- Email: [email protected]
A simple visualization tool to support concurrent engineering design
Computer-Afded
PII: s0010-4485(97)00015-8
Desfgn. Vol 29, No 10, pp. 727-735,
1997
p 1997 Elsevier Science Ltd. All rights reserved Printed I” Great Britain 0010.4485/971$17.00+0.00
Applications A simple visualization tool to support concurrent engineering design S C Lut, A B Rebellot,
R A Millert, G L Kinzelt*
carefully combining selected processes, e.g. component design and manufacturing, to facilitate the decision making process. Design for manufacturability (DFM) is, therefore, a key factor in determining the success of concurrent engineering and the competitiveness of products. DFM is especially important in the domain of net shape manufacturing processes, where the part geometry restricts the die design which in turn significantly affects the producibility and the quality of the resulting part. However, most net shape parts are typically designed based on the functional requirements alone. The manufacturability is not considered until the design is nearly completed, or even worse, until die design is started. At this stage, usually only minor changes are made to the design to try to accommodate the process. The remaining incompatibilities with the process may require the use of special die mechanisms which make the die unnecessarily complex and costly, or may require compromise in the selection of processing conditions which always affects quality. Many times, even minor changes are not allowed due to time pressure, and the process engineers have to live with these poor designs. This greatly increases the costs and scrap rates, and decreases the die life and productivity. The key to success in DFM is the use of the right designsupport tools which promptly provide relevant manufacturing-related feedback at an appropriate level of detail. In this paper, we present a new geometry-driven approach based on a volumetric part representation for manufacturability evaluation. In contrast to evaluation using conventional form feature-oriented design rules, this approach provides more consistent and robust results based on the overall part geometry. It extracts the underlying geometric characteristics which actually affect part quality or increase manufacturing difficulties from the part model. It also provides a fast evaluation tool that can assist the designers in making decisions about die design. All the information is then presented to designers in a form which can be easily interpreted via visualization techniques. Thermal and flowrelated problems in die casting are used as examples to demonstrate this idea. It should be noted that the methodology developed in this study is general and can be applied to other net shape manufacturing processes, e.g. injection molding, equally well.
Due to the nature of the die cashng process, the part geometry restricts the die design significantly and hence affects the quality of the part. However, as is often the case in other manufacturing processes, the manufacturability of die castings is not considered until the design has been nearly completed and detailed. Primarily, this is due to the limited capability of current Computer-Aided Engineering (CAE) tools to support design evaluation, especially during preliminary design. In this paper, we present a new volumebased geometric reasoning and visualization approach to support this task. This system is very efficient in terms of computation time and can evaluate the whole range of designs regardless of their shape complexity. In addition, it is very simple-to-use and the results are self-evident. The current focus is on thermal- and flowrelated problems in die casting. Our approach, however, is general and can be applied to other manufacturing processes. 0 1997 Elsevier Science Ltd Keywords: design for manufacturability, visualization, geometric reasoning
die casting, volume
INTRODUCTION Concurrent engineering is a product management philosophy to increase competitiveness and reduce timeto-market. It strives to incorporate various life-cycle concerns into the early stages of design such that the resulting design will not only meet the functional requirements but also be manufacturable and profitable. However, a completely balanced cross-functional-team attempting to address simultaneously all the issues involved in a product development cycle is difficult to realize with the current state-of-the-art 4. In practice, it is best implemented by ‘To whom correspondence should be addressed at: Department of Mechanical Engineering, The Ohio State University, 206 West 18th Street. Columbus, OH 432 IO- I 107, USA tEngineering Research Center for Net Shape Manufacturing, The Ohio State University, Columbus, OH, USA ZDepartment of Computer and Information. The Ohio State University, Columbus, OH, USA Paper Received:
17 Fehrrrcr~~ 1996. Rcviwd:
and R Yagel*
23 Februar_v 1997
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PREVIOUS WORK Feature-oriented
approach
