Institute of High Performance Computing of Singapore
ABSTRACT
There are many fabrication processes in modern manufacturing, but current modeling and simulation tools only simulate a few unit processes based on different geometry models. To overcome the data exchange problem between different models, this paper studies various in-process geometry models together with their working systems / prototypes for traditional manufacturing processes. Novel hybrid multiple-machining and layered manufacturing processes are presented to identify critical issues. Working towards a vision of pervasive modeling and simulation, a unified Voxel-based in-process geometry model for multiple-machining and layered manufacturing simulations is proposed and discussed.
Keywords: Modeling and Simulation, In-process Model,
Multiple Machining, Layered Manufacturing
INTRODUCTION Compared with the sharp decline in computing cost,
worldwide material and machine tool prices are surging. Saving material and manufacturing cost through pervasive application of modeling and simulation (M&S) is not only technically possible, but also makes business sense in today’s increasingly competitive environment.
There are many fabrication technologies in modern manufacturing industries. In addition to the traditional manufacturing processes such as machining, forging, casting, and welding, Layered Manufacturing (LM) technologies have developed rapidly in the past decade. A wide variety of models and simulation methods for traditional manufacturing processes especially machining, have been developed for different purposes based on a range of principles and techniques [1]. For instance, the B-rep model is used for prismatic parts, the section method was developed for pre-
forging design, the Z map has been customized for 3-axis milling while the Dexel and the Octree have been developed for 5-axis machining.
LM differs significantly from traditional fabrication technologies in the sense that a part is produced by adding rather than removing materials. Unlike traditional machining simulation, LM simulation research is still in its infancy [2-3], although water level section methods for LM simulation have been published in a few papers.
Despite the fact that simulations are becoming more widely used, there is a lack of integration with manufacturing processes. Most work focuses on the individual process being simulated. Significant gaps remain in M&S technology – particularly in the provision of a general in-process model (IPM) that can be integrated across diverse manufacturing processes [4]. To overcome the data exchange problem between different models, we extend the concept of the in-process model from machining process to manufacturing process and propose a unified in-process geometry model for multiple machining and layered manufacturing simulations. This paper reports our studies on various IPMs for traditional manufacturing simulation together with the developed working systems/prototypes, and discusses a novel unified Voxel-based IPM for multiple machining and layered manufacturing.
IPM FOR TRADITIONAL MANUFACTURING The in-process model represents the state of the product at
each step in the machining process. It is a 3D geometrical construct that reflects the results of the machining operations. This model allows the user to visually verify that the machining operations have been defined accurately and that their sequence is correct. It can be automatically re-generated when there are changes in the product design, machining parameters or sequence of the operations [1]. In this section, the geometric representation techniques of IPMs for traditional manufacturing simulation are presented. Boundary Representation (B-rep)
The first choice of IPM should be naturally the geometry model used in commercial Computer Aided Deign (CAD) system, B-rep. The benefits of using the same geometry model for CAD as the IPM are obvious. The CAD geometry model is matured and available through CAD development kit, so there is little need to develop a new geometry model kernel. Sharing a common geometry model with CAD, the IPM facilitates seamless integration of CAD-CAPP-CAM.
An automatic forging design and manufacture system was developed by the authors in 1986, in which pre-form forging IPMs were the same as the CAD system CV/MUDUSA running on VAX-11/750 computer [5-7]. However, the creation of pre-form forging IPMs took days of calculation and often failed due to Boolean operation failure.
With a great deal of research effort in the last two decades, the B-rep geometry model has been improved significant in term of Boolean operation stability, but the B-rep based IPMs are still limited to 2.5-axis milling (Figure 1). Park reported a prismatic IPM generation method that employed a polygon extrusion algorithm to sweep a ball-nose cutter [1].
Figure 1: 2.5-axis IPMs
Section Representation
Since the integrated B-rep IPMs can not be created inside a CAD geometry model, a new, ad-hoc cross-section-wire-frame based approach was proposed in a forging die CAD/CAM (Computer Aided Manufacturing) system [5]. The aim was to use a series of paralleled cross-section drawing to represent 3D shapes. Figure 2b depicts the section representation of circled 3D shapes in Figure 2a.
The cross section IPM is widely used in many commercial CAD/CAM systems. I-DEAS from SDRC uses water level cross-section as an IPM for generative machining. In a traditional NC programming environment, a significant
amount of time is spent trying to visualize the in-process stock as it goes through various process stages. With I-DEAS, the wireframe section in-process stock model can be created for downstream applications such as toolpath generation, process planning, fixture designing, and clamp positioning.
