PROCESS PLANNING FOR SHAPE DEPOSITION MANUFACTURING

Transcription

1 PROCESS PLANNING FOR SHAPE DEPOSITION MANUFACTURING a dissertation submitted to the department of mechanical engineering and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy By Krishnan Ramaswami January 1997

2 c Copyright 2000 by Krishnan Ramaswami All Rights Reserved ii

3 I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Friedrich B. Prinz (Principal Adviser) I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Kosuke Ishii I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David Beach Approved for the University Committee on Graduate Studies: iii

4 Abstract Solid Freeform Fabrication (SFF) refers to a class of rapid manufacturing process that builds parts by incremental material deposition and fusion of thin 2-1/2 dimensional layers. Over this past decade, SFF has taken the manufacturing industry to new heights. However, parts produced by SFF processes exhibit a stair-step surface texture due to the presence of 2-1/2 dimensional layers and exhibit limited material properties. These issues are addressed by a modified SFF process called Shape Deposition Manufacturing. Shape Deposition Manufacturing (SDM) is a novel layered manufacturing process in which multi-material structures with embedded components can be fabricated. In SDM, the layers are truly three dimensional in nature and are built using a combination of material addition and material removal processes. The need for an automated and robust process planner is more in the case of SDM as it attempts to build fully functional parts directly from CAD models. This thesis focuses on the process planning issues in Shape Deposition Manufacturing. The major issues in process planning for SDM involves the generation of 3-D layers and generation of deposition and CNC cutter paths for these 3-D layers. In SDM, the CAD model is decomposed into 3-D layers of varying thickness based upon both geometric and material criteria. The layers are further decomposed into manufacturable volumes called compacts. Silhouette edges and silhouette loops are identified to help the decomposition of models into 3-D layers and compacts. Unlike techniques used in existing SFF methods which divide models into equally spaced slices, the present algorithm decomposes models into compacts which are iv

5 not necessarily planar and equally spaced. Solely based on geometric evaluations a feasible sequence of material addition and removal processes is found for these compacts. Each compact is deposited to the near-net shape using material deposition techniques. Deposition paths are generated for the 2-D cross-section obtained by the XY projection of the compact. The compact is then machined to the required shape through a series of CNC cutting operations. The absence of fixturing problems and tool accessibility problems helps in fully automating the generation of CNC cutter paths. Several parts of varying complexity were built using this process planner and the results will be discussed. v

6 Acknowledgements I take this opportunity to express my sincere appreciation to my adviser Prof. Fritz Prinz for his support and guidance in pursuing this research. He kept me free of financial worries and provided the much needed encouragement over the last four years. He provided an excellent research atmosphere that was very helpful in the successful completion of this work. I would like to thank Prof. Kincho Law for serving as the chair of my thesis committee. I would also like to thank the other members of my thesis committee, Prof. David Beach, Prof. Kos Ishii and Prof. Paul Losleben for their valuable comments and useful suggestions. Thanks are also due to Prof. Yasushi Yamaguchi of Univ. of Tokyo for many exciting and useful discussions. I am grateful to my former colleagues of the Engineering Design Research Center at Carnegie Mellon University and the current colleagues of the Rapid Prototyping Lab at Stanford University for their support and encouragement in the course of this research. In particular, I would like to thank Dr. Levent Gürsöz for the inspiring conversations during the initial stages of this work, and Dr. Robert Merz for his valuable suggestions on different aspects of this work. I would also like to thank Sylvia Walters for efficiently handling all the administrative details. I want to thank my friends in the different parts of this country for their support and friendship. In particular, my friends in Pittsburgh and Bay area deserve special credit for making me feel at home by providing an enjoyable social atmosphere. Finally, I wish to express my special thanks to my father and the other members of my family for their support and encouragement during the course of this work. vi

7 Contents Abstract Acknowledgements iv vi 1 Introduction Problem Statement Solid Freeform Fabrication Review of SFF processes Limitations of SFF Present Work Thesis Outline Shape Deposition Manufacturing The SDM Process Process planning Summary Spatial Decomposition Introduction Overview Definitions Basic concepts Related work Requirements vii

8 3.3 Algorithm Summary Deposition Path Generation Deposition Methods in SDM Generation of deposition paths Types of deposition paths Summary CNC Cutter Path Generation Introduction Rough Cutting Two Dimensional Profile cutting Offset of TwoD Profiles Summary D Cutter Path Generation Finishing operation Collision Free Paths Collision types Collision Detection and Avoidance Summary Software Issues Terminology CAD system requirements CAD System Comparison Implementation issues Applications Geometrically complex parts IMS-T Next generation metal tooling viii

9 8.2.1 GM Injection molding Tool Non-conventional parts Parts with interacting geometric features Conformable, Embedded Electro-mechanical parts Assembled mechanisms Conclusions and Future work Contributions Future work A Kinematic Transformations 99 A.1 Coordinate systems A.2 Kinematic equations Bibliography 104 ix

10 List of Figures 1.1 THE WORKING PRINCIPLE OF SFF THE SDM PROCESS A SCHEMATIC OF THE SDM SETUP DIFFICULTIES WITH CONVENTIONAL CAD/CAM PROCESSES PROCESS PLANNING STEPS IN SDM SEQUENCE OF OPERATIONS TYPES OF SURFACES SILHOUETTE EDGES AND LOOPS PART AND ITS SUPPORT COMPACT DECOMPOSITION OF THE PART COMPACT DECOMPOSITION OF THE SUPPORT CYCLIC ORDERING COMPACT DECOMPOSITION USING INFINITE SWEEP FIRST THREE STAGES OF THE ALGORITHM DECOMPOSITION ALONG CONCAVE SILHOUETTE EDGES MODEL WITH SELF-INTERSECTING PROJECTED SILHOUETTE LOOP DECOMPOSITION TO ELIMINATE SELF-INTERSECTIONS OF PROJECTED SILHOUETTE LOOP SPLITTING SILHOUETTE LOOPS TO AVOID CYCLIC ORDERING COMPACT DECOMPOSITION WITH PROCESS SEQUENCE WORKING PRINCIPLE OF MICROCASTING WORKING PRINCIPLE OF LASER DEPOSITION SYSTEM x

11 4.3 TYPES OF DEPOSITION PATHS MAT OF A RECTANGLE MAT BASED DEPOSITION PATH RECTANGULAR HULL CONSTRUCTION ZIGZAG PATH GENERATION TOWER DEPOSITION PATTERN CONVEX DECOMPOSITION FOR DEPOSITION CROSS HATCH DEPOSITION CNC CUTTING STAGES IN SDM PLANING OPERATION VOLUME V rc TO BE ROUGH CUT STEPS IN THE ROUGH CUT ALGORITHM TYPES OF ROUGH CUT PATHS DEGENERACIES IN CURVE OFFSET OFFSET COMPUTATION OFFSET MODEL WITHOUT DEGENERACIES TYPES OF CUTTER REGIONS SURFACE SHRINKING FOR FLAT-END MILLED REGIONS INTERSECTION CURVES FOR 3-AXIS MILLED REGIONS TYPES OF GOUGING CAD SYSTEM COMPARISON CHART CAD MODEL OF IMS-T COMPACT DECOMPOSITION OF THE SUPPORT IN IMS-T IMS-T2 MANUFACTURED WITH SDM INJECTION MOLDING TOOL CAD MODEL OF TILTED FRAMES SILHOUETTE CURVES AND LOOPS SPATIAL DECOMPOSITION OF TILTED FRAMES TILTED FRAMES xi

12 8.9 VUMAN EMBEDDED ELECTRONIC STRUCTURE CAD MODEL OF SIMON GAME PIECE SDM-SIMON GAME CRANK AND PISTON MECHANISM A.1 COORDINATE SYSTEMS xii

13 Chapter 1 Introduction 1.1 Problem Statement In a global competitive environment that is intense and dynamic, the development of new products and processes increasingly is a focal point of competition. As an example, CAD/CAM systems are required that can quickly produce physical objects directly from CAD models. Rapid fabrication is useful for such manufacturing tasks as prototyping, low-volume parts production and for producing the custom tooling for high-volume production. A new class of manufacturing process, Solid freeform fabrication, addresses this challenge. Solid Freeform Fabrication (SFF) is a class of rapid manufacturing process that builds parts by incremental material deposition and fusion of thin 2-1/2 dimensional layers. Over this past decade, Solid freeform fabrication has taken the manufacturing industry to new heights. However, parts produced by SFF processes exhibit a stair-step surface texture due to the presence of 2-1/2 dimensional layers and exhibit limited material properties. These issues are addressed by a modified SFF process called Shape Deposition manufacturing (SDM).In SDM, layers are truly three dimensional in nature. In SDM, parts are built by incremental material deposition and material removal of these 3-D layers. Naturally a new manufacturing process such as SDM poses new challenges in process planning. This thesis focuses on the process planning issues in Shape Deposition Manufacturing. 1

14 CHAPTER 1. INTRODUCTION 2 The need for an automated and robust process planner is important in the case of SDM as it attempts to build fully functional parts directly from CAD models. The major issues in process planning for SDM involves the generation of 3-D layers and generation of deposition and CNC cutter paths for these 3-D layers. 3-D layers of varying thickness are generated from CAD models. The thickness of the layers are based on geometric and process constraints. Deposition paths are generated for depositing these layers. The deposited layer is then machined to the required shape through a series of CNC cutting operations. The CNC cutter paths are generated for roughing and finishing operations. The generation of CNC cutter paths has to be fully automatic as human intervention with so many layers would render the process impractical. 1.2 Solid Freeform Fabrication Solid Freeform Fabrication [42], [70] is an emerging manufacturing technology that builds parts directly from CAD models using only material addition rather than the conventional material removal processes. SFF, which is also known as desktop manufacturing, is actually a subset to the rapid-prototyping area of net-shape manufacturing. In SFF, a three dimensional solid or surface model of CAD design is geometrically sectioned into planar layers of constant thickness (Figure 1.1). Each cross-sectional planar layer is then sent to a SFF machine. Each layer is created by incremental material build-up of the two-dimensional cross section to a uniform thickness. The overhanging regions of the part are supported either by a sacrificial support material, (Figure 1.1) or by predesigned supports like pillars and trusses that are built into the part model. The support structure is removed after the model building is completed. One of the main advantages of SFF is its ability to build complex parts from a CAD model in a very short time with very little human intervention. With SFF, the prototype of a complex part can be built in a short time, therefore designers and engineers can evaluate a design very quickly. This will help in substantially reducing the total time from concept to full-scale production. SFF is also used in making

15 CHAPTER 1. INTRODUCTION 3 3-D Geometry Decomposition Planar Cross-Section Sacrificial Support Material Primary Material Figure 1.1: THE WORKING PRINCIPLE OF SFF molds and dies with lower toolmaking time and cost. Due to its sequential, layered approach SFF can be used to build parts that would be impractical or impossible to build with traditional approaches. Some examples would be parts with internal channels or parts with mechanisms assembled during fabrication Review of SFF processes Stereolithography (SLA) SLA [33] is the first commercially available SFF process. An elevator platform is submerged in a vat of liquid photo-polymeric resin and held near the surface. A low-power ultraviolet laser scans the surface of the liquid to partially cure the layer. After a layer is built, the elevator drops a user specified distance and a new coating of liquid resin covers the solidified layer and a new layer is scanned by the laser. When all layers are completed, the part is removed, cleaned and post-cured in a fluorescent oven with ultraviolet light to solidify any uncured resin. The part is finished by sanding and/or glass-bead blasting. For parts with overhanging features, support structures are needed. The support structure consists of vertical members extending from the platform to the part. The process planning effort in SLA is trivial. It consists of determination of layer cross-sections and generation of laser scan paths for the cross-section. A more challenging planning effort would be the

16 CHAPTER 1. INTRODUCTION 4 automatic design of support structures [29]. Fused deposition modeling (FDM) In an FDM process [32], a spool of thermoplastic filament feeds into a heated nozzle which traces an exact outline of each cross-section layer of the part. The movement of the nozzle is controlled by a computer. The material solidifies in 0.1s after exiting the nozzle. After one layer is finished, the nozzle moves up a programmed distance in z direction for building the next layer. Due to the short solidification time, FDM process does not need supports. But in some cases, a support may still be required to reduce part distortion. The process planning effort in FDM consists of generation of paths for nozzle motion. In complex parts, design of support structure needs to be handled. Laminated object manufacturing (LOM) The LOM process [19] produce parts from bonded paper, plastic, metal or composite sheet stock. In this process, a layer of sheet material is glued or welded to the previous layer, and then a laser beam follows the contour of the part cross-section to cut it to the required shape. The excess material of every sheet is either removed by vacuum suction or remains as next layer s support. The process planning involves generation of contours to be followed by the laser. Solid ground curing Cubital s Solider [39] process uses a photo-masking technique to solidify a whole layer of liquid photo-polymer at one time. A mask is generated by electrostatically charging a glass plate with a negative image of the layer s cross-section. The mask is then positioned over a uniform layer of liquid photo-polymer and exposed under the ultraviolet light such that only the area shaded by the mask is left in liquid form. The liquid polymer is removed and is replaced with hot wax. After the wax has cooled, the layer is milled flat to the specified thickness. The mask plate is discharged and the cycle is repeated. When the part is constructed, the supporting wax is removed either by melting or by using a solvent. The process planning effort is mainly in the generation of mask.