Form feature-oriented technology is a commonly used approach to support manufacturability evaluation. In this approach. high level manufacturing-related information is stored in a feature model in the form of feature names and parameters/attributes. The features’ names can then be matched with standard design rules, and their attributes can be used to determine producibilitys. Originally, this approach was used primarily in manufacturability assessment regarding process planning in the machining process where localized form features usually correspond quite well to the machining operations. Later on, a similar strategy was attempted for net shape manufacturing processes such as die casting and injection molding (e.g. Refs 4. 6 and 13). However. the same relationship simply does not exist in those processes. For net shape manufacturing, the processes are characterized by building a die/mold to form the shape of a component, tilling the die cavities with the molten metal, and cooling, packing. and ejecting. All the phenomena are related primarily to the whole part rather than being restricted to the local features. Therefore. the manufacturing concerns in these processes are related to the smoothness of wall thickness transition and the existence of flow obstructions. These are general geometric characteristics rather than regular form features. It is extremely difficult to derive them from a feature-dependent part representation, especially for complex shapes. In general. a feature-oriented evaluation can best be used to examine the manufacturability of individual features, and may be limited interactions among features. In net shape manufacturing processes where the overall geometry dominates the producibility, it is extremely difficult for this approach to guarantee problem coverage. Many specific problems of using features in the domain of net shape processes can be found in Refs 11 and 8.
Numerical simulation Numerical simulation of manufacturing processes based on finite element. finite difference, or boundary element methods are becoming more common. These approaches are in general very powerful, and have provided engineers much insight into the processes. However, many problems arise because those simulation tools were not developed to support part design. They rely heavily on the engineers’ expertise for preparation and interpretation of the results. Generally, the user must have strong numerical modeling skills and a deep understanding of the physics embedded in the numerical model to make the right decisions while building an input model and performing the simulation. They typically involve a large number of calculations, resulting in long run times. At the initial stage of a design, many “what if” questions need to be answered. Designers will want to explore many design alternatives to achieve a compromise. To support this, the evaluation tools in this stage should provide prompt feedback and should be simple to use. From this perspective. it is questionable whether the level of computation in typical numerical simulations is affordable and whether the accurate numerical results are really required in preliminary design. In fact. most decision-making in preliminary design relies primarly on qualitative information regarding the
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design: S C Lu et al. geometric compatibility of the design with the selected manufacturing process. For example, a qualitative judgement might be: the excessively heavy section of a die casting adversely affect cycle time and part quality, and hence should be identified and avoided’“. This is in contrast to a quantitative evaluation given by a detailed description of the temperature held inside the die and the casting. Besides, at the early stages of a design, many process parameters remain undertermined so the numerical solutions, based on speculative input, do not mean much. Furthermore, the assumptions behind the model are critical to the correct interpretation of the results. Even if problems can be intelligently identified, these types of tools do not provide any insight into how the problems can be fixed. All those problems inhibit designers in applying the numerical tools to assist interactive decision-making in preliminary design. Therefore, they are used only for post-development design verification by experienced process engineers and typically only on the most expensive projects or parts with known problems. Their impact on the design process is limited. Hence, there is a need for development of other tools to complement the numerical tools.
APPROACH In this paper, we present a new geometry-driven evaluation that can overcome many of the problems mentioned above. This approach is based on a “binary voxel model”” generated by voxelizing a CAD model. In the voxelization process, an object is decomposed into a collection of identical cubic units, called voxels. The digitized object is then embedded in a large 3-D Frame Buffer such that each voxel is associated with a value indicating whether it belongs to the die or to the part. Distance transformation is then applied to extract the geometric characteristics of interest from the voxelized object, ie. the heavy section and the flow distance. Volume rendering is then utilized to help the user visualize the results. This approach is discussed in more detail in the following sections.
APPLICATIONS The approach presented here is centered around specific manufacturing problems and the current focus is on thermaland how-related problems in die casting. For thermalrelated problems, the task is to improve the geometrical compatibility of a design with the die casting. In the case of flow, the focus is to provide a design-aid that can determine roughly the suitability of potential gate locations.
