Heterogeneous Solid Modeling for Layered Manufacturing

Heterogeneous Solid Modeling for Layered Manufacturing D. Duttal, M. Shpitaln? ( 1 ) Dept. of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, USA ZLaboratoryfor Computer Graphics and CAD, Dept. of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, Israel Received on January 4,2000

Abstract We consider layered manufacturing as a fabrication technique for metallic, functional parts. While commercial machines still do not support metals, several research systems are already in existence in universities and research laboratories. Such systems can create multi-material parts and can vary material composition within the layer. A key enabling technology for the automation of such layered manufacturing systems is heterogeneous solid modeling. Current CAD systems do not provide the capability to deal explicitly with material heterogeneity. We provide an overview of this new field, propose a method for modeling and representing material in addition to geometry and topology, and discuss some related research. Keywords: CAD/CAM, Geometric Modeling, Rapid Prototyping.

1

INTRODUCTION

Layered manufacturing is a new method of fabrication. In layered manufacturing (LM), a part is built by depositing material, layer-by-layer, under computer control. In conventional manufacturing (e.g., CNC machining), a part is fabricated by selectively removing material from a workpiece. This is inherently a 3D process. In contrast, layered manufacturing is a 2.5D process-stacking up layers. A distinct advantage of creating a part layer-by-layer is that its geometric complexity has a significantly less impact on the fabrication process. In industry, layered manufacturing is often referred to as “rapid prototyping” reflecting the most common use. LM is widely used for the rapid fabrication of physical prototypes of functional parts (important in the design stage), patterns for molds, medical prototypes (implants, bones), consumer products, etc. The unique feature of LM is ”direct” fabrication-it does not involve tooling, fixturing and other peripheral activities of conventional manufacturing. Therefore, it is possible to start from a CAD model and create the physical part in a very short time (e.g., hours instead of days). Since 1990 extensive research and development work has been carried out in the field of rapid prototyping [I-31 and, in particular, work on laser sintering and deposition [4-61. Commercial implementations of layered manufacturing became available in the late 1980s with the Stereolithography machine by 3D Systems of California. Since then, this industry has flourished and a partial list of current LM systems includes Selective Laser Sintering, Fused Deposition Modeling, Solid Ground Curing, Laminated Object Manufacturing, etc. An attractive feature of LM, that is just beginning to surface, is the selective deposition of material (on a layer) and changing of material between layers. This leads to the direct fabrication of multi-material structures since embedding of prefabricated (electronic or other) components is possible (e.g., an outer shell of tool steel with interior copper cooling channels). Furthermore, different materials, in varying proportions, can be deposited on a single layer and the part can be endowed

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with microstructure. Advances in mechanical and structural design have led to the development of mathematical techniques for the design of the topology and material micro-structure of such “heterogeneous” objects (see also Figure 1). For example, the homogenization design method (HDM), developed at the University of Michigan, in Project Maxwell, yields material microstructure and density distribution for a part that corresponds to designer-prescribed properties [7]. Using HDM, parts with negative Poisson’s ratio can be designed. Conventional manufacturing techniques cannot realize such novel and efficient designs.

Figure 1: A Heterogeneous object While commercial LM systems of today are used for rapid prototyping applications, the fabrication of heterogeneous objects represents the true potential of layered manufacturing. A key enabling technology for harnessing this potential is heterogeneous solid modeling (HSM) and application algorithms. In the remainder of this paper we briefly describe our research on HSM and new (layer manufacturing process planning) algorithms using HSM. 2

HETEROGENEOUSSOLID MODELING

Presently, all commercial LM processes require that the CAD model of the part to be manufactured be converted to the STL format prior to fabrication. Roughly speaking, the STL representation is a faceted surface description of the solid part with an orientation for each facet (a