17 CHAPTER 1. INTRODUCTION 5 Selective laser sintering(sls) SLS [12] uses laser to sinter successive layers of powder instead of liquid. In the SLS process, a thin layer of heat-fusible powder is a spread over a surface by a counter-rotating roller. A laser traces the crosssection of the layer on the powder surface, sintering the portions exposed to the laser beam. The roller spreads another layer of powder over the sintered one and the process continues till the part is completed. The unsintered powder on every layer acts as support during the building process. Post processing of SLS parts involves the removal of binder. The process planning effort involves the generation of laser trajectories. With some materials, the product may suffer shrinkage and warpage due to sintering and cooling. In such cases, an interesting process planning problem would to be offset for shrinkage in the CAD model. Three-dimensional printing (3D Printing) 3D printing [53] is another powder based SFF technique. In this process, an inkjet sprays liquid binder onto a layer of powder tracing out the cross-sectional pattern. Another layer of powder is spread over the previous one and the process is repeated. After completion the part is subjected heat treatment to enhance the bonding of the glued powder and then the unbonded powder is removed. The unbonded powder of each layer serves as the support during the layering process. Generation of cross-sectional pattern for the inkjet is the main process planning issue. During the sintering process there might be significant shrinkage. Modification in the CAD model to account for this shrinkage will be an interesting process planning problem. Ballistic particle manufacturing (BPM) In BPM, a piezo-driven inkjet nozzle is used to shoot molten material droplets that cold-weld onto a previously deposited layer. The cross section of the layer is scanned by the nozzle. After a layer is formed, the base plate is lowered by a specified distance and a new layer is created over the previous layer and this is repeated till the part is completed. Support structures are needed to support overhanging features. The support material that is used is a water-soluble synthetic wax. The process planing effort is to generate deposition paths for the nozzle. In order to avoid excess material in any area, different deposition path patterns have to be explored.

18 CHAPTER 1. INTRODUCTION 6 Recursive mask and deposit(md ) MD [68] is based on thermal spraying in which parts are manufactured by successively spraying cross-sectional layers. A disposable paper mask of the part cross-section is cut out with a laser. The mask is placed on the top layer of the growing part and the material is thermally sprayed through the mask by a robotically manipulated spray gun. Since the material being sprayed can be changed layer by layer or within a layer, multi-material parts can be manufactured by this process. Support is provided by a portion of mask in low melting material and by a sacrificial low melting support material for high melting materials. The process planning effort involves generation of laser beam trajectories to cut each cross-section.[45] Limitations of SFF While the SFF processes are very useful for rapidly creating prototypes, there are inherent limitations in these processes for creating high quality functional parts. The limitations could be classified under geometric and process and material categories. Geometric limitations In all SFF processes, layers consist of two-dimensional cross-sections that are built up to a uniform thickness. This will result in a stair-step surface texture (Figure 1.1). Also, many of the SFF process uses a faceted geometry as the input model. In a faceted representation, a higher tessellation resolution is needed for creating an accurate model. While a higher resolution works for simple models, it becomes almost impractical in the case of complex models with freeform surfaces. Process and Material limitations None of the SFF processes have the capability to produce parts with properties equivalent to those made with conventional manufacturing technologies. SFF parts have to be post-processed before they can be used. Most of the post-processing methods either modify the properties of the material or alter the shape of the part. For example, in 3D printing, liquid infiltration is done in order to produce dense parts and this might affect the resulting material properties. In SLS, parts might suffer shrinkage due to sintering and cooling. In theory, shrinkage can be compensated by modifying

19 CHAPTER 1. INTRODUCTION 7 the original CAD model, but it is very difficult to predict the actual shrinkage for any complex shape. Shrinkage might also cause the buildup of residual stresses. Residual stresses will also be caused due to temperature gradients between layers. These residual stresses might lead to distortions and delaminations. The poor surface quality could also be partially attributed to the material deposition process. During the material deposition process, the surface tension of the material prevents the generation of geometrically well-defined surfaces between layers. The current SFF processes are restricted to a limited set of materials. Processes like SLA, Solid ground curing and FDM are restricted to polymers. Processes like SLS and 3D printing use a wider range of materials but have shrinkage problems. Thus while offering the benefit of building complex parts directly from CAD models in a short time, SFF suffers from poor geometric and material tolerances. On the other hand, conventional methods using CNC machining can deliver high geometric and material quality, but are limited in part complexity. CNC machining is also expensive and requires human intervention for generating CNC cutter paths and for designing and selecting fixtures. Thus a process that combines the layered principle of SFF processes and the accuracy of CNC machining will seem to be a step in the right direction. Shape deposition manufacturing (SDM) is such a process that takes advantage of both material addition and material subtraction. 1.3 Present Work This work addresses the process planning issues in SDM. Being a new manufacturing process, SDM poses new challenges in process planning. As a first effort, the process planning steps in SDM are identified. The major steps in process planning for SDM involves the generation of compacts 1 and generation of deposition and CNC cutter paths for these compacts. An algorithm for the decomposition of any CAD model into compacts is described. This decomposition facilitates the manufacture of complex, 1 A compact is a manufacturable volume in SDM and will be described in Chapter 3.

20 CHAPTER 1. INTRODUCTION 8 multi-material objects in SDM. The concept of silhouette loops is introduced to help in this decomposition process. Silhouette edges are identified and are arranged in the form of silhouette loops and the decomposition requirements are expressed in terms of silhouette edges and loops. The decomposition algorithm also generates the process sequence for these compacts. Algorithms for generating deposition paths are described. Some of the factors that influences the derivation of deposition paths are identified. Algorithms for deriving spiral and zigzag deposition paths are described. Methods are also outlined to derive a few other deposition paths from these two types of paths. Algorithms for generating CNC cutter paths for compacts is described. A fully automated approach for CNC cutter path generation is described that takes advantage of the benefits such as absence of fixturing and tool accessibility problems, offered by the SDM process. A new representation, manhattan solid, has been proposed for generating efficient rough cutting algorithms. The generation of 2-D cutter paths is made robust by proposing a robust algorithm for offsetting 2-D crosssection. A new classification scheme based on the curvature information has been proposed for the surfaces of the model that helps in generation of fully automatic 3-D cutter paths. A great deal of effort was spent in identifying the ideal CAD system for the implementation of these algorithms. The process planner was implemented in two different CAD systems both of which partially met the requirements. The algorithms have been verified by building several complex test parts. 1.4 Thesis Outline SDM is a modified solid freeform fabrication process that can manufacture arbitrarily complex shaped structures directly from CAD models in an automated environment. In addition, the SDM process allows the manufacture of multi-material and embedded structures that cannot be produced with the traditional manufacturing techniques. Chapter 2 gives an overview of the SDM process outlining the various processing steps needed to produce a part. Chapter 2 also outlines the process planning issues in SDM. In SDM, the CAD model is decomposed into 3-D layers of varying thickness based

21 CHAPTER 1. INTRODUCTION 9 upon both geometric and material criteria. The layers are further decomposed into compacts that have all their newly deposited surfaces to be non-undercut. Two approaches to this problem of spatial decomposition are explained in Chapter 3. Both the approaches rely on the generation of silhouette edges. The concept of silhouette edges and the process of generating them will also be explained in Chapter 3 Each compact is deposited to the near-net shape using material deposition techniques. Deposition paths are generated for the 2-D cross-section obtained by the XY projection of the compact. Chapter 4 describes the generation of deposition paths. Due to the nature of the deposition methods, the generation of deposition paths has to avoid revisiting the same position and should not leave any gaps. Chapter 4 also describes the various deposition methods used in SDM. SDM is different than other SFF processes in that it uses both material deposition and material removal processes to build a layer. The material removal process in SDM is done using CNC machining. Chapter 5 describes the generation of CNC cutter paths in SDM. CNC cutter path generation can be broadly separated into two categories, 2-D and 3-D cutter path generation. This chapter mainly deals with 2-D cutter path generation. 2-D cutting can be further classified into rough cutting and 2-D profile cutting, both of which require the offset of 2-D cross-section. Chapter 5 also describes the generation of offsets of 2-D models. Chapter 6 deals with the 3-D cutter path generation. Success has been eluding researchers in automating the generation of CNC cutter paths. It can be partially attributed to fixturing problems and tool accessibility problems. In the case of SDM, the absence of both these problems motivates us to find a method to successfully generate fully automatic 3-D CNC cutter paths. In Chapter 6, such a method is described. The surfaces of the model are subdivided and classified based on the cutting method. Cutter paths are then generated for each of these surface types. During the various process planning steps in SDM, the CAD model undergoes a series of geometric operations. In order to withstand the complex geometric operations, a powerful geometric engine should serve as a backbone for the process planner. Chapter 7 describes the requirements of a geometric engine for the process planner. It also describes the geometric modelers that were used for process planning

22 CHAPTER 1. INTRODUCTION 10 in SDM and some of the implementation difficulties in using those modelers. In Chapter 8 a variety of test parts that were built with the process planner are shown. The process planning problems in building some of those parts are described. Chapter 9 concludes the thesis by outlining the accomplishments of this work. Some of the process planning issues that are not addressed in this work are discussed. Some suggestions for improving some of the methods given in this work are outlined. Appendix A describes the inverse and direct kinematic transforms that are needed to convert the cutter paths into machine codes.

23 Chapter 2 Shape Deposition Manufacturing Solid Freeform Fabrication (SFF) has been widely investigated as a way to automatically fabricate parts directly from CAD models for applications in the area of rapid prototyping and short-run manufacturing. But it remains a goal to be able to directly build high performance metal shapes using SFF techniques. Fully dense metal parts that have accurate dimensions and good surface appearance are often required for such applications as custom tooling and production-ready prototypes. Shape Deposition Manufacturing (SDM) is a manufacturing technique that attempts to address the issue of directly creating fully functional metal shapes. In addition, SDM also has the potential to produce multi-material, functionally graded, embedded heterogeneous structures made of metal, plastic and ceramic materials. 2.1 The SDM Process Shape Deposition Manufacturing [25],[43],[44] is a manufacturing process that creates functional metal parts by incremental material deposition and material removal. It combines the benefits of SFF (handling complex geometries), CNC milling (accurate and precise with good surface quality) and weld-based deposition (superior material properties). The steps involved in building parts with SDM is shown in Figure 2.1. In SDM, the CAD model is decomposed into simpler building block called compacts. The compacts are deposited as near-net shape using a deposition method 11

24 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 12 Figure 2.1: THE SDM PROCESS such as plasma or laser based deposition process. After deposition, each layer is accurately machined to net shape using CNC milling or EDM. Processes such as shot-peening are used to control the build-up of residual stresses. Sensors, electronic components, prebuilt mechanical parts or circuits can be embedded into each layer. After completing one layer, the next layer is deposited and the process is repeated till the part is completed. In SDM, support for overhanging features is provided by the sacrificial support material. Each layer is embedded in the support material. The CAD model of the support structure is obtained as the compliment of original CAD model. The support structure is built along with the original model and follows the SDM cycle shown in Figure 2.1. After the part is completed, the support material

25 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 13 is removed either by a melting or etching process. Multi-material and functionalgradient parts can be built by depositing different materials within each layer following thesamecycle. The SDM setup consists several subprocessing stations for material deposition, material removal, cleaning and stress relieving. The parts are built on a pallet that is transported between different stations by a transfer robot. Each station has a pallet receiver mechanism that locates and clamps the pallet. Pallet transfer between individual stations is handled by a control program in the computer. The control program also downloads and executes the trajectories on the individual stations. A schematic of the setup is shown in Figure 2.2. Thermal deposition techniques Figure 2.2: A SCHEMATIC OF THE SDM SETUP have been explored in SDM in order to produce high quality parts. While spraying techniques suffer from poor bonding properties, traditional welding based approaches suffer from penetration problems created by excessive heat input. In SDM, material is deposited by plasma or laser based droplet-deposition process that ensure good metallurgical bonding between layers without excessive heating of the substrate material. Other deposition processes that are currently being explored include selective casting of two-component or UV-curable resins, hot pressing of powders, sputtering and ceramic deposition. In SDM, material removal is done using a 5- axis CNC milling machine. The CNC cutter paths generated by the process planner

26 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 14 are downloaded to the machine in the DNC mode. Other material removal stations that will be included in the future include EDM (electro discharge machining) and a 3-axis CNC milling machine for handling abrasive materials. The residual cutting fluids or the residue from the deposition process are removed in a washer that has the capability to spray a water-jet at different speeds. A shot peener is used to relieve stresses in the part. The shot peener uses a conventional pressurized media delivery system. Some of the current application areas of SDM are Shape conformable embedded electro-mechanical structures Manufacture of custom tools Injection molds with cooling channels Tools with multi-material inserts Tools with embedded sensors Functional prototype parts Complex shaped parts made of hard-to-machine materials. 2.2 Process planning In conventional CAD/CAM systems that rely on CNC machines to build parts, process planning plays a significant role. Process planning in such systems requires identification of machining features. Sarma and Wright [54] identifies two levels of planning for the conventional CAD/CAM systems. Macroplanning is a higher level planning that deals with access directions of features, process sequencing and selection of appropriate fixtures. Microplanning deals with tool path planning and selection of tools and process parameters. Although progress has been made towards automating these planning tasks, significant human intervention is still required which results in long lead times and expensive parts. Some of the difficulties in automating the conventional CAD/CAM processes are:

27 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 15 Inaccessibility of some areas of the model by the cutting tool Figure 2.3a. This could be caused either due to insufficient tool length or due to inaccessible surfaces in the model. Part-specific fixturing Figure 2.3b. In order to access undercut surfaces, special fixture or refixturing is needed. The design and selection of fixtures involves considerable human expertise and is difficult to automate. Inaccessible by tool Fixturing problems Figure 2.3: DIFFICULTIES WITH CONVENTIONAL CAD/CAM PROCESSES Generation of cutting tool trajectories for complex geometries. Geometric reasoning becomes a difficult task in the case of complex geometries. Problems like gouging and collisions becomes more difficult to handle in complex geometries. Multiple re-fixturing might be necessary to cut certain shapes without collisions. Verification tools are needed to ensure the correctness of the generated paths. On the other hand, one of the clear advantages with SFF processes is the ability to produce physical objects from CAD models in a completely automated fashion with very little process planning effort. SFF processes operate on planar geometries that makes them essentially independent of the part complexity. Support structures eliminate the need for custom fixturing and permit undercut features to be built up. The process planning effort in most of the SFF processes involves the generation of 2-D cross-sections and generation of scan paths for the 2-D cross-sections. Since it is possible to solve these issues in a robust and autonomous fashion, producing parts

28 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 16 using the SFF processes requires very little human intervention. Of course, issues such as shrinkage compensation and support structure determination would make the process planning effort in SFF processes more challenging. In SDM, there is a full 3-D shape control of all surfaces and it also uses material removal operations like CNC cutting. Both these make the process planning effort in SDM more complex than that of SFF processes. Figure 2.4 shows the process planning steps involved in SDM. In SDM, the CAD model is first decomposed into layers of varying thickness based upon both geometric and process criteria. Each layer is further subdivided into simpler building blocks called compacts that are of single material and which have all their newly deposited surfaces to be non-undercut surfaces. The compacts are then sequenced for subsequent planning operations. The compacts are deposited as near-net shapes using the deposition paths. The parameters for deposition paths, such as path spacing, deposition feedrate and height of deposit are dependent on the deposition method used and material being deposited. This information is obtained from the process database. The deposited compacts are machined to net shape using CNC cutting operations. The CNC cutter paths are transformed to machine coordinates and into the machine readable format. The CNC cutter paths are generated with different types of cutting tools with varying sizes. The feed-rate and the spindle speed are based on the cutter used and the material being cut. This information is derived from the tool database. Deposition paths and CNC cutter paths are then generated for the next compact and the path generation cycle is repeated till all the compacts are processed. One of the key challenges in process planning for SDM is to develop robust algorithms to automatically decompose any CAD solid model into a set of layers and compacts. This problem involves extensive geometric reasoning and is very difficult to be solved manually. Thus, it is essential that this is done in an automated fashion. With a host of interesting geometric issues, a robust solution to this problem will be a challenging task. The other major area in process planning for SDM is path planning. Path planning encompasses generation of deposition trajectories and cutting trajectories. Though there are some common issues in deposition and cutting path generation, there are some basic issues that separates these two problems. The

29 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 17 CAD Model Compact Generation Non-Monotonic Layer Adaptive layer Generation Min/Max Layer Thickness Process Database Layer/Compact Sequence Deposition Path CNC Cutter Path Tool Database Machine Code Figure 2.4: PROCESS PLANNING STEPS IN SDM

30 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 18 deposition path generation is highly influenced by the process whereas the cutting path generation is governed more by geometry than by the process. Trajectories generated for droplet-based deposition methods used in SDM control the integrity of the deposited material. It is very important to maintain accurate path spacing and torch angles to avoid gaps or overlaps in the deposit. A variety of trajectory patterns should be explored to overcome issues like unsymmetrical deposition properties, localized heating and thermal cycling. On the other hand, cutter path generation is mainly dictated by geometric complexities. As explained before, automation of CNC cutter path generation has not been possible. But in SDM, it is very essential that it is automated as human intervention with so many layers would cause considerable delays in the process. Also, with the original model decomposed into compacts, it is intuitively difficult to generate the CNC trajectories. At the same time, this process offers some benefits which helps towards this automation. The compacts won t have any undercut features and since the compacts won t be too high, all areas of the compact will be within the reach of the tool and there is no need to consider fixturing problems. Thus generation of CNC cutter paths in an automated fashion would be another major task of the process planning system. 2.3 Summary This chapter described the SDM process and the process planning issues in SDM. SDM is a layered manufacturing process that employs material deposition and material removal processes for creating a part. Process planning is an important component in any manufacturing process. In conventional manufacturing processes that employ CNC machining, process planning involves selection and design of fixtures and generation of CNC cutter paths. This still needs significant human intervention resulting in long lead times and expensive parts. In SFF processes, process planning involves generation of 2-D cross-sections by slicing the CAD model and generation of scan paths for these 2-D cross-sections. This needs very little human intervention. Process planning in SDM has some similarities and differences with the above mentioned methods of process planning. In SDM, similar to SFF, the

31 CHAPTER 2. SHAPE DEPOSITION MANUFACTURING 19 CAD model has to be decomposed into simpler models but the difference is that these simpler models are 3-D models and are no longer 2-D cross-sections. Then similar to CNC process planning, cutter paths have to be generated for these 3-D models, but the difference is that the cutter path planning has to be fully automatic and is free of fixturing problems.

32 Chapter 3 Spatial Decomposition 3.1 Introduction As mentioned before SFF parts are processed by decomposing 3-D CAD models into thin cross sectional layers which are used to plan the material deposition strategy for each layer. The physics of the material deposition process (e.g. surface tension) frequently prevents the generation of geometrically well defined surfaces between cross sections. Instead, surfaces with a stair step appearance may be created. In contrast, Shape Deposition Manufacturing (SDM) takes advantage of both material addition and subtraction. The SDM strategy is to first decompose a CAD model into simpler building blocks called compacts. A key challenge in SDM is to develop robust algorithms capable of automatically decomposing any 3-D model into a set of layers and compacts which can be fabricated by combined additive and subtractive process. To define the nature of the geometric problems involved, we describe the sequence of fabrication steps first. Each layer consists of a primary material and a sacrificial support material. For example, consider the object in Figure 3.1 which is decomposed into three planar layers. The layers comprising the primary material are classified as follows: Class 1 has only non-undercut features Class 2 has only undercut features 20

33 CHAPTER 3. SPATIAL DECOMPOSITION 21 Class 3 is a combination of 1 and 2. Both Undercut Non-undercut Class 1 Class 2 Class 3 Figure 3.1: SEQUENCE OF OPERATIONS Figure 3.1 shows the sequence of operations for these three class of layers. For class 1 the primary material is deposited first and then machined to net shape. Next, the sacrificial support material is deposited and planed together with the primary material. This sequence is reversed for class 2 objects. Class 3 geometries must be decomposed into compacts such that the strategies of class 1 and class 2 can be invoked recursively depending on the local geometry. As an example, a support compact is deposited and cut first followed by deposition and cutting of the primary material. Finally the rest of the support material can be deposited to complete the layer. This description serves to indicate some of the issues in shape decomposition for SDM processing. The following section aims at generalizing the definitions of geometric entities which will then lead into the development of the decomposition algorithm [52].

34 CHAPTER 3. SPATIAL DECOMPOSITION Overview Definitions The surfaces of the model are classified into three categories (Figure 3.2). If ˆN(u, v) b N N N N N Non-undercut Undercut Non-monotonic Figure 3.2: TYPES OF SURFACES is the normal vector on any point (u, v) of the surface S and ˆb is the unit vector in the build-up direction, then S is an undercut surface if ˆN(u, v) ˆb <0 for all (u, v) in the domain of S S is a non-undercut surface if ˆN(u, v) ˆb 0 for all (u, v) S S is a non-monotonic surface if it has both undercut and non-undercut portions. A layer is a section of the model that is bound between two horizontal planes. A layer can consist of multiple materials and can have a variable thickness. In general, a layer cannot be processed in one SDM process cycle. A compact is the fundamental building block of the SDM process. A compact is composed of single material and has all its newly deposited surfaces to be nonundercut surfaces. A compact can be processed in one SDM process cycle. The next four definitions are illustrated in Figure 3.3. Silhouette edges are defined as those curves on the surface of the model along which ˆN(u, v) ˆb = 0. Silhouette edges serves as the boundary between undercut and non-undercut portions of the surface.

35 CHAPTER 3. SPATIAL DECOMPOSITION 23 a b b a c a - Convex surface silhouette edge b - Convex boundary silhouette edge c - Concave boundary silhouette edge Silhouette loops Figure 3.3: SILHOUETTE EDGES AND LOOPS A convex silhouette edge is a silhouette edge where the surface across the edge is convex. Thus a convex silhouette edge has its adjacent undercut surface below its adjacent non-undercut surface. A concave silhouette edge is a silhouette edge where the surface across the edge is concave. Thus a concave silhouette edge has its adjacent undercut surface above its adjacent non-undercut surface. Silhouette loops are the loops formed by the connecting the silhouette edges into a closed contour. A silhouette loop can consist of both concave and convex silhouette edges. Build-up direction is the direction along which the part is built up. At present, parts in SDM are built along the z direction. Thus, without loss of generality, z direction (0,0,1) is assumed to be the built-up direction in the rest of this chapter Basic concepts Some of the concepts in this section and the subsequent sections will be explained with the help of models of part and support shown in Figure 3.4. The main goal is to decompose the given CAD model into compacts that could be processed in a single step. We should also determine the sequence of compacts based on its geometry. Figure 3.5 and Figure 3.6 shows the spatial decomposition of the part and the support

36 CHAPTER 3. SPATIAL DECOMPOSITION 24 CAD model of part CAD model of support Figure 3.4: PART AND ITS SUPPORT respectively. It will be shown later that this is not the only solution. The part model P2 P3 P1 Spatial decompostion of part model Figure 3.5: COMPACT DECOMPOSITION OF THE PART is decomposed into layers P1, P2, P3 and doesn t need any subdivision. The layers S1,S2 of the support model do not need any subdivision, but layer S3 has to be subdivided into compacts S3 1 and S3 2. The process sequence for this set of layers and compacts will be P1-S1-S2-P2-S3 2-P3-S3 1. Silhouette edges are used as the starting point in the decomposition algorithm. There are two types of silhouette edges in a given model, surface silhouette edges and boundary silhouette edges. Surface silhouette edges are those that exist inside a surface and boundary silhouette edges are those that serve as the common boundary

37 CHAPTER 3. SPATIAL DECOMPOSITION 25 S1 S2 S3 S3_1 S3_2 Spatial decomposition of support model Figure 3.6: COMPACT DECOMPOSITION OF THE SUPPORT edge between two surfaces. The surface silhouette edges are present only in nonmonotonic surfaces and are used to subdivide the surface into monotonic surfaces. At the end of this subdivision, the model will consist only of boundary silhouette edges. These boundary silhouette edges are connected to form closed silhouette loops. Figure 3.3 shows the silhouette edges and loops in the example part. Partition surfaces are obtained as ruled surfaces by sweeping a certain set of silhouette edges along the z direction. These partition surfaces are used to decompose the model into layers and compacts. Since a compact can consist of both undercut and non-undercut surfaces, a compact with undercut surfaces can be processed only when all other compacts with which the current compact shares its entire undercut surface have been created. Each

38 CHAPTER 3. SPATIAL DECOMPOSITION 26 compact is accumulated on the pre-built non-undercut surfaces of other compacts and provides new non-undercut surfaces for supporting other compacts to be processed later. Since silhouette loops represent the common boundary between undercut and non-undercut portions, they play a very important role in the generation of compacts. Any portion of the model with purely concave silhouette edges cannot be a compact because the non-undercut surface cannot be reached from top as there is an undercut surface hanging over a non-undercut surface. The exception to this is if the concave silhouette edge has its adjacent non-undercut surface as a vertical surface. A convex silhouette edge and a concave silhouette edge appear as a pair, because a convex silhouette edge for the part model is a concave silhouette edge for the support model and vice versa. For instance, a spherical surface of a positive ball has a convex silhouette circle while that of a negative ball has a concave silhouette circle Related work The concepts of silhouette edges and loops are well known in the context of hidden line/surface removal algorithms. Appel[4] proposed a hidden line removal algorithm based on quantitative invisibility, which stands for the number of covering surfaces such that quantitative invisibility at visible points is equal to zero. He pointed out that quantitative invisibility changes when a point passes through a silhouette edge. Hornung[28] as well as Schweitzer and Cobb[55] indicated that connected silhouette edges form a closed loop. Walter[64] uses silhouette edges as a means for surface rendering. He generates silhouette edges as point sequences and uses them to compute sight indices that are then used to clarify the visibility of the surface. However, these studies were aimed at generating projected images rather than decomposition of CAD models. Silhouette edges were used just for eliminating hidden parts of lines or for determining the ends of scan lines. Researchers in the graphics area have also looked at the problem of generating surface silhouette edges. Schweitzer and Cobb[55] use a surface intersection method to compute silhouette edges on tensor product polynomial surfaces. In their approach, normal surface N, obtained by the surface representation of the normals at each point

39 CHAPTER 3. SPATIAL DECOMPOSITION 27 on the surface S, is intersected with xy plane to obtain the silhouette edges. Their method was limited to bicubic patches and the algorithm has limitations when the normal surface is degenerate. Beusmans[6] outlines a method to generate silhouette edges of a model using its spherical image. The spherical mapping relates the points on the surface of a model with points on a unit sphere representing all possible surface normals. The algorithm makes use of the fact that the spherical image of a silhouette edge is confined to the great circle on the unit sphere. In this method, the extraction of silhouette edges is free of degeneracies and fairly straightforward subject to the generation of the spherical image of the object Requirements The requirement for each compact is as follows: A ray cast along the z-axis from the top should enter the compact through its non-undercut surface and exit through its undercut surface. Any non-undercut surface of a compact cannot be covered by its own undercut surfaces. The ray hits a non-undercut surface and an undercut surface at most once. These requirements can be expressed in terms of the silhouette edges and silhouette loops as below. Concave silhouette edges: There shouldn t be any concave silhouette edge in a compact. In a model with concave silhouette edges, the non-undercut surface is covered by its own undercut surface. Here, the silhouette edge indicate a local self-overlap like in a bellow. Self-intersections of a projected silhouette loop: The xy projection of the silhouette loop shouldn t have any self-intersections. If the projection of a silhouette loop has self-intersections, then there exists at least one ray that will hit a non-undercut surface and an undercut surface more than once. Here, there exists a global self-overlap like in a spiral shape.