Thermal-related problems: Geometric characteristics identification Most thermal-related problems in die casting are caused by the presence of relatively large thermal masses. Thermal masses are those regions of a part that take a relatively long time to solidify. Their presence is often accompanied by shrinkage voids in the part, and soldering and oxide deposits on the cavity surface. According to experienced die casters and die casting design handbooks, the geometric characteristic which should be eliminated to prevent the aforementioned thermal-related defects is the heavy regions of the part 15.‘.‘.
A simple visualization
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Naturally, geometry is not the only factor that cause these defects. In die casting, the control of process parameters and other die design factors, including cooling line design, length and distribution of spray, and gating system design have a substantial effect on the solidification of castings Is. Even though adjustment of these factors can improve the solidification, the most economical way to avoid thermalrelated part defect is to design a part geometry without these problem-related characteristics. In fact, most of the other design decisions, except part geometry, remain undetermined in the preliminary design stage. The main benefit of geometry-based evaluation is that it can make the specification of the other design factors easier, the die less expensive. the lead time shorter, and the quality better.
Gate design support In the die casting process, metal is injected into the die cavities through small apertures called gates to form the part. Gate placement has a dominant effect on the filling pattern, which in turn significantly affects part quality. A good starting point with regard to gate design is to have the gates placed so that there are no extremely remote regions from the gates and the part filling is balanced in terms of flow distance. Measuring the flow distance involves finding the distance traversed through the casting from any point in the casting to the gate. This information will help the designer determine the number and potential locations of the gates. This will help eliminate some poor gate designs which would cause flow-related defects like incomplete fill. Currently diecasters estimate this distance using their experience and visual inspection. This is a tedious and error-prone task to say the least, and depends greatly on the experience of the diecaster. Thus, a program that can calculate the flow distance automatically and consistently will be valuable.
Part representation One of the most critical issues in this application is the identification of an appropriate representational scheme to support the manufacturability evaluation. Conventional CAD models, such as B-Rep and CSG, provide a reasonably robust environment in terms of geometric modeling and manipulation. However, it is quite difficult to derive diecastability-relevant geometric characteristics, e.g. wall thickness, consistently and efficiently from these models. In our application, the binary voxel-based model is used to support diecastability evalution. It has many advantages over conventional CAD models, especially for this type of application. Based on this representation, some volumetric geometric characteristics, such as total volume and surface area, though approximate, are readily available. Since solidification and filling of diecastings are volumetric phenomenon, the geometric characteristics which dominate these phenomena are volumetric in nature. The voxel model lends itself to the identification of those geometric properties affecting part solidification and filling. Since manufacturability evaluation is performed on the collection of uniform cells, the reasoning algorithms is not sensitive to the shape complexity. Furthermore, the uniformity of voxel representations enables us to model and control their behavior easily during reasoning. Lastly, the generation of the voxel model (e.g. Ref. 10) is substantially easier and required much less user intervention than complex meshes
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used in numerical tools. The above reasons choice of voxel models for our application.
GEOMETRIC
justify
the
REASONING
All the thermal-related geometric characteristics identified above are based on the concept of thickness. Unfortunately, thickness is an everyday term that is difficult to define precisely in die casting. In practice, experienced die casters visually check the wall thickness on engineering drawings, perhaps with the help of a ruler. The evaluation is totally experience-based, and hence there can be no guarantee of consistency. To systematically model wall thickness, Cocks’ suggested the use of the diameters of maximum inscribed spheres as a presentation of wall thickness for diecastability evaluation. The same idea has been adopted in applications for injection molding*. Basically, it requires the computation of the diameters of many inscribed spheres which just touch the part boundary. Based on this, local mass concentration can be identified by comparing the diameter of the spheres, as shown in Figure 1. This approach provides die casting engineers with a systematic means to model thickness. However, manual computation of inscribed spheres is very cumbersome. Even with the help of CAD systems, the calculation of inscribed spheres is a tough task for a polygon model, not to mention the various surface definitions in a regular B-Rep model. A voxel model is used because it provides us with a limited number of points from which the inscribed spheres can be approximated through the use of the distance transformation. The details are discussed in the following.