Figure 2: Section representation of 3D shape A part can be sectioned along the X, Y and Z axes (Figure
3). The Z-axis section is usually called water level section. For 3-axis milling, the water level section could have many loops, which causes complications in the set operation between sections. X and Y sections are single half loops and the Z value is unique for every points. Thus simplifying the set operation considerably.
Figure 3: Section representation A working system for using IPM in pre-forging design is
described in [5]. A drawing sheet with part sections is first
created first using the BACIS command language of CV/MEDUSA CAD system. Since there are many sections in a drawing sheet, each section wire-frame is assigned to a different layer according to its Y distance, and a certain number of sections can be looped through layers. Then each cutter section is moved to its cutter location and compare with the part sections. The overlap between the cutter section and the part section will be removed from the part section. A real milling IPM is obtained from the collection of the result sections.
The display of sections is provided by line segments and can be confusing when there are too many lines, i.e. there is a need to render the IPM as a realistic 3D image. In order to calculate the surface normal required for rendering, the section wire frame is divided along the X direction by the same step over of Y direction. A so-called regulated section is formed to facilitate the calculation of surface normal and interpolation of points between the sections. A given node in one section is linked to a node in the next section. A node’s normal can be calculated from the four neighboring nodes. Figure 4 shows the regulated section representation.
Figure 4: Regulated section representation
The regulated section can also be used to accelerate set operation between cutter section and part section. Calculation of intersections and trimming between two sections are time consuming and the re-ordering of the line segments requires more computing time. This can be improved with the regulated sections, where the line segments are indexed by both cutter section and part section. Only the line segments with the same index are compared and trimmed, there is mo need to trim two line segments. If all the line segments fall on the regulated nodes, there is no need to trim two line segments. The set operation can be simplified to the comparison of two Z values, which is very fast and stable. Hence, the Z map representation of IPM emerges [6].
Z Map
If all the section line segments fall on the nodes, the object surface can be represented by the Z values of the nodes. A map of Z values represents the object geometry. In t computer language terms, the Z map can be expressed as a two-dimension array Z[i, j], where i represents the index in X direction and j represents the index in Y direction. The XY
position of the Z map can be calculated by i or j times grid size.
Figure 5: Needle bed sample of classic Z Map model The best analogy for a Z map is a needle bed, where
needles are uniformly distributed over the XY plane (Figure 5). The tip of every needle touches the object surface that it represents. A milling simulation can be seen as the tool cutting through the needle bed. These needles can be described in mathematical terms as z-axis aligned vectors, passing through grid points on the XY plane. A Z map representation can be used effectively for surfaces that are visible looking “downwards” on the XY plane. Since 3-axis milling parts are composed of surfaces visible from the z direction, they can be expressed effectively by the Z map representation. With a Z map representation, the machining process can be simulated by cutting the Z map vectors with the cutter.
Figure 6 shows an example of 3-axis milling simulation system that was developed by the first author in 1990. The system was using DOS Extender for Z Map and SVGA for Z Map rendering. The GUI and NC toolpath wireframe display was coded with High C graphics library. The GUI and mouse control developments were very hard job and this was not resolved until the arrival of Windows 95 and OpenGL.
Figure 6: Example of Z Map IPM based milling simulation using DOS Extender and SVGA The vectors in a Z map have direction and length and are
infinitely thin without volume. The top of each vector, where the Z map and object meet, is just a point having no shape. Only at this point the Z map and the object meet with each other. Z map models cannot provide accurate object geometry outside these points. There are many ways of interpolating the geometry between grid points in order to render a Z map model. For example, forming a triangle from three neighboring Z values.
It is obvious that the XY resolution of the Z map grid determines the precision of a Z map model. A finer grid has greater precision but requires increased memory. For a part of 1m*1m, the size of the Z map is 1000x1000 if the precision is 1mm, but it increases to 2000x2000 if the precision is 0.5mm. Reducing the model size and achieving suitable precision becomes a critical issue in a Z map.
One of the solutions is to balance Z precision and XY precision. We used an integer array to replace the more common floating array of a Z map, which reduces the Z map size by half. At the same time, this improves the Boolean operation speed because the comparison of integers is much faster than the comparison of floats. The memory requirement of a Z map is halved again by compressing the Z map file section by section, similar to image compression.
Because of the simplicity of its data structure and fast computation time, the Z map model is used by most commercial CAM software [7-9]. However, a Z map can not approximate vertical wall very well since it always has a slope as showed in Figure 7. This is not a problem for forging die design since there
are always draft angles in forging parts, but it is a serious problem for milling parts since profiling nearly always creates vertical walls.