40 CHAPTER 3. SPATIAL DECOMPOSITION 28 Even if each compact fulfills the above two requirements, it might so happen that the compact cannot be processed due to a sequence conflict between the compacts. The compacts have to be ordered based on their relative z positions. The compact with a lower z value must be sequenced before the one with a higher z value. The z position of a compact is its minimum z value. All the compacts must be simply ordered in a sequence to be processed. However it is sometimes impossible to sort all compacts in a sequence based on the relative z positions. This could happen if there exist cyclic ordering relation as shown in Figure 3.7. Here A covers B, B covers C, and C covers A. This means A cannot be processed before B, B cannot be processed before C, and C cannot be processed before A. Therefore none of them can be processed in the given form. In terms of silhouette loops, this requirement can be stated as follows. Cyclic ordering among silhouette loops If the ordering relations between silhouette loops of compacts form a cycle, those compacts cannot be processed in a sequence. A B A < C C < B B < A C Figure 3.7: CYCLIC ORDERING 3.3 Algorithm The algorithm decomposes the given model such that the resulting set of compacts satisfies the following conditions.

41 CHAPTER 3. SPATIAL DECOMPOSITION No concave silhouette edges in a compact. 2. No self-intersections of the projected silhouette loop of the compact. 3. Silhouette loops of different compacts do not have a cyclic ordering among them. Concave silhouette loop P1 P2 Figure 3.8: COMPACT DECOMPOSITION USING INFINITE SWEEP The algorithm has some similarities to the Weiler-Atherton hidden surface algorithm which subdivides the polygons by clipping with other polygons based on a depth sort of the polygons[66]. In our approach we subdivide a solid model by clipping with silhouette edges.

42 CHAPTER 3. SPATIAL DECOMPOSITION 30 In order to decompose a model using silhouette edges, one approach is to use swept surfaces obtained by sweeping those silhouette loops that violate the conditions above, along the z-direction. Since an infinitely long prism separates the entire space into two regions, a sufficiently long swept surface of the silhouette loop will split the model. Figure 3.8 shows the decomposition of the example part using this method. Here, the concave silhouette loop is swept along the positive z-direction to split the model into two compacts, P1 and P2. It can be observed that both the compacts satisfy the three conditions. In SDM, these compacts might have to be split further using horizontal planes in order to satisfy some process constraints. In keeping with the nature of the process, in our second method we use horizontal planes together with swept surfaces to decompose the model. The use of horizontal planes has the following advantages: Some process constraints that impose maximum depth requirements can be accommodated. The maximum depth requirement is dictated by factors such as cutting tool length (such that all portions of compact that needs to be cut is accessible by the tool) and maximum deposition height (such that we get good quality deposits). The bonding between compacts is usually better across horizontal sections. The swept surface along the z-direction could be bound by the horizontal planes. The steps involved in this algorithm are given below: 1. Generation of monotonic surfaces Non-monotonic surfaces are sub-divided into monotonic surfaces by splitting them along the silhouette edges on the surface (Figure 3.9). At the end of this step, all the surfaces of the model can be categorized into either undercut or non-undercut. 2. Generation and Classification of silhouette edges Silhouette edges separating undercut surfaces from non-undercut surfaces are identified for the entire model (Figure 3.9). These edges are then classified into

43 CHAPTER 3. SPATIAL DECOMPOSITION 31 Step 1 : Monotonic surface generation Step 2: Generation of silhouettes Step 3: Decomposition along horizontal planes Figure 3.9: FIRST THREE STAGES OF THE ALGORITHM concave and convex silhouette edges based on the configuration of the adjacent surfaces. 3. Model decomposition along horizontal planes All continuous segments of concave silhouette edges are detected and the model is split along horizontal planes passing through both the lowest and highest points of the concave silhouette segment (Figure 3.9). 4. Generation of silhouette loops

44 CHAPTER 3. SPATIAL DECOMPOSITION 32 The algorithm recalculates silhouette edges on subdivided model and creates silhouette loops by tracing the silhouette edges. One silhouette edge is selected first to start the silhouette loop. Then the silhouette edge which joins it next is added to the loop. This process is continued till the first edge is reached again. The same procedure is repeated until all the silhouette edges have been added to silhouette loops. The silhouette loops are projected onto the xy-plane and the intersections among the projected silhouette edges are examined. Decomposition along open concave silhouette edges Figure 3.10: DECOMPOSITION ALONG CONCAVE SILHOUETTE EDGES 5. Decomposition along concave silhouette edges Concave silhouette edges are swept along the z-direction to form partition surfaces. These partition surfaces are used to decompose the model. The method for generation of partition surface depends on the nature and interaction of concave silhouette edges. If the projected silhouette loop containing the concave silhouette edges has self-intersections between the concave silhouette edges, the sub-loop having its ends at the intersection point(s) is used to obtain the swept partition surface.

45 CHAPTER 3. SPATIAL DECOMPOSITION 33 If the silhouette loop contains both concave and convex silhouette edges, then there will be isolated concave silhouette edges. Each of these isolated concave silhouette edge will have an undercut surface and a nonundercut surface as its adjacent faces. The partition surface is obtained by sweeping the boundary of the adjacent undercut surface along the z- direction.(figure 3.10). If the entire silhouette loop is made up of concave silhouette edges, the silhouette loop is swept in the z-direction to generate the partition surfaces. This step eliminates all the concave silhouette edges. Silhouette loop CAD model Projected silhouette loop Figure 3.11: MODEL WITH SELF-INTERSECTING PROJECTED SILHOUETTE LOOP 6. Decomposition to eliminate self-intersections of projected silhouette loop The algorithm detects all self-intersections of the projected silhouette loops. If there are self-intersections, there will be an even number of them. The overlapping portion of the self-intersecting loop is swept to form the partition surface that is used to decompose the model.

46 CHAPTER 3. SPATIAL DECOMPOSITION 34 To illustrate this, consider the example shown in Figure The model consists of four triangular prisms joined to form a spiral shape. Figure 3.11 also shows the silhouette loop and projected silhouette loop for this model. It should be noted that silhouette loop is entirely made up of convex silhouette edges. By sweeping the overlapping portion(figure 3.12) of the silhouette loop the model is decomposed into two compacts C1 and C2 as shown in Figure Overlapping portion of silhouette loop C2 C1 Figure 3.12: DECOMPOSITION TO ELIMINATE SELF-INTERSECTIONS OF PROJECTED SILHOUETTE LOOP 7. Decomposition to eliminate cyclic ordering At this stage no projected silhouette loop has self-intersections. The algorithm detects intersections between any pair of silhouette loops and determines the ordering relation according to the relative depth of them. If there is a cyclic ordering among the silhouette loops, one of the models containing the silhouette

47 CHAPTER 3. SPATIAL DECOMPOSITION 35 loop causing the cyclic ordering is split (Figure 3.13) by sweeping the overlapping portion of the silhouette loop. It can be observed that this case is similar to the self-intersection case. Overlapping portion of A to be split A B A < C C < B B < A C A3 B A2 < C C < B B < A3 A2 C A1 Figure 3.13: SPLITTING SILHOUETTE LOOPS TO AVOID CYCLIC ORDERING 8. Determination of process sequence Figure 3.14 shows the decomposition of the example part and the support using this algorithm. The part is split into two compacts P1 and P2 and the support is split into three compacts S1, S2 and S3. Now the compacts have to be ordered to determine the process sequence. This is based on the nature of shared faces between different compacts. If a compact contains an undercut face (S1), then the compact containing the corresponding non-undercut face (P1) has to be processed before it. Thus for each compact, a list of compacts to be

48 CHAPTER 3. SPATIAL DECOMPOSITION 36 processed before it is placed before it in the compact sequence list. This process is repeated for all compacts. The process sequence for this set of compacts will be P1-S1-S2-P2-S3. P2 S3 S2 P1 S1 Sequence - P1 -> S1 -> S2 -> P2 -> S3 Figure 3.14: COMPACT DECOMPOSITION WITH PROCESS SEQUENCE 3.4 Summary An algorithm for the decomposition of any 3-D model into layers and compacts was described. This decomposition method enables the manufacture of complex, multimaterial objects in SDM. Geometric model decomposition is accomplished through a sequence of geometric operations. Silhouette edges and silhouette loops are identified to help in the decomposition of model. The geometric requirements to be satisfied by

49 CHAPTER 3. SPATIAL DECOMPOSITION 37 a compact are expressed in terms of these silhouette edges and loops. The algorithm then progresses to decompose the given model into compacts whose silhouette edges and loops do not violate any of those requirements. Unlike techniques used in SFF methods which divide models into equally spaced slices, the present algorithm decomposes models into layers which are not necessarily planar and equally spaced. This has the advantage that the surface information of the original model is preserved and utilized for further process planning steps including CNC cutter path generation. In addition, processing methods permitting, relatively thick layers can be fabricated at once resulting in an increased building rate. Another key step of the present algorithm is the determination of the process sequence. Solely based on geometric arguments a feasible sequence of material addition and removal processes is found.

50 Chapter 4 Deposition Path Generation In SDM, material is deposited by a variety of deposition techniques. Most of the parts were built using plasma or laser based droplet-deposition process. In addition to these, some of the other deposition processes being explored in SDM include selective casting of two-component or UV-curable resins, ceramic deposition, sputtering, plasma arcjet coating and hot pressing of powders. The deposition path generation is dependent on the nature of the deposition process. Deposition path generation for processes that have fine, statistically distributed particles are somewhat independent of geometric complexity. On the other hand, deposition paths for processes that have coarse, discreetly deposited particles are influenced by geometric complexity. Also, the property of the deposited material will be influenced by the deposition path trajectory. Thus it is important to understand some of the deposition methods that are used in SDM. Also, one of factors that limits the quality of parts in SDM is the accumulation of residual thermal stresses. It might be possible to reduce this effect by selecting an appropriate deposition path. The next section describes some of the deposition techniques used in SDM. In the following section, methods are described to generate different types of depositions paths. 38

51 CHAPTER 4. DEPOSITION PATH GENERATION Deposition Methods in SDM Microcasting Microcasting [43],[67] is a droplet-based deposition process that combines the benefits of welding and thermal spraying. Figure 4.1 shows the working principle of microcasting. An arc is established between a tungsten electrode and a charged contact tip in gas-filled environment. A wire that is Gas feed Wire feed Gas feed Power Supply + - Inerting shroud Tungsten Electrode Shielding Gas Substrate Figure 4.1: WORKING PRINCIPLE OF MICROCASTING fed through the charged contact tip melts in the arc forming a molten droplet. The molten droplet falls from the wire when its weight overcomes the surface tension. The droplet is accelerated by gravity and falls on the substrate. In contrast to the small droplets produced by thermal spraying, microcast droplets are relatively large (1 to 3 mm dia.). Due to their large volume-to-surface ratio, they remain superheated until impacting the substrate and contain sufficient energy to locally remelt the underlying substrate to form metallurgical bonding upon solidification. Laser Deposition system The laser deposition process [20] is similar to laser

52 CHAPTER 4. DEPOSITION PATH GENERATION 40 cladding or laser welding. Figure 4.2 shows the schematic of the laser deposition system. Metal powder is injected into a melt pool at the laser focus on the substrate. As the laser scans over the surface, the injected powder fuses onto the substrate. Since the laser can be positioned accurately, and the material is deposited only where the laser strikes the surface, it is possible to deposit near-net shapes using this deposition method. Laser Powder Deposit Substrate Figure 4.2: WORKING PRINCIPLE OF LASER DEPOSITION SYSTEM 4.2 Generation of deposition paths Some of the factors that will influence the type of deposition path are : Accumulation of thermal stresses - Thermal stresses will accumulate if there is an uneven heating of the surface. Thus, if the deposition path is unsymmetrical, it will result in thermal stresses. Number of deposition segments - If there are many discontinuous deposition

53 CHAPTER 4. DEPOSITION PATH GENERATION 41 segments, the deposition gun might have to be switched off between different segments or might have to be moved fast. Robustness - The deposition paths should be generated irrespective of the complexity of the geometry. Uneven material deposition - We should try to avoid revisiting the same position in the path as this will result in extra material deposition in those areas with the associated reheating. Uneven material deposition will also result in those areas of the path where the deposition gun spends more time. (eg., places where the deposition gun reverses its direction) Avoiding gaps in the path - All portions of the given geometry should be covered by the deposition gun. Since, gaps would result in serious problems, it is better to be conservative in depositing the material Types of deposition paths Deposition path planning is in many ways similar to path planning for pocket milling. The work by Held [26] serves as a good reference for research in the context of cutter path generation for pocket milling. The above factors make the deposition path generation a more constrained problem compared to pocket milling and thus warrants a different approach. The deposition paths are generated for the 2-D cross-section obtained by the XY projection of the compact. These cross-sections have to be offset by a certain distance before generating the deposition paths. The offsetting operation is similar to the one described in Chapter 5, Section 5.4. Geometrically, the deposition paths could be classified into two types (Figure 4.3): Spiral paths - It comprises of a series of contours that are parallel to the boundary of the 2-D cross-section. Zigzag paths - The path segments correspond to back and forth motions in a fixed direction within the boundary of the 2-D cross-section. It is possible to derive a variety of deposition path patterns from these two paths.