Heavy section The distance transform (DT) is a tool used in image processing. Basically, it computes in each voxel of an object the shortest distance to the so called “designated” voxels. In the case of wall thickness calculation, the “designated” voxels are specified to be those voxels on the boundary. In this case, the DT represents the radius of the inscribed spheres. i.e. the shortest distance to the part boundary. Based on this transform, heavy sections can be identified by extracting voxels with relatively large distance values because they are farther away from the part boundary, as illustrated in Figure 2.
Heavy Section Figure I Identification inscribed spheres
of local
mass
concentration
through
use of
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design: S C Lu et al. whose individual lengths are a and b. For 5 X 5 neighborhoods there are 3 types of prime vectors whose individual lengths are a, b, and c. These prime vectors are not necessarily linearly independent, but they are not integer multiples of any other prime vector. By varying the local processing window and the length of the prime vectors, we can define many different metrics. For example, for a 3 X 3 case we can at least define 3 types of metrics: city block (a = 1 b = 2 or x), chessboard (a = 1 b = l), and 3-4 chamfer metric (a = 3 b = 4). It should be noted that a and b must be selected such that 2a 2 b and b 2 a to meet the triangular inequality rule. If defined this way, the general chamfer distance between two discrete points p(x,.y,) and q(x2,y2) is: D(p,q)=b*m+a*n
Figure 2 2-D example showing the procedure to extract the heavy section using the Voxel model and distance transform
is defined in terms of metrics. Euclidean distance is commonly used in continuous space and the every day world. However, the computation of this “true” distance is in fact a global operation. Even in voxel models, computing the Euclidean distance from a voxel to its closest “designated” voxel(s) requires knowledge of the whole image, and thus is computationally prohibitive. To obtain a DT efficiently, many other metrics have been introduced in the discrete world to approximate the Euclidean distance (e.g. Refs 3,17). The computation of distance based on these discrete metrics is performed locally in a small neighborhood, a limited number of voxels at a time. In principle, the discrete distance between two points is calculated by accumulating the local distance along the shortest discrete path between them. Consider two points p and q in the space Z defined by a uniform grid. A discrete path Sk is a series of distinct points p =pl ,p2.. .pIl = q in Z such that pi and pI-l are connected by one of the prime vectors vi defined for a given metric 18. Each prime vector is associated with a length, i.e. the local distance, which when summed along the path, constitutes the total length of the path L(SJ. That is
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V& E S
where S is the set of all possible paths between p and q. Figure 3 shows 2-D examples of two classes of metrics defined in 3 X 3 and 5 X 5 neighborhoods. In the case of 3 X 3 neighborhoods, there are two types of prime vectors
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Figure 3 2-D examples of two classes of metrics defined in 3 X 3 and 5 X 5 neighborhoods
730
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-y2
1
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When a = 1 and b = 1, we obtain the chess board distance, i.e. D@,q)=Max(x, -x2, yl - y2). On the other hand, for the case of city block, no diagonal steps will be made, so the distance defined in this metric is simplyD(p,q)= yI - y2 + xl -x2. In general, a more accurate distance can be obtained by expanding the processing window. In the extreme case, if the processing window is expanded to cover the whole object, a true Euclidean distance can be obtained. In the design of diecastings, the most important concern is to keep the thickness of the walls uniform. Therefore, evaluation tools should indicate the relatively thick and thin sections of a casting. From this perspective, the cityblock metric can be used because it is a valid metric, i.e. (a) D,h(P, , P2) 2 0 VP,, P2 E Z (b)D,,(P,P2)=0
M P, =P2
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Ref. 16). On the other hand, depending on the size of the machine a company prossesses, there are different ranges of wall thicknesses that are preferred for different die casting alloys. A part can be manufactured most economically with die casting standard practice if its walls are within these ranges. Actually, there are no hard and fast rules governing the maximum and minimum wall thickness of a diecasting, and besides, this quantitative range is only a rough guideline. Still, quantitative approximation to the wall thickness can provide designers with insight in many cases. For a more accurate distance measure, integer-based chamfer metrics are usually used along with the corresponding scale factor. This type of metric has the advantage of being both computationally efficient and accurate. The integer value is chosen by scaling the theoretical optimum local distance to whole numbers, and a scalar is then used to obtain the calculated distance. In this application, we use the 3-4-5 chamfer metric defined on a 3 X 3 X 3 local window. Based on previous work, even with this integer approximation, the relative error of the chamfer distance can be easily kept under 1O%.3.‘” Borgerfors’ proposed an efficient 2-pass algorithm for computation of DT with several discrete metrics, including city-block and the chamfer metrics. This algorithm requires (see
2 wj
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wherem=Min
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that the volume be traversed only twice to calculate distance to the boundary for each voxel.