Figure 7: Classic Z Map model with vertical walls Extended Z Map
Since the precision of the Z map is determined mainly by XY resolution along the vertical walls, increasing the resolution along these walls while reducing memory is a key issue. Fortuitously, one important feature of 3-axis milling can be leveraged. Viewing from the top, the vertical walls only cover a
small percentage of the Z direction projection, so it should be possible to use finer resolution along the vertical walls while maintaining a rough resolution in the planar area. This was the initial idea for an extended Z map.
In our research, at least one grid on a z-map is segregated into sub-cells. Only grids corresponding to intricate features on the surface of an object are assigned sub-cells to improve the representation of object features. Figure 8a illustrates the plan view of the z-map grid with sub-cells 52the front sectional view, while Figure 8b shows the sectional view.
(a)
(b) Figure 8: Extend Z Map with sub-cells along vertical walls
The size of the grid can be reduced through using sub-cells.
But the precision of the XY dimension is still limited by the size of sub-cells. For a sub-cell of 0.1mm, the best precision is 0.1mm in XY plane. There is a need to represent XY dimensions precisely. Instead of using vectors in the sub-cells, we use sticks in the sub-cells that have volumes and surface geometry. A B-rep surface model can be represented precisely using a map of B-rep sticks (Figure 9).
Figure 9: Stick method
Milling simulation with stick method involves Boolean operation between cutter and stick. Figure 10 shows different stick shapes after cutting. The experiments with B-rep stick model are very slow and a huge B-rep model is created. To simplify stick and Boolean operation, a polygon is used instead of real surface in a stick cell. The data structure of a polygon is much simpler than that of a B-rep which needs a group of complicated pointers to maintain a double wing data structure.
Figure 10: Different shapes of stick elements
The real world objects are not always uniform in the XY plane and can be any shape. Nodes are used to enhance sub-cell precision in object face representations. For example, one edge of the sub-cell may have two overlapping nodes to represent a vertical face. The nodes of a sub-cell may not be uniformly distributed over XY plane. Figure 11 depicts an exploded plan view of a portion of the z-map grid with nodes 54. Figure 12 illustrates how stick method represents a circular hole and vertical walls.
Figure 11: Extended sub-cells to approximate vertical wall
Figure 12: Extend Z map to represents a circular hole
Figure 13 shows shop floor examples of extended Z Map IPM based NC simulation and verification that was developed in Singapore Institute of Manufacturing Technology and implemented in precision engineering industry for a decade. The detailed description of the extended Z map IPM can be found in two patents [10, 11].
Z map has many alias or hybrid cousins such as ray casting, Z buffer etc. When a group of virtually light rays pass through an object from Z direction, there will be intersections between the light ray and the object. These top and bottom Z values are stored in the depth buffers of the graphics card and used for hidden surface removal algorithm. This process was called ray casting or tracing technology and is used for many graphics application such as volume rendering. UNIFIED MODEL FOR MM AND LM SIMULATION
Layered Manufacturing (LM) refers to the process of fabricating three-dimensional objects from CAD-generated solid models, layer by layer. A computer generated model of a part usually contains surface information. Slicing programs mathematically slices the model into sequential horizontal layers and generates the specific toolpath for each layer. This toolpath file is then downloaded into the LM hardware for fabricating the part layer by layer.
LM has revolutionized the process of prototyping complex geometric designs, but the geometric design of LM parts is still using traditional B-rep models, interfacing through a STL (Stereo Lithography) format. Several problems are difficult to solve using conventional geometry based approaches. These problems include estimation of mass properties, interference detection, tolerancing and implementation of CSG (Constructive Solid Geometry) operations.
Most of the published LM simulation methods are modeled on water level sections which is the boundary of material deposition at this height. A wire frame model with a collection of these sections gives a rough visual description of the final shape of the LM part. It can be used to predicate the surface roughness in a certain orientation. A covered section wire frame with thickness would provide a much better visual image but demands more memory. Further improvement utilizes OpenGL to display a toolpath build file section by section. The simulation opens a graphical window, specifies different colors for different materials, and starts the deposition process along the toolpath on the layer. When a material is finished, the simulation runs for other materials on the same layer. When a layer is finished, a new layer will be deposited on top of the finished layer, until all the layers of the part are stacked sequentially. Surface and internal defects can be verified from the envelope view or sectional view.