54 CHAPTER 4. DEPOSITION PATH GENERATION 42 Spiral Path Zigzag Path Figure 4.3: TYPES OF DEPOSITION PATHS Spiral Paths Spiral paths could be generated by two methods - Recursive offsetting method and MAT based method.the distance d between successive offsets will be a function of the deposition width w and is dependent on the type of deposition process. Recursive offsetting method In this method the 2-D cross-section is shrunk recursively using the offset operation. The shrunk cross-sections could be obtained by two methods. By offsetting the original cross-section by d, 2d and so on till a null shrunk cross-section is obtained. A i s = A o i d ˆb (4.1) A i s is the i th shrunk cross-section A o is the original cross-section

55 CHAPTER 4. DEPOSITION PATH GENERATION 43 ˆb is the unit binormal vector i =0, 1,...n where A n s = NULL By offsetting the previous cross-section by d and repeating the process till a null cross-section is obtained. A i s is the i th shrunk cross-section ˆb is the unit binormal vector i =1,...n where A n s = NULL A 0 s = A o, the original cross-section A i s = A i 1 s d ˆb (4.2) The deposition path is obtained by employing the collection of the shrunk crosssections, [A i s,i=0,...n 1], as centerline trajectories for the deposition gun. MAT based method The Medial Axis Transform (MAT) was defined by Blum [7] as an alternate description of the shape of an object. The MAT of a 2-D model could be defined as the closure of the set of the centers of maximal circles which can be fit inside the object (Figure 4.4). In the literature, algorithms have been described to generate the MAT of 2-D models [23],[36]. The algorithm Maximal circles MAT Figure 4.4: MAT OF A RECTANGLE described by Gursoy and Patrikalakis [23], handles multiply connected regions with boundary elements that can be composed of straight lines, circular arcs and NURBS curves. The radius of the maximal circle is stored as an attribute of

56 CHAPTER 4. DEPOSITION PATH GENERATION 44 the points of MAT. Figure 4.5 shows the steps involved in obtaining a deposition path based on the MAT of the model. MAT of the model A path obtained from MAT Figure 4.5: MAT BASED DEPOSITION PATH In order to generate the deposition paths based on the MAT based method, the MAT of the 2-D model is generated along with the radius function at each point. The successive offset cross-sections are obtained from the MAT by growing the MAT model in multiples of d. The grown cross-section at the k th level can be thought of as the union of circles of radius k d and centers along the MAT. If the growing distance k d is greater than the radius of the maximal circle at any point, then that point is not grown and the grown cross-section will be divided into sub-regions at these points. The process is stopped if all points have their maximal circle radii less than the growing distance. In contrast to

57 CHAPTER 4. DEPOSITION PATH GENERATION 45 the recursive offsetting method, with the MAT based method it is possible to have uniform overlaps between successive paths by splitting the radius function into equal intervals. It can be noted that with spiral paths, we might get overdeposition or gaps in portions of the 2-D model. The former occurs at distances less than d of offsets to unrelated portions of the boundary. The latter occurs at regions between offsets that are of width greater than d, wherein portions of offset segments might have been eliminated to avoid self-intersections of the offset. Also, the fact that the thickness of the model at a generic region may not be an integral multiple of d will lead to overlaps or gaps. Zigzag paths ln Zigzag path generation a series of parallel segments are generated along a direction V. The common choices of V are the X or Y direction. But the optimal direction would be parallel to the longer axis of the rectangular hull of the cross-section. The rectangular hull is the minimum-area rectangle that encloses the cross-section. Toussaint[61] describes a linear time algorithm to obtain the rectangular hull of a simple polygon. His algorithm makes use of a theorem proposed by Freeman and Shapiro[21]. Theorem 4.1 The rectangle of minimum area enclosing a convex polygon has a side collinear with one of the edges of the polygon. Based on this theorem the algorithm for constructing the rectangular hull (Figure 4.6) can be described as below. Construct a polygonal model of the given cross-section. Construct the convex hull of the polygonized model. Algorithms for constructing the convex hull could be found in the books related to computational geometry [48], [56]. Generate a set V of vectors parallel to the sides of the convex hull.

58 CHAPTER 4. DEPOSITION PATH GENERATION 46 a) Polygonal model b) Convex Hull c) Rectangular Hull Figure 4.6: RECTANGULAR HULL CONSTRUCTION For each vector V in V, construct a rectangle R oriented along V by finding the extremal points along V and along V,whereV is to V. The rectangular hull is given by the rectangle R min with the minimum area. Parallel line segments are generated corresponding to the short or long axis of rectangular hull of the 2-D cross-section. These set of segments are intersected with the 2-D model to generate the set of parallel segments confined within the boundary of the cross-section as shown in Figure 4.7. The end points of the segments at the boundary are joined to generate continuous path segments. The relative merits of spiral paths and zigzag paths have been studied by Wang et al. [65] in the context of NC tool path generation. In their observation, the difference in total path length to cover various convex polygonal regions between the spiral and zigzag paths is not very large, typically < 5%. This will be true only if an optimal direction V selected for the zigzag path. Thus if the direction for the zigzag path is chosen using the above mentioned method, zigzag paths and spiral paths are not very much different in terms of minimizing the total path length. Farouki et al. [18] have discussed the advantages and limitations of these paths in the context of layered manufacturing processes.

59 CHAPTER 4. DEPOSITION PATH GENERATION 47 a) Parallel Line segments b) Intersecting with the original shape Figure 4.7: ZIGZAG PATH GENERATION But with an evolving process like SDM, it is difficult to select the correct deposition pattern. For most of the shapes, it might be possible to select the zigzag or the spiral path as the deposition pattern. If these patterns are found to be unsuitable, it is possible to find other deposition patterns as described below. First pass of tower pattern Second pass of tower pattern (shown in blue ) Figure 4.8: TOWER DEPOSITION PATTERN Tower pattern This type of pattern has been discussed in Fessler et. al.,[20]. This pattern can be derived from the zigzag pattern by selecting every alternate segment of the zigzag pattern in the first pass and selecting the remaining

60 CHAPTER 4. DEPOSITION PATH GENERATION 48 segments in the next pass as shown in Figure 4.8. In this pattern, the deposits will have a larger surface area to volume ratio during the cooling phase and this will allow them to deform freely as they cool before they are constrained by the adjacent deposits Figure 4.9: CONVEX DECOMPOSITION FOR DEPOSITION Convex decomposition In this pattern, the given shape would be decomposed into convex regions [8]. Each convex region could be deposited using the zigzag or the spiral pattern. Thus, for example the shape shown in Figure 4.9 is decomposed into seven convex regions and each of these seven regions can be deposited using the spiral pattern. One of the advantages with this pattern would be that the total path length would be near-minimal. If the shape is decomposed into many convex regions, this pattern will also have the advantages of the tower pattern. Cross hatch pattern If zigzag paths are generated in two perpendicular directions, it will result in a cross-hatch pattern as shown in Figure In the case of the rectangular hull, the two directions would be parallel to the sides of the rectangle. This pattern would avoid any gaps in the deposit. Its impact on the residual stresses is not clear.

61 CHAPTER 4. DEPOSITION PATH GENERATION Summary Figure 4.10: CROSS HATCH DEPOSITION Two droplet based deposition methods, microcasting and laser deposition system, and algorithms to generate deposition paths were described. It was seen that the deposition paths should be generated such that it prevents accumulation of thermal stresses, avoids uneven material deposition and avoids gaps in the path. Two types of deposition paths, spiral and zigzag paths were identified. Spiral paths were generated by either recursive offsetting method or MAT based method and zigzag paths were generated by an algorithm based on rectangular hull construction. Three other deposition patterns that could be derived from spiral and zigzag paths were described. The selection of a particular pattern depends on the type of the deposition method and the quality requirements of the part. In SDM, the choice of the deposition pattern type has been made based on heuristics and experience. Over time, as we get a better understanding of the physics of the deposition process, it will be possible to select an appropriate deposition pattern for a given deposition process.

62 Chapter 5 CNC Cutter Path Generation 5.1 Introduction Research in CNC cutter path generation could be broadly classified into two areas. Automatic tool path generation using feature recognition techniques. Generation of CNC tool paths for sculptured surfaces. In feature based techniques [1], [2], [62], full automation is possible only with complete enumeration of all the manufacturing features which is practically impossible. Thus manual input becomes essential at one stage in any feature based technique. In non-feature based techniques, most of the work has been done in generating cutter paths for surface models rather than solid models. And there too full automation has been difficult due to gouging problems. In both these methods, automation becomes impossible in the presence of undercut features. Problems related to tool accessibility in deeper areas of the model and fixture related problem makes the automation of CNC cutter path generation a daunting task. In SDM, the compact is machined to the required shape through a series of CNC cutting operations.the compact to be machined is free of undercut features and with the small height of layers there won t be any tool accessibility problems. Since the CAD model will be decomposed into layers and compacts, the intuitive feeling for features is lost and hence feature based techniques are not suited. Also, the generation 50

63 CHAPTER 5. CNC CUTTER PATH GENERATION 51 CAD Model of the Layer (With Process and Tool Information) Rough Cut Operation Results in near-net shape of the layer 2-D Profile Cutting Provides tool accessibility If model non-prismatic Finishing Operation 3-D cutting resulting in final shape Figure 5.1: CNC CUTTING STAGES IN SDM of CNC cutter paths has to be fully automatic in this process, as human intervention with so many layers would cause considerable delays. Figure 5.1 shows the CNC cutting stages in SDM. The first two steps, rough cutting and 2-D profile cutting, primarily deals with 2-D geometric features and are classified under 2-D cutter path generation and the last step, finish cutting, deals with 3-D geometric features and is classified under 3-D cutter path generation. This chapter describes the steps involved in generating 2-D cutter paths [50], [51] and the next chapter deals with 3-D cutter path generation. 5.2 Rough Cutting The first step after the deposition of material is a rough cutting operation aimed at generating the near-net shape of the layer. The deposited layer is typically times the height of the model and is about 1 1 times the size of the model in the 2

64 CHAPTER 5. CNC CUTTER PATH GENERATION 52 XY direction(figure 5.2). The layer is machined to the safe height (model height + tolerance) through a series of planing steps(figure 5.2 a-c). The planing path is a) Deposited Material Bounding box of model b) Deposited material c) Planing steps Figure 5.2: PLANING OPERATION generated corresponding to the maximal XY rectangle of the deposited layer starting at the top of the layer till the safe height is reached in steps of the depth of cut allowable for the tool. At the end of the planing operation the deposited material would be reduced to the height of a box enclosing the layer. The rough cutting operation involved in producing the near-net shape of the layer from this box is realized thorough an operation which we call manhattan 1 decomposition. In the literature there are very few references for efficient rough cutting algorithms. In a recent work by Lee et al [37] the octree representation of a model is used in efficient tool selection for the rough cutting operation. Manhattan decomposition is an extension of the octree representation of a model. In manhattan decomposition, adjoining full octants at the same level of the octree are joined to form manhattan solids and the cutter paths are generated for these manhattan solids. The steps involved in the algorithm are : 1. The model of the volume to be rough cut (V rc ) is obtained by subtracting the model of the layer from the model of the box left after the planing operation (Figure 5.3). 1 A manhattan solid is defined as a solid in which the angle between the faces of the solid will be either 90 o or 270 o

65 CHAPTER 5. CNC CUTTER PATH GENERATION 53 V rc Figure 5.3: VOLUME V rc TO BE ROUGH CUT 2. V rc is enclosed in a hexahedron. This hexahedron is subdivided into eight hexahedron by equally dividing the height, depth and width of the hexahedron (Figure 5.4a). Let L = min(depth,width). Each hexahedron is classified into full (completely inside the solid), empty (completely outside the solid) and partial (partially inside/outside the solid). The classification of hexahedron is based on the octree encoding algorithm by Krishnan et. al [35]. The full hexahedrons are examined for cutting (steps 3-5) and the partial hexahedrons undergo further sub-division (step 6) 3. The full hexahedrons are then joined with the neighboring full hexahedrons in the X and Y directions to form the manhattan solid(s). The largest tool diameter that could be used at this stage is d = min(l i ) where L i is the min(depth,width) of the i th hexahedron in the solid. There will be 2 l layers of manhattan solids, where l is the level of octree decomposition. For each of these solid, the shape to be machined Section SM is got as the projection of manhattan solid(s) on the XY plane (Figure 5.4b). 4. The cutter path is then generated for Section SM s at different height levels depending on the allowable depth of cut of the tool. A flat end-mill is used for this operation.