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triangle), but without any adjacency information. Although simple and universally accepted, there is a growing dissatisfaction with the STL format among LM users [8]. All other representation schemes also represent the boundary and assume a homogeneous interior. Limited capabilities are offered by octree- and voxel-based representations; these, however, are not practical in mechanical design. Nonetheless, recent research has been dedicated to developing product modelling systems for rapid prototyping [9-11). Table 1 summarizes the evolution of CAD systems from simple automated drafting systems to current solid modelers. Solid models are critical to automation tasks in process planning, assembly planning, engineering analysis, etc. and the field has been an active area of research in computer science and several engineering disciplines. Advances in solid modeling technology are closely linked to the growth of the rapid prototyping industry. The solid model of an object contains geometry information stored as data and topology information incorporated in the data structure. Current solid modelers do not typically support representation and processing of information about the object's interior (material, density or other heterogeneities). However, if layered manufacturing is to become "product-model driven" (like CNC machining is today) advances in heterogeneous solid modeling is critical. Next, we describe our method for heterogeneous solid modeling. It builds upon existing technology and hence compatibility with current systems is established. 2.1 Theory Traditional geometrickiolid modeling has focussed on modeling objects to capture their geometry and topology [12]. Subsets of the Euclidean space R3 are used as the modeling space T where mathematical models of physical objects are created. In order to represent objects having heterogeneous material domains, the modeling space T must now include a material dimension (M) in addition to the spatial dimensions R3. If we consider objects made of a finite number of discrete materials, the simplest choice for the material dimension M would be the set of integers 2 . However, to model more complicated objects with continuous material distribution, a suitable choice for the new mathematical space is T = R3 X R", n being the number of primary materials. Therefore, R3 is the geometry space and R" is the material space with each dimension representing one particular primary material. Each point in the object can be composed of one or more primary materials. Thus, the material at any point can be identified by volume fractions of each of the primary materials.

Noting that these volume fractions must sum to 1, we can precisely define the space of volume fractions V as (An underline is used to denote a vector in the corresponding space, such as y):

i=l

where v, (i-th component of v) represents the volume fraction of material i. Thus, any point y in R" can represent a material composition only if it lies on the subspace (or surface) V in R". Note that porosity of a local region can also be modeled by including void as one of the primary materials and therefore V in Eqn 1 has (n-1) degrees of freedom. A material composition function, F, can be defined that maps a geometrical point in the heterogeneous object to a material pointy. This one-to-one mapping is given by

F : R"

E

R']

I

=1

Each point in the heterogeneous object S' can now be characterized in product space T as &, vQ)} where represents the position of the point and vQ) represents the material mixture at that point. The surrounding space is distinguished from the void inside the object by assigning the surrounding space v(x) = 0. Our implementation of the Heterogeneous Solid Modeler is based on a hybrid scheme with a B-Rep kernel [13]. The data structure of the kernel is appropriately modified to accommodate the material dimension of the object. The link to the material function module is required at all levels of the data structure for the purposes of querying. The system supports Boolean operators that a designer can use to combine (heterogeneous) primitives and create complex objects. Alternatively, the material composition can also be specified after the object geometry has been created.

x

3

PROCESSING

HETEROGENEOUS

SOLID

MODELS FOR LAYERED MANUFACTURING Manufacturing process planning involves determining machining processes and parameters to convert a workpiece to the final part. In layered manufacturing, process planning tasks include determining part orientation, support structures, slicing, toolpaths and build parameters 1141.

Motivating Applications

1950s

Computer Graphics & NC machining

Geometry

CADICAM LM & Optimal Design

Geometry & Topology Geometry, Topology & Material

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I llF (3

where

Year

1960s 1970~-80~ 1996-

+v

Object Attributes

Computer Representation Electronic Drafting and Wireframe Polygonal and Surface Models Solid Models Heterogeneous Solid Models

CAD MODEL 'ROCESS PLANNING

&

supports

Slicing

Path Planning

I I

4 MANUFACTURE

Figure 2: Key Process Planning Tasks in Layered Manufacturing These process-planning tasks span the model and layer domains. In the model domain, the task (part orientation) requires considering the entire CAD model and in the layer domain the task (path planning) requires information about individual layers. Processing heterogeneous solid models for planning tasks such as slicing and path planning involves considering the geometry and the material distribution within the model. In the remainder of this paper, we consider slicing. First we describe the geometric problem and then discuss issues related to slicing of heterogeneous solid models. 3.1 Slicing in Layered Manufacturing Slicing is the generation of planar contours which when stacked approximate the 3 0 object. During the manufacturing process, material is deposited within the contour, one layer at a time. Typically, to obtain the contour profile, the CAD model (or an STL file) of the object is intersected with evenly spaced horizontal planes (referred to as uniform slicing). A consequence of building an object by depositing material layer by layer is that its surface exhibits a staircase effect, as shown in Figure 3.

