dimensional parameters, collectively termed as geometric parameters. In 3D nomenclature, angles i, i and i are the angles of (vii) (viii) (ix) (x) (xi) (xii) (xiii) rotation of surface patch about X, Y, Z axis respectively, where positive i rotation directions about the coordinate axes are counter clock wise, when looking toward the origin from a positive coordinate position on each axis. Modeling the transitional surfaces of the surface patches. A transitional surface forms a smooth localized transition between neighboring surfaces at their edge of intersection. Developing an interface (Cutter design module) to pull the generic definition of custom-engineered cutting tools directly in a CAD modeling environment for further validation. Selecting the representative custom-engineered cutting tools and reverse engineer them to collect point cloud data to compare surface features with that of actual cutting tools. Performing detailed finite element analysis of the selected cutter Redesigning and optimizing the geometry of the cutter as per the feedback of analysis. Manufacturing a few selected special cutting tools for technology demonstration. Demonstrating the utility of the new convention through direct engineering applications on the proposed model Advantages of the Proposed Methodology The advantages of an accurate 3D definition of a complex object like a cutting tool include: Virtual and Physical Prototyping for verifying the geometry and topology of the object. Implementation of the NURBS curve and sweep surfaces for the shape design of the cutting edge / surfaces for the customized cutter gives more control for cutting edge profile modification and generation of varied surface profiles.

22 Chapter 1. Introduction 22 The cutting tool design modeler developed in the course of this work can also act as a module of any existing commercial CAD packages. Simulation of CNC machining or grinding process before actual cutting operation can be performed. Geometric analysis of tool wear through Reverse Engineering (Surface-point cloud comparison) can be done easily and accurately. Detailed finite element analysis can be performed on the detailed 3D CAD model of the cutter and one can have more precise results for stress, strain, displacements, etc. during machining The Layout of the Thesis A brief overview of the work carried out in the thesis and organization of the same are summarized below. Chapter 1 presents the background, motivation and problem definition of the thesis work. Here, brief information is given for the manufacturing processes, cutting tools available and the need of geometric modeling in the design of special cutters. It is followed with a brief review of the relevant literature. This chapter concludes with the objectives and scope of the work along with the methodology adopted to accomplish the work. Geometric modeling of a flat end mill is presented in Chapter 2. The chapter develops detailed surface models of the flat end mill and a modeling algorithm is proposed here. Further, the implementation of the algorithm is performed in OpenGL and CATIA V5 environment for the validation of the methodology. One of the downstream technological applications of the 3D model in terms of finite element based engineering analysis of the cutter is also presented and results are compared. Chapters 3 deal with one of the existing insert based custom-engineered form milling (CEFM) cutter. In this chapter, a unified geometric model of the insert and the cutter body of the CEFM cutter is developed. The approach is established by rendering the 3D cutter model, through Cutter design interface (developed during the work). The accuracy of the proposed model in also verified through Reverse Engineering (RE) technique. The design improvements and redesigning of the special shaped milling cutters for a few applications are also discussed here.

23 Chapter 1. Introduction 23 Chapter 4 deals with a novel design of a generic multi-profile form milling (MPFM) cutter, developed for machining multiple sculptured surfaces. The work develops a 3D based representation scheme of generic MPFM cutters in terms of NURBS curves along with 1-rail and 2-rail sweep surfaces. Shape design of a generic tooth and the cutter body is discussed in detail. The chapter also presents the modeling algorithm and the implementation of the methodology. Chapter 5 presents the development of a novel multi-radius form milling (MRFM) cutter. Force and torque measurement is performed during cutting simulation for the novel MRFM cutter and the traditional concave milling cutter and the results are compared. The chapter concludes with an example of finite element analysis of the novel cutter with the actual cutting conditions. Chapter 6 summarizes the significant findings of the work performed, outline the current limitations raised by the proposed methodology as well as provide some recommendations for future work that would further enhance the unified representation scheme along with design methodology and modeling of various custom-engineered (special) cutters that dominate mechanical machining industries.