66 CHAPTER 5. CNC CUTTER PATH GENERATION 54 d Full Partial b) Section of Manhattan solid SM a) Octree Generation (top view) c) Section after tool offset SM by d/2 Figure 5.4: STEPS IN THE ROUGH CUT ALGORITHM 5. Section SM is offset for the tool radius before the path is generated (Figure 5.4c). Since the cross-section will contain only edges that are parallel to X or Y axes and since the cutter diameter is chosen as min(l i ), the offset section can be generated without much computational effort. The path could be either lawn mower type of cutting or spiral cutting (Figure 5.5). Due to the cylindrical shape of the tool, there will be an un-cut area of the manhattan solids at convex corners. The full hexahedrons corresponding to these un-cut areas go into further subdivision after subtracting the areas that were machined. 6. The partial hexahedrons and the hexahedrons generated from the previous step are subdivided as mentioned in step 2 and the steps 3-5 are repeated till the required resolution level is reached. The subdivision in width or depth direction will be stopped if at any level, the width or depth of a hexahedron is smaller than the smallest tool available and will be stopped in the height direction if the height becomes smaller than a certain tolerance value.

67 CHAPTER 5. CNC CUTTER PATH GENERATION 55 Lawn Mower type Cutting Spiral Cutting Figure 5.5: TYPES OF ROUGH CUT PATHS 5.3 Two Dimensional Profile cutting After the rough cutting operation a two dimensional profile cutting is done in order to provide tool accessibility for the final five-axis contouring operation. In the case of the prismatic models, this two dimensional cutting operation will also serve as the final contouring operation. The model (M 2d ) for this operation is the bottom cross-section of the layer. Since the layers in SDM manufacturing will not have any undercut features, profiling the bottom cross-section will not pose any cutter interference problems. The generation of cutter path in this step requires an offsetting of (M 2d ) by the radius of the cutter. The offsetting operation is described in the next section. The method for generation of cutter paths depends on the type of offset operation used. If the linearized offset method is used, the cutter path is generated by traversing along the vertices of the offset model. 5.4 Offset of TwoD Profiles Extensive research has been done in offsets of curves with most of the methods being approximate offsets [11],[47], [60]. The offset curve C o (t) of a curve C(t) is defined as C o (t) = C(t) + r * ˆb(t) where ˆb(t) is the binormal vector to the curve at parameter

68 CHAPTER 5. CNC CUTTER PATH GENERATION 56 value t. The offset curves generated thus, will have degenerate cases [47] as shown in Figure 5.6. These degenerate offset curves when used for machining will result in gouging or un-cut areas. Also, the curves are assumed to possess a well-defined tangent vector at each point. In our approach we make use of an offset algorithm for a polygon model to generate the offset of the two dimensional model. The curves forming the edges of the model are approximated by linear segments E B D C A A - Requires additional curve segments B - Entire curve segment to be removed C - Loop and Cusps D - Self intersecting offsets E - Portions of curve segment to be removed Figure 5.6: DEGENERACIES IN CURVE OFFSET such that the deviation between the linear segments and the curves is less than the tolerance of the NC machine. Thus the new model (M 2dl ) consists of linear segments as its edges (Figure 5.7a). This new model is now offset for the radius of the cutter. In order to avoid gouging, it is ensured that no portion of the offset is closer to the model than the offset distance. The steps involved are: For each edge of the model, a face model is formed. Let v 1 and v 2 be the vertices of the edge. Let α i be the angle between the edges meeting at vertex v i where the angle α i is measured at the inside of the cross-section. Depending on value of α i the location of offset vertices of the face model are determined (Figure 5.7b).

69 CHAPTER 5. CNC CUTTER PATH GENERATION 57 e v a) Linearized model v nv nv t b v 1 r d 2 1 nv 1 1 v 1 1 v 1 nv 1 nv 1 nnv 1 b) Face model of edge e c) Modified face model of edge e Figure 5.7: OFFSET COMPUTATION If α i π, (convex corner) nv i = v i +( d i ˆt + r ˆb) (5.1) else if α i π (concave corner) nv i = v i + r ˆb (5.2) where, d i = r tan (π α i )/2fori =1, 2 (5.3) r = radius of the cutter ˆt = unit tangent vector along the edge (from v 1 to v 2 )

70 CHAPTER 5. CNC CUTTER PATH GENERATION 58 ˆb = unit binormal vector pointing in the direction of the face The face model corresponding to the edge is formed by the vertices v 1,nv 1,nv 2,v 2,v 1 taken in that order. The face models of all the edges are then merged with the original model M 2dl to form the offset model M 2do The boundary edges of M 2do gives the required offset model (Figure 5.8). As shown in Figure 5.8, all the degenerate cases are handled in a robust manner by this method. Figure 5.8: OFFSET MODEL WITHOUT DEGENERACIES In the case of convex corners, when the angle between the edges is too small, d 1 could be very high thus moving the offset vertex far from the corner. Though this will not result in any gouging while cutting it will delay the machining process. This could be taken care by generating one more vertex whenever the angle is less than π /2. (Figure 5.7c) nnv 1 = v 1 + r(cos α 1 /2 ˆt +sinα 1 /2 ˆb) and d 1 used in equation 5.3 is modified to be r tan (π α 1 )/4. Similar relation will apply for vertex v 2 except for the change of sign of ˆt. In such cases, the face model would be formed by the vertices v 1, nnv 1,nv 1, nnv 2 (if α 2 π/2),nv 2,v 2. The cutter path is generated by traversing along the vertices of the offset model.

71 CHAPTER 5. CNC CUTTER PATH GENERATION Summary A sequence of CNC cutting operations have been proposed to generate the required shape of the compact in an automated fashion. Cutter path generation for the operations that deals with 2-D geometric features have been described. A new method of decomposition, manhattan decomposition, that is an extension of octree decomposition, has been proposed for generating efficient rough cutting paths. The degeneracies that could occur during the offset of 2-D cross-sections, an operation that is required for generating 2-D cutter paths, have been identified. A robust offset algorithm has been described that handles all those degeneracies by offsetting the polygonized model. The 2-D cutting operation serves as the final contouring operation in the case of prismatic solids and serves to provide tool accessibility for 3-D cutting in the case of non-prismatic solids.

72 Chapter 6 3-D Cutter Path Generation 6.1 Finishing operation The final cutting operation employed in realizing the shape of the layer is the finishing cutting operation. The CNC cutter path is to be generated for the layer composed of free-form surfaces. This is in many ways similar to the conventional NC tool path generation problem. In contrast to conventional methods, we don t have undercut features and fixturing problems. Since our layers are thin, all areas of the layer will be within the reach of the tool. Our approach has to be fully automatic as manual intervention with so many layers in the model will introduce considerable delay in the process and it is also intuitively difficult for a person to debug the path in the absence of the whole model. Though NC cutter path generation is an actively researched area, few papers related to automatic 5-axis NC cutter path generation are published. Most of the earlier papers [9],[16],[30] primarily dealt with 3-axis milling using a ball end mill cutter. Some of the recent publications [14],[40] have addressed the issues of 5-axis milling. In the work by Li and Jerard [40], a method is described for the generation of gouge-free 5-axis tool paths for composite surface patches. Their method uses the polygonal representation of the surfaces. Elber [14] describes an approach which reduces the accessibility problem of 5-axis milling on a convex surface to a 3-axis accessibility problem which subsequentally helps in generating 5-axis tool paths for 60

73 CHAPTER 6. 3-D CUTTER PATH GENERATION 61 convex surfaces. In our approach we decompose the model into three types of regions (Figure 6.1. Flat-end milled regions : Regions of the model that could be cut with a flat-end mill that is positioned with its axis aligned along the normal to the surface. Peripheral milled regions : Regions of the model that could be cut with a flat-end mill with its side tangential to the surface. Three axis milled regions : Regions of the model that are cut with the x,y,z axis movements of the cutter. The ball-end milled regions comes under this category. Flat-end milled Peripheral milled Three axis milled Figure 6.1: TYPES OF CUTTER REGIONS Due to the geometrical nature of the layers in our process, it should be possible to machine all surfaces with the ball-end mill cutter. But for low curvature surfaces, flatend mills are shown to give a better surface finish and are found to reduce the overall cutting time compared to the ball-end mill [63]. Thus based on curvature information, the regions of the layer are assigned to one of the above mentioned categories.

74 CHAPTER 6. 3-D CUTTER PATH GENERATION 62 The theory behind surface curvatures is well understood in differential geometry [13],[34]. For our model decomposition, we need only the Gaussian curvature of a surface. The Gaussian curvature at the parameter value (u,v) of a surface S is K(u, v) =κ 1 κ 2 where κ 1 and κ 2 are the principal curvatures at the parameter value (u.v). Thus if X(u,v) is a regular parametric surface, the Gaussian curvature could be expressed as [13], where, K = eg f 2 EG F 2 (6.1) e = N, 2 X u 2 f = N, 2 X u v g = N, 2 X v 2 X E = u, X u X F = u, X v X G = v, X v N = X u X X / X v u X X v (6.2) (6.3) (6.4) (6.5) (6.6) (6.7) (6.8) where, denotes an inner product. Those regions of the surface for which K = 0, is developable or ruled, those for which K > 0, is concave or convex and those for which K < 0 is saddle. Thus by finding the zero set of K it is possible to separate the regions into developable/ruled or concave/convex or saddle. In [15], the numerator of equation 6.1 is computed symbolically as a scalar field by using unnormalized surface normal ˆN which is given by the numerator of equation 6.8. The numerator of equation 6.1 is then given by

75 CHAPTER 6. 3-D CUTTER PATH GENERATION 63 êĝ ˆf Num = ˆN 2 where ê, ˆf, ĝ are of the same form as equations 6.2, 6.3, 6.4 with N replaced by ˆN. The numerator of Num is then represented as NURBS, and the zero set of it is found using the contouring techniques developed for free-form surfaces. This will be the zero set of K as well. Then by assuming the curvature continuity of the surfaces, trimmed surfaces are created, each of which is completely convex, concave or saddle. The saddle regions can be identified by the sign of Num at a single point in each trimmed surface, while the convex and concave regions are identified by finding the sign of one of the principal curvatures at a point. Thus, this method is attractive for separating well-behaved surfaces into convex, concave and saddle regions. But this method ignores the possibility of developable regions and assumes the surface to be regular and curvature continuous. Also, the computation of scalar fields for higher order NURBS surfaces required the surfaces to be split into Bezier patches. In the presence of the imperfect surfaces, a fully numerical technique may be better suited. A grid of points is formed in the surface. The principal curvatures κ 1 (p) and κ 2 (p) are computed at each point on the grid. p is then grouped into a sub-grid based on the values of principal curvatures. If κ 1 (p) > 0, κ 2 (p) > 0, p is grouped in the concave grid. If κ 1 (p) < 0, κ 2 (p) < 0, p is grouped in the convex grid. If κ 1 (p) > 0, κ 2 (p) < 0 or p is grouped in the saddle grid κ 1 (p) < 0, κ 2 (p) > 0 If κ 1 (p) = 0,orκ 2 (p) = 0, p is grouped in the developable grid. The original surfaces are then trimmed to the sub-grids to form the trimmed surface patches each of which is completely convex, concave, saddle or developable. These trimmed surface patches are further categorized as: Convex patches - Since convex patches could be machined with the flat-end mill cutter, they are categorized as flat-end milled regions.

76 CHAPTER 6. 3-D CUTTER PATH GENERATION 64 Saddle patches - The parts of saddle patches for which one of the principal curvatures has a low positive value are categorized as flat-end milled regions and the rest is categorized as three axis milled regions. Concave patches - Only those parts of concave patches where both the principal curvatures are low, are categorized as flat-end milled regions and the rest comes under three axis milled regions. Developable patches - The developable patches could be machined using the side of the cutter if the cutter axis is aligned along the principal direction with zero curvature. Hence the developable patches are categorized as peripheral milled regions The cutter paths are then generated for the three regions. Figure 6.2: SURFACE SHRINKING FOR FLAT-END MILLED REGIONS Cutter path for flat-end milled regions : No surface offset operations are needed for flat-end milled regions[40]. In this, the operation involved in compensating for the tool radius is surface shrinking, in which the the curves bounding the surface are moved along the surface by a distance given by the radius of the tool (Figure 6.2). Cutter paths are generated by indexing the tool along the the shrunk surface with the orientation of the tool along the surface normal.

77 CHAPTER 6. 3-D CUTTER PATH GENERATION 65 Isoparametric curves along with the surface normal information are used for this purpose. Cutter path for peripheral-end milled regions : Cutter path generation for peripheral end milled regions requires the computation of offset surfaces at a distance equal to the radius of the cutter. Since the peripheral end milled regions are composed of developable or ruled surfaces, there won t be any degeneracies that occur in surface offset operations. The cutter paths are generated by orienting the tool along the principal direction with zero curvature. a) Surface to be 3-axis milled b) Intersection curves Figure 6.3: INTERSECTION CURVES FOR 3-AXIS MILLED REGIONS Cutter path for three axis milled regions : Most of the literature for CNC cutter path generation [9],[30],[59] has been written for this category. In most of these cases ball-end mills are used. Here we consider two approaches. One is the use of adaptively extracted isocurves [16] to generate cutter paths. This method requires the computation of the offset surfaces. In a work by Tang et al. [59], an offset algorithm has been described that not only offsets surfaces but offsets boundary curves of the surfaces to generate tool paths that are smooth and have minimal un-cut area. But the offset surface may contain degeneracies like self-intersections [3] which are difficult to detect effectively. Hence, from a practical consideration, we have used intersection curves obtained by intersecting the region with parallel planes to generate the cutter paths (Figure 6.3). The intersection curves are offset for the radius of the tool in a manner similar to that described in the previous section and these offset curves are used to cutter trajectories with the cutter oriented along the z-direction.