Chandru (1995) proposed a Voxel-based modeling for LM parts design [12], but there is little information about voxel-based modeling of LM processes, although it has been a popular approach for multiple machining process simulation [13].
The term Voxel represents a volume element in space decomposition geometrical model schema, just like the term pixel denotes a picture element in raster graphics (Figure 14). Voxelization is the process of converting a 3D object into a Voxel model. Volume graphics, voxelization and volume rendering have attracted considerable research in recent years. However, all of this work is directed at the display of volume data, mainly for medical applications.
Figure 14: Voxel method Further analyzing the Voxel model, it is believed that the
Voxel-based volume modeling is a very promising approach to the unified IPM for multiple machining and layered manufacturing simulation. As a natural clone of the LM technology, the Voxel model of an object and the object fabricated using an LM closely resemble each other since both are made of layers of small cells. It eliminates the STL format and eases accomplishments of tasks such as estimation of errors in the physical parameters of the fabricated objects, tolerance and interference detection. Furthermore, Voxel based models permit the designer to analyze the LM object and modify it at the voxel level leading to the design of custom composites of arbitrary topology. In this paper a simplified Voxel-based IPM is proposed to unite the new LM and traditional machining simulation. Figure 15 depicts an example of the Voxel model.
Figure 15 Example of Voxel model The memory requirements of traditional Voxel models are
enormous. There is a need to store the voxel array in compressed form and use algorithms that will operate directly on the compressed data, especially when the material is homogenous, where internal voxels could be represented by boundary voxel extension. It is possible to convert the voxel array into some other more compact representation and reconvert them into voxels when required. The original geometric representation must be kept and voxelization algorithms are used when necessary. This is especially valuable
since design data are mainly generated from conventional CAD system.
A voxel-based system should be able to update the display at interactive rates. Current graphics rendering systems cannot provide a level of rendering performance on Voxel models that is comparable to their polygon-rendering performance. Parallel algorithms and hardware support for volume rendering are the focus of current research efforts. We only render boundary voxel by a patented color list, which effectively avoid expensive ray-casting of huge internal voxels. The rendering of a Voxel model is easily achieved by rendering a points cloud. However, internal voxel display is not possible with this method and needs more study.
Figure 16 illustrates the framework of the unified Voxel-based IPM for LM and MM. The Voxel based LM simulation can be achieved by the voxelization of the road shapes, which are similar to a pipe along the LM toolpath. Boolean addition between the road shape voxel and the base voxel is fast and stable, independent of the model shape, which is a critical issue with B-rep. One layer of road shapes would make a B-rep based solid modeler very slow, since B-rep Boolean operation is dependent on model shape.
Figure 16: Framework of Unified IPM for MM and LM During the novel combined LM and MM, such as shape
deposition manufacturing, an LM part needs to be inserted with an electronic device and milled to a certain shape. The unified LM-machining simulation displays the machining process in which the initial LM generated workpiece is incrementally converted into the finished part. The Voxel representation is used to model efficiently the state of the IPM, which is generated by successively subtracting tool swept volumes from the workpiece. The Voxel representation also simplifies the computation of regularized Boolean set operations and of material removal volumes. By using the material removal rate measured by the number of removed voxels, the feedrate can be adjusted adaptively to increase machining productivity. The preliminary results of the IPM are shown in Figure 17. Figure 17b demonstrates the Voxel model of a test part created from its solid model as depicted in Figure 17a, which is the first step
towards to the unified in-process geometry model for multiple-machining and layered manufacturing simulation. Further research is on-going and more results will be published in the near future. CONCLUSIONS
Manufacturing advanced products with heterogeneous materials such as embedded electronics requires applying the combined MM and LM technologies. Modeling and simulation of hybrid MM and LM processes is essential for the integration of various activities related to product design, manufacturing process planning, toolpath generation, and machine inspection. However, no unified in-process geometry model for MM and LM has been found. Based on the study of various modeling and simulation methods including B-rep, section method, Z map, and extended Z map, a Voxel-based in-process geometry model for the novel hybrid multiple machining and layered manufacturing processes is proposed and discussed in this paper. The preliminary experiment demonstrates encouraging results. With nearly twenty years of research and development on IPMs for machining, it is believed that the Voxel-based volume modeling is a very promising approach to the unified IPM towards the vision of pervasive modeling and simulation in manufacturing industry
ACKNOWLEDGMENTS The authors would like to thank Dr Matthew Pritchard and
Dr Fang Fengzhou for their internal review of the paper with valuable comments and polishing of the writing.
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