With each layer, we associate a cusp height (6) that reflects the error between the manufactured surface and the progenitor (nominal) surface. The cusp height has a direct relationship to the manufactured surface quality in that the lesser the variation in cusp height the better is the surface. For curved surfaces, it is immediately evident that constant thickness slicing can never yield a uniform cusp height as shown in Figure 3(a). Hence the motivation for varying the slice thickness based on the surface curvature (also referred to as adaptive slicing). Cusp height control for a layer manufactured surface can be dimensional as well as positional. Thus far we have discussed dimensional control only, i.e., a uniform 6. Positional control refers to whether the cusps lie on the outside of the nominal surface (requiring excess material to be removed) or lie within the nominal surface (requiring a filler material). This control can be expressed in terms of the following three containment conditions, as shown in Fig 3, between the CAD model P and manufactured object Q: (a) P a Q and Q a P, (b) P c Q and (c) Q P and We refer to condition (b) as excess deposition and condition (c) as deficient deposition. In situation (a) some portion of P is inside Q and some other portion of Q is inside P, and therefore (a) is undesirable. Our adaptive slicing module (ASM) developed at the University of Michigan allows the user to exercise positional control on the cusp heights to insure that situation (a) does not happen. The layer thickness at any point P is computed by taking into account the curvature of the corresponding surface along the build direction. The surface is locally approximated by the circle of curvature along the vertical direction on the tangent plane. Based on this circular approximation and the user specified allowable cusp height 6, the layer thickness d is computed at that point. Our ASM algorithm requires the native CAD model (not STL files) since the curvature information is of prime importance. For a complete description of the algorithm, we refer the reader to [15]. 3.2 Slicing Heterogeneous Solids To generate a heterogeneous slice, each material domain in the heterogeneous object is intersected with a horizontal plane at that z-height. Each slice now comprises of several material regions corresponding to the different material domains. Within each region, the material composition can either be constant or varying according to some designer-specified composition function (i.e., function F in Eqn 2). The circular approximation of the vertical normal section can still be used to calculate the layer thickness. However, both the exterior surfaces of the model as well as surfaces that adjoin different material regions (referred to as internal surfaces) need to be considered.

2

(a) uniform

(b) excess

(c) deficient

Figure 3: Slicing Containment Conditions

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decisions will have to be made about how best to use deposition and removal techniques, and manufacturing data generated for the fabrication of heterogeneous objects.

Since internal surfaces do not contribute to the external surface accuracy of the heterogeneous object, one approach is to ignore them while calculating the layer thickness. However, this issues requires further investigation since the strength of the part can be affected by the (lack of good) bonding between adjacent multi-material regions In our approach, all surfaces of the material domains of the heterogeneous model are considered. Each slice comprises of several material regions with constant or varying composition. The material distribution for each region of the slice is evaluated from the material distribution function corresponding to that domain of the object. Full details on slicing heterogeneous solids are developed in [16].

5 ACKNOWLEDGMENTS The first author acknowledges financial support from U S . and Office of Naval Research grant N00014-97-1-0245 U S . National Science Foundation grant MIP 9714951.

3.3 Other Tasks Using Heterogeneous Solids

2

The orientation determination for heterogeneous objects is an interesting problem that has not been investigated adequately. For conventional (homogeneous) objects, the criteria typically used for orientation is minimization of supports, quality of user-specified surfaces, entrapped volumes, etc. But, for heterogeneous objects, it is necessary to consider material features. This is an unexplored area. What is a material feature? How does one recognize, reason about and process such information for utilization in manufacturing planning. For example, orientation that yields layers with minimum amount of heterogeneities (e.g., distinct material regions, varying composition, etc.) would be attractive. Path planning within such layers will require computation of iso-curves that segment the layer into regions of single material or regions with gradual variation in material composition. Feature based methods for layered manufacturing and design of heterogeneous objects are being investigated [I 71. 4 CONCLUSION Layered manufacturing is a fundamental development in manufacturing that will likely parallel the introduction of numerical control machines. Given the variety and importance of engineering materials, LM is uniquely poised to enable the realization of highly efficient products (parts, assemblies, etc.) that is not possible using conventional manufacturing methods. However, for complex parts, it is likely that the synthesis of material removal and material deposition will provide the maximum benefits and flexibility (see Figure 4).

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Figure 4:A Concept Manufacturing Cell Synthesizing material deposition and removal. Heterogeneous solid modeling will be the key to automation in such manufacturing cells. Using new (material) feature recognition and processing techniques,

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