78 CHAPTER 6. 3-D CUTTER PATH GENERATION Collision Free Paths In the previous section, the cutter paths were generated without considering the cutter interference problem [38]. Cutter interference could be caused due to the interaction between different regions of the model and those between the model and machine components. The paths are generated to be executed in a 5-axis NC machine with two revolute joints and three prismatic joints. While the joint limits of the prismatic joints are of less importance (as the size of the parts are usually well within the limits), the joint limits of revolute joints have to be considered while generating the paths Collision types The paths can have collision from the following sources. Single surface gouging (SSG) : Gouging results when the tool overcuts the part surface (Figure 6.4 a). SSG is often encountered when the tool size is too large relative to the concave radius of curvature. Multiple surface gouging (MSG) : This type of gouging occurs when the tool positioned in correct position results in an interference with the adjacent surface(s) (Figure 6.4 b). Collision with Machine Structure (CMS) : This occurs when the machine components (tool head, coolant supply, etc.,) collide with the workpiece. Revolute Joint Limits (RJL) : Though this is not an actual collision, the limits on the revolute joints can be modeled as artificial stops Collision Detection and Avoidance Two objects are in collision if the distance between them is zero. Thus collision detection is related to distance computation between objects. The collision detection for the first two types of collision (SSG and MSG) will involve identifying collision

79 CHAPTER 6. 3-D CUTTER PATH GENERATION 67 a) Single Surface Gouging b) Multiple Surface Gouging Figure 6.4: TYPES OF GOUGING between the tool and the part surface. SSG will be handled during cutter path generation in the case of flat-end milled and peripheral-end milled regions. In the case of three-axis milled regions we might have SSG since cutter paths were generated from iso-curves. Since the paths for different regions were generated independently without considering the interactions with neighboring regions, the cutter paths have to be checked for MSG and CMS. RJL will be an issue only in the case of flat-end milled and peripheral end-milled regions. It could be handled either at the cutter path generation stage or at this stage. In order to avoid a computational overhead at the cutter path generation stage, RJL is also handled at this stage. The joint limits are modeled as artificial stops and is captured under CMS. Since there are going to be a large number of points on the part surface along which the tool will travel, the number of collision checks will be very large. Thus an efficient algorithm has to be used for collision detection. The algorithm described by Quinlan [49] is adapted for this purpose. A hierarchical boundary representation is built for the part model, tool, machine components and the artificial stops. The bounding representation consists of an approximately balanced binary tree with the property that the union of all the leaf

80 CHAPTER 6. 3-D CUTTER PATH GENERATION 68 spheres completely contains the surface of the object. Collision occurs when the distance between different objects is less than an epsilon value (which is based on the desired accuracy of detection). The bounding representation helps in narrowing down the pairs of surfaces for which distance has to be computed. After narrowing down to the pairs of surfaces, the distance between those surfaces have to be computed. Since a method to compute distances between any two surfaces is not known, the surfaces will described by convex polygons and the distance algorithms for convex objects will be used to compute the distance. One well known convex representation of a surface is the triangulated surface. For those points for which collision occurs, an alternate solution has to be proposed to avoid collision. In most cases the solution might be to go for ball end mill cut. But there are a couple of issues that makes this problem tricky. First, there will not be one-to-one correspondence between the different types of cutter regions. Next, there won t be one-to-one correspondence between the polygonized surface and the actual surface. Hence as a first step, the solution is to generate the cutter paths for all types of cutter regions and test them for collision and drop those points at which collision occurs. If some regions of the model are still left un-cut, the next cutter size is chosen and the process repeated. 6.3 Summary An algorithm has been proposed for fully automatic 3-D cutter path generation for a compact. Based on the curvature data, the surfaces of the model were grouped under four categories, concave, convex, saddle and developable surface patches. These patches were subsequently grouped into three types, flat-end milled, peripheral-end milled and three-axis milled cutter regions. Methods of cutter path generation were described for each of those regions. This chapter also described the way to avoid cutter interference problem that could be caused due to the interaction between different regions of the model and those between the model and machine components. A robotic collision detection algorithm has been modified and used for this purpose. Before being downloaded into the CNC machine, the cutter paths would have to be

81 CHAPTER 6. 3-D CUTTER PATH GENERATION 69 transformed relative to the CNC machine coordinate system. Appendix A describes these kinematic transforms. The algorithm presented in this chapter could be enhanced by considering the problem of maintaining continuity in cutter paths across surface patches and the three types of cutter regions.

82 Chapter 7 Software Issues The CAD model undergoes a variety of geometric operations during different stages of process planning. In order to withstand the complex geometric operations, a powerful and robust geometric engine should serve as a backbone for the process planner. The geometric engine should also have the capability to create new models and accept different input formats. Some of the terms used in the context of geometric modeling are described in the next section. 7.1 Terminology The following definitions have been culled from various geometric modeling and solid modeling texts [17],[27],[41],[46]. B-rep stands for Boundary representation. Here the object is represented in terms of its surface boundaries: vertices, edges and faces. It is the widely used representation of a solid model. Traditionally B-reps were restricted to planar, polygonal boundaries. In the past decade, there have been many efforts to incorporate parametric surfaces as boundaries in B-rep and these are also referred to as exact B-rep. CSG stands for constructive solid geometry. In CSG, simple primitives are combined by means of regularized Boolean set operators. An object is stored as a tree with operators at the internal nodes and primitives at the nodes. Transformations such as rotation and translation are also represented as nodes. 70

83 CHAPTER 7. SOFTWARE ISSUES 71 NURBS stands for nonuniform rational B-splines. These are rational B-spline curves that are becoming the standard curve and surface descriptors in CAD. NURBS entities are defined by a set of control points and rational blending functions. Manifold topology. Most of the B-rep geometric modelers support only solids with two-manifold topology. Every point on a two-manifold topology has some arbitrarily small neighborhood around it that can be considered topologically the same (homeomorphic) as a disk in the plane. If there is any point on the boundary that does not satisfy the two-manifold condition, the object is classified as non-manifold. 7.2 CAD system requirements Traditionally, surface modeling has been the widely used representation for CNC path planning. It is only in the past five years, solid models are being used for CNC path generation. In systems that use solid models, the solid modeling information is used to check collisions and the cutter paths are still generated on a surface-by-surface basis. Thus the solid needs to be represented as an exact B-rep in such systems. In SFF processes, linear tessellated geometry has been used to represented the solid. This kind of representation originally evolved for applications in rendering, but has become popular in SFF due to its ease of generation. In SDM, due to the nature of geometric operations and its ability to handle complex shapes, a more sophisticated geometric engine is needed. Some of the requirements of the geometric engine in SDM are: Availability in the form of an API API stands for Application Procedural Interface, wherein the geometric engine is provided in the form of libraries consisting of user-callable routines. The process planner for SDM is implemented using a high level programming language such as C or C++ by calling different geometric routines at different stages of the planner. An effective way to provide this interface is in the form of an API library. Ability to handle mixed-dimensional operations In SDM, the same compact is used for a variety of tasks such as deposition path generation, 2-D cutter path

84 CHAPTER 7. SOFTWARE ISSUES 72 generation and 3-D cutter path generation. As part of the geometric querying process, both the two-dimensional and the three-dimensional representations of the solid are used. Thus the geometric engine should be able to accommodate entities of mixed dimensionality. Ability to handle non-manifold topology Though almost all physical artifacts are two-manifold objects, the domain of two-manifold topology does not have closure under set boolean operations. Thus non-manifold configurations can occur as a result of boolean operations involving manifold objects. In the case of SDM, non-manifold configurations could result during slicing in the compact decomposition process. Also, SDM has the capability to produce multi-material objects and it is very difficult to handle such objects with two-manifold topology. Ability to handle freeform (NURBS) surfaces As opposed to standard SFF processes, one of the main differences in geometry in SDM is its capability to reproduce freeform surfaces. Thus, in order to make take advantage of this, the geometric engine should be able to handle NURBS surfaces. Some of the key challenges in handling NURBS surfaces involves providing robust surfacesurface intersection routines and providing geometric queries on those surfaces. Graphical front-end It would be useful if the geometric engine has an user interface that will help in creating and editing solid models. The graphical front-end would also be helpful as a debugging tool. Neutral formats The models for SDM can come from different sources and the process planner should have the capability to handle these models. If the models were created using the same geometric engine as used by the process planner, then the process planner should be able to read in those models. But if the model was created using a different geometric engine, then it has to be converted into a neutral format and the geometric engine should have the ability to accept those neutral formats. Some of the standard neutral formats for geometric models are:

85 CHAPTER 7. SOFTWARE ISSUES 73 STEP STEP stands for STandard for the Exchange of Product model data and it is an ISO standard that was developed to allow exchange of engineering product data. In STEP, the geometric information is captured by an application protocol called AP203. Some of commercial solid modelers have a STEP AP203 translator module and some of the remaining ones are developing a STEP AP203 translator. IGES IGES stands for Initial Graphics Exchange Specification and is the precursor to STEP. IGES permitted the exchange of product definition data by representing geometric and topological data in a neutral format. It was difficult to represent solid model information in an unambiguous manner using the IGES format. Most of the commercial CAD packages have the capability to output their results in the IGES format. STL It is the defacto standard among the SFF systems. In this format, the model is represented by a collection of triangular facets. In order to represent a solid model in this format, the faces of the model have to be tessellated. Though it is a very simple representation and could be generated by any CAD system, it is approximate and lacks in topological information. In addition to the capability of reading models in these neutral formats, the geometric engine should also be capable to output its model in these standard neutral formats. Geometric functionality In addition to providing the basic functions such as boolean operations, the geometric engine should be rich in its functionality. In the implementation of the process planner, there will often be situations where there will be a need to know geometric properties such as surface normals, surface curvatures, curve tangents, etc. Another useful functionality would be the sweep functionality which was needed as part of the compact decomposition algorithm. Though it might be possible to implement geometric property evaluations and sweep functionality as part of the process planner, it would be efficient if it is implemented within the geometric engine.

86 CHAPTER 7. SOFTWARE ISSUES 74 Robustness Last but not the least, the geometric engine should be robust. The process planner is intended to be free of human intervention and if the underlying geometric engine fails often, it would be difficult to achieve that goal. The CAD model will undergo a variety of geometric operations within the process planner wherein it might encounter some degenerate geometric configurations. It would be best if the geometric engine handles such degenerate cases. If not, it should at least be able to identify them and report them as errors. Also, the geometric engine should be consistent in its results and should never return incorrect results. If the calling routine is unaware of an incorrect result being returned, it might lead to disastrous consequences. 7.3 CAD System Comparison There weren t many systems that met all the CAD requirements. One of requirements that is essential for the process planner is some sort of API functionality as it would have been infeasible to implement the process planner without API functionality. As far as we know, there were only five systems that had API functionality. These were: 1. NOODLES : NOODLES is a geometric modeling kernel developed at the Engineering Design Research Center of Carnegie Mellon University. NOODLES is based on non-manifold boundary representation and is available in the form of an API library. It is robust and handles mixed dimensional operations. One of the greatest drawbacks with NOODLES is that it cannot handle freeform surfaces. Thus all models created with NOODLES will have faceted geometry. Also, being a non-commercial system there is no provision to interchange models in neutral formats except for the STL format. NOODLES provides the basic primitives and boolean operations among those primitives to aid in model creation. It also permits geometric and topological queries on its geometric entities. An interface called DISH was developed at EDRC of Carnegie Mellon University to provide a graphical front-end for NOODLES.

87 CHAPTER 7. SOFTWARE ISSUES ACIS : ACIS is a geometric modeler from Spatial Technology Inc.. ACIS is the most popular geometric modeler available in the form of an API library. ACIS handles freeform geometry and permits geometric queries on its entities. Though it claims to handle non-manifold geometry, it is fundamentally a manifold modeler with limited non-manifold functionality. It is also not truly mixed-dimensional and it primarily deals with three-dimensional geometry with special functions to handle two-dimensional and mixed-dimensional operations. Though it doesn t come with a powerful graphical interface, there are commercial solid modeling packages such as AutoCAD from AutoDesk Inc. that can be used as the graphical front-end for ACIS. ACIS doesn t have provision to handle models in neutral formats, but there are quite a few commercial systems that can handle two-way translation of ACIS models into neutral formats such as IGES, STEP and STL. ACIS is not very robust and in our experience, it was failing or producing incorrect results in some situations. But the encouraging fact is that ACIS is continually under upgrade and development and hopefully in the future it will be a robust geometric modeler. 3. Pro/DEVELOP : Pro/DEVELOP is a toolkit that offers the ability to access geometric information created with Pro/ENGINEER of Parametric Technology Corporation. Pro/ENGINEER is one of the most popular CAD systems. It is known to be a robust CAD system. It is a parametric, feature-based modeling system with ability to handle freeform geometry. But, it was not a serious candidate in our case as Pro/DEVELOP has only a small fraction of the functionality provided by Pro/ENGINEER and also Pro/ENGINEER doesn t have mixed-dimensional capability and is a manifold modeling system. 4. SHAPES : SHAPES is a geometric modeling library from XOX Corporation. SHAPES is a truly non-manifold boundary representation system and it can handle freeform surfaces. It is dimension independent and thus can handle mixed-dimensional operations. It is fairly robust. Some of its drawbacks are its lack of functionality, non-availability of powerful user interface and inability to interchange models in neutral formats. It offers only limited geometric queries

88 CHAPTER 7. SOFTWARE ISSUES 76 on its entities and there aren t any commercial systems that can translate models in neutral formats to SHAPES models. 5. Parasolid : Parasolid is a boundary-representation geometric modeler developed by EDS Unigraphics. Parasolid is supplied as an API library and supports freeform surfaces. It has a powerful user interface available as part of the Unigraphics CAD system. Unigraphics also has the facility to do a two-way translation of parasolid models into neutral formats. Parasolid offers geometric and topological enquiries on its entities. Though it offers some support for nonmanifold operations, parasolid is not fully non-manifold. It is not dimension independent, but it offers some support for mixed-dimensional operations. Though its robustness has not been fully tested, the initial indications are that it won t be very robust due to its ambiguous handling of non-manifold and mixed-dimensional operations. These CAD systems were evaluated against the CAD system requirements. Figure 7.1 shows a chart indicating the performance of different CAD systems against those requirements. In the chart, the amount of filling of a CAD system/function box indicates the availability of that function in that CAD system. 7.4 Implementation issues The first version of the process planner was implemented in NOODLES [58] in C language. NOODLES was selected as the initial system as it was available in-house and it could handle non-manifold topology [24] and it was available as an API library. Being the first prototype of the planner, it underwent several revisions and also helped us in refining our data structures. This planner failed in some degenerate geometric configurations which were caused by points on the model that were very close to each other. These problems were overcome by tweaking some of the parameters of the modeling system. But the biggest hurdles were the lack of support for freeform geometry and inability to handle models in neutral format. Some effort was spent to add freeform functionality in NOODLES, but since it was turning out to be a major

89 CHAPTER 7. SOFTWARE ISSUES 77 NOODLES ACIS Pro SHAPES DEVELOP ParaSolid API Mixed Dimensionality Non-manifold Free-form Surfaces Graphical front-end Neutral formats Geometric Functionality Robustness Figure 7.1: CAD SYSTEM COMPARISON CHART effort, it was dropped and the next version of the process planning system for SDM was implemented using ACIS [31] geometric modeler in C++ language. ACIS was selected as it claimed to have non-manifold and mixed-dimensional capability and it was available in the form of an API library and it was a very popular system. But as the implementation of process planner in ACIS progressed, we started facing quite a few robustness issues. Some of the ACIS functions were replaced by our own functions and this took care some of the problems. On the positive side, ACIS comes up with a new release every few months wherein they attempt to make it more robust. On the downside, the new releases are not downward compatible and thus it warrants

90 CHAPTER 7. SOFTWARE ISSUES 78 rewriting portions of the planner. Initially, without a powerful graphical interface model creation was very difficult in ACIS. This problem was overcome with the release of AutoCAD version 13. Currently, the process planner is being implemented in SHAPES and Parasolid.

91 Chapter 8 Applications Several parts were built in SDM using this process planner. The parts were varied in nature and all the aspects of the process planner were put to test. Most of the parts were built successfully using the process planner. In the case of some parts, the process planner had to be modified to overcome some errors. Most of these errors were due to the underlying geometric modeling kernel. Building these parts also helped in a better understanding of some of the finer aspects of the process which subsequentally helped in improving the process planner. The parts that were built using SDM could be broadly classified into three categories. Geometrically complex parts Next generation metal tooling Non-conventional parts In the following sections, some example parts will be shown in each of the above categories highlighting the process planning aspects wherever necessary. I would like to thank my colleagues in SDM lab of CMU and RPL lab in Stanford for their effort in building these parts. 79

92 CHAPTER 8. APPLICATIONS Geometrically complex parts These are parts with complex geometrical shapes that would require significant time and effort with the conventional methods. In the conventional manufacturing methods, these parts would be almost impossible to produce without human intervention. In SDM, with the availability of a process planner, these parts could be produced in a fairly automated fashion IMS-T2 Figure 8.1: CAD MODEL OF IMS-T2 IMS-T2 is one of the first test parts built using the SDM process. It was one of the test parts that was used in a world-wide assessment of rapid prototyping technologies [5]. At the time when this part was built, the process planner was in its early stages and was built on top of the NOODLES geometric modeling kernel [58]. The compacts were generated manually and the cutting paths were generated using the process planner. The model shown in Figure 8.1 was constructed as a CSG tree

93 CHAPTER 8. APPLICATIONS 81 in NOODLES. Since NOODLES is a polygonal modeler all the freeform surfaces of the model were approximated by facets. The support model was decomposed into 8 compacts. The compacts C1 C7 shown in Figure 8.2 were generated by doing a rigid sweep of all the undercut surfaces of the model in the Z direction. C8 (Figure 8.2) was obtained by subtracting the union of previous seven compacts with the part model from a block bigger in size than the bounding box of the model. These compacts along C7 C6 C5 C2 C3 C4 C1 a) Compacts C1 - C7 C8 b) Wireframe rendering of compact 8 Figure 8.2: COMPACT DECOMPOSITION OF THE SUPPORT IN IMS-T2 with part model were sliced into 29 layers using horizontal planes to satisfy the process constraints. This resulted in a total of 79 compacts. The 2-D cutter paths for rough cutting and profiling were generated for the bottom cross-section of these compacts. Because of the polygonal representation of the compacts, there were some tiny facets for which 3D cutting strategies could not be generated. The presence of so many facets resulted in large CNC files. These factors prompted us to seriously consider a nonlinear geometric modeling kernel. After this part was completed, some effort was

94 CHAPTER 8. APPLICATIONS 82 spent in adding the nonlinear functionality to NOODLES. Since this seemed to be a long-term effort, ACIS [31] was adopted as the geometric modeling kernel for the next version of the planner. Figure 8.3 shows the stainless steel IMS-T2 part produced with the SDM process. Copper was used as the support material and was etched out after the part was completed. The materials were deposited using microcasting. This part helped us to identify some of the process planning issues and also demonstrated the usefulness of the planner. Figure 8.3: IMS-T2 MANUFACTURED WITH SDM 8.2 Next generation metal tooling Next generation metal tooling are dies for injection molding with a strong steel exterior, conformable cooling channels, multi-material inserts such as copper and INV AR TM and embedded sensors. Such tools have quite a few advantages. The steel exterior would provide a solid base for the die, cooling channels and copper inserts would help in heat distribution and avoid forming hot spots in the tool, materials with low coefficient of thermal expansion such as INV AR TM would control distortion in geometry and the embedded sensors such as thermocouples would help to measure certain parameters during molding.

95 CHAPTER 8. APPLICATIONS GM Injection molding Tool The design for the tool was provided by GM as engineering drawings. The CAD model of the mold halves were created in the test harness provided by ACIS [31]. Internal U shaped cooling channels and models corresponding to copper inserts were also created in the model. All the concave silhouette loops were on horizontal planes and the model and support were sliced along these planes. Since all the compacts were 2.5D structures, the deposition paths and 2-D cutter paths were generated corresponding to the bottom cross-section of each compact. This part didn t require any 3-D cutter paths. Figure 8.4 shows the injection molding tool made with the SDM process. The Figure 8.4: INJECTION MOLDING TOOL part is made from 316L stainless steel. One half of the tool has four copper deposits. The part material was deposited using the laser system and microcasting was used to deposit the support material. Some of the small features that could not be cut with end-mills were machined with EDM.

96 CHAPTER 8. APPLICATIONS Non-conventional parts The most widely recognized advantage of layered manufacturing is the relative ease of fabricating complex geometric shapes. But a process such as SDM that builds parts by incremental material deposition and material removal has far-reaching potential. We could fabricate parts that are either impossible or almost impossible to manufacture with conventional manufacturing methods. These parts are referred to as nonconventional parts. The non-conventional parts could further be categorized as Parts with interacting geometric features Conformable, embedded electro-mechanical parts Assembled mechanisms Parts with interacting geometric features Figure 8.5: CAD MODEL OF TILTED FRAMES These are parts with complex geometric interactions that makes them almost impossible to manufacture as a single piece with conventional methods. The parts in this category will make full use of the compact decomposition algorithm.

97 CHAPTER 8. APPLICATIONS 85 Tilted frames Figure 8.5 shows the CAD model of a part that is very difficult, if not impossible to manufacture by conventional methods. The part was designed and subsequently built using SDM by Merz[43]. This model serves as a good test case for the compact decomposition algorithm. Figure 8.6 shows the silhouette edges and loops for this model. Figure 8.6: SILHOUETTE CURVES AND LOOPS The model is then sliced into layers with horizontal planes passing through the lowest and the highest points of the concave silhouette edges (Figure 8.7a). Except for layer3, the decomposed models in all other layers do not violate any of the requirements to be satisfied by a compact. Layer3 is further decomposed as shown in Figure 8.7b such that all the compacts satisfy the three requirements. The support model is decomposed in a similar fashion and the compacts are sequenced for SDM processing. The deposition paths were generated corresponding to union of the top and bottom cross-sections for each compact. The zigzag deposition strategy was used. 2-D cutter paths were generated corresponding to the bottom cross-section of the compacts. For some of these cross-sections, there were self-intersections of the offset model which

98 CHAPTER 8. APPLICATIONS 86 Layer4 Layer3 Layer2 Layer1 b) Further decomposition of layer3 a) Decomposition using horizontal planes Figure 8.7: SPATIAL DECOMPOSITION OF TILTED FRAMES were effectively handled by the planner. All the faces that had to be cut with a 3-D cutter were identified as peripheral milled regions and the corresponding cutter paths were generated. Figure 8.8 shows the tilted frames part produced using the SDM process. The part was made out of stainless steel and copper was used as the support material. Microcasting was used to deposit the materials. We faced some difficulties with the ACIS kernel when building this part. Some of the models produced after the compact decomposition were incorrect. This can be attributed to the non-uniform handling of non-manifold features in ACIS. Some slight changes to the model helped us to alleviate the problems.

99 CHAPTER 8. APPLICATIONS 87 Figure 8.8: TILTED FRAMES Conformable, Embedded Electro-mechanical parts One other category of parts that are made possible by the SDM process are the embedded electronic parts [67]. These are parts in which the housing could be composed of different materials to provide strength, lightness and toughness. Inside the housing, electronic circuits that are pre-fabricated are embedded. The housing can be of conformable shapes. Such parts are compact, will be rugged in harsh environments and can made to have a very good aesthetic appeal. In the current planner, the pre-fabricated electronic circuits are inserted manually. VuMan VuMan [57] is a personalized wearable computer that can store maps for navigational aids or detailed assembly drawings for service or maintenance applications. VuMan was built in the AutoCAD TM solid modeler. The AutoCAD TM model is saved in the ACIS format. Only the support model had to be decomposed into compacts. Both the model and the support were decomposed into three layers using horizontal planes to facilitate the insertion of the printed circuit boards (PCB). The model was made out of two-component polyurethane and was deposited manually and partially cured before machining. The bottom layer of the support and the top layer of the part involved 3-D cutting strategies. In this part, all three types of cutter regions were present. The conical portions were cut using the peripheral end mill strategy, some

100 CHAPTER 8. APPLICATIONS 88 of the cylindrical portions were cut with the flat end mill strategy and three axis mill strategy was used for some of the blended regions. Figure 8.9: VUMAN EMBEDDED ELECTRONIC STRUCTURE Figure 8.9 shows the completed VuMan structure and cut-away view of VuMan CAD model. As mentioned earlier, the part was built out of two-component polyurethane mixture and wax was used as the support material. The PCBs were electrically interconnected using pin receptacles. Component parts which were not fully embedded were protected during deposition with plastic covers which were machined away during the final machining operation. Simon game Figure 8.10: CAD MODEL OF SIMON GAME PIECE

101 CHAPTER 8. APPLICATIONS 89 Simon game is a popular 2-button hand-held game. This is another example of embedded electronic structure built with SDM. The CAD design of Simon part was first done in NOODLES as a CSG tree. The CSG tree primitives and operations were then replicated in the ACIS test harness to create the ACIS model. Figure 8.10 shows the CAD model of the simon game part. Figure 8.11 shows the simon game piece Figure 8.11: SDM-SIMON GAME manufactured with SDM. It is made of two component polyurethane and wax was used as the support material. The wax was melted out at the end. Two Prefabricated PCBs were inserted manually at an intermediate stage of the process Assembled mechanisms SDM was also used to produce simple mechanisms. It is possible to produce fully assembled functional mechanisms in an integrated fashion with the SDM process. This is mainly made possible by the presence of the sacrificial support structure that holds the moving parts of the assembly while the part is built. Once the support structure is removed the moving parts are free to move again. Figure 8.12 shows the photograph of a simple crank and piston mechanism made with SDM. The CAD model was built in the ACIS test harness. All the concave silhouette loops were on horizontal planes and the compacts were generated by slicing along these planes. The deposition paths and 2-D cutter paths were generated corresponding to the bottom cross-section of each compact. The part was made from stainless steel with copper

102 CHAPTER 8. APPLICATIONS 90 Figure 8.12: CRANK AND PISTON MECHANISM as the support material. Stainless steel was deposited using the laser station and microcasting was used to deposit the support material.