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Flow-distance To help the designer make decisions about the gate design, an evaluation tool based on the voxel model has been developed. It provides the designer with an accurate and systematic means of finding the flow distance for userspecified potential gate locations. Based on the candidate gate locations, it computes the flow distance from every discrete point in the part (represented by the voxels) to these locations. The algorithm is based on calculation of the 3-D DT of a point to the potential gate location. In this case, the 3-D DT computes for each voxel of the diecasting. the shortest distance to the region specified as the gate. It behaves approximately like a line of sight algorithm from the voxel through the space occupied by the diecasting to the region specified as the gate. The user can specify the gates by selecting points on the surfaces of the parts that define the gate cross-section. The qualitative flow distance provided is ordinal in nature. This facilitates comparison of the various regions of the part allowing the user to find regions of comparatively long flow distances.
Visualization After the identification of the geometric characteristics, another challenge in this application is to appropriately present this to the designer. Visualization techniques play an important role here. In typical numerical tools, designers have to use slicing/sectioning to visualize the analysis results. This is in contrast to looking at the results directly in a 3-D perspective. To envision the overall spatial distribution of the variables. users have to build a mental picture of the results by remembering the 2-D pictures in previous sections. Obviously, this is not desirable.
Figure 4
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For better perception and comprehension, the results should be displayed directly in 3-D. In this application, we developed visualization tools that allow designers to view the problem regions, e.g. thickest sections, inside a semi-transparent object (like an X-ray film). This not only lets the designers view the regions of interest in perspective with the rest of the results but also helps them find the locations of these regions relative to the 3-D geometry. This goal is achieved through the use of volume ray casting. In this approach. a series of rays, which are either parallel to the viewing direction (parallel projection) or passing through the eye (perspective projection), are shot from each pixel on the screen window to the objects in the world space. For each ray, the algorithm calculates the point ir enters the volume and the point it leaves the volume. It then calculates the form of the ray based on these two points. As a ray passes through the volume,the voxel values are sampled along its length to obtain the color and intensity. This compositing process is continued until the ray accumulates enough opacity, hits an opaque voxel, or leaves the volume. casting supports volume semi-transparency; Ray however, it is relatively slow in its basic form. In addition, a typical semi-transparent volume rendering is amorphous and blocky. This is especially true for binary models. For our application, rendering speed and image quality are important issues that have to be addressed. In addition, it is more useful for the presentation of the information to be such that the problem regions stand out. In this following, we briefly discuss how these problems are addressed. To improve the speed of display, a new, efficient, volume rendering algorithm was developed by combing the template-based raycasting ” and distance-based space leaping2”. A 26 connected integer-based ray was used because of its speed, ability to perform uniform sampling, and the binary nature of our voxel model. A conversion table was used to account for the incompatibility between this ray (26-connected) and the DT used in this application
Heavy section analysis results for the example part provided by an industrial partner
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(6-distance or 3,4,5 chamfer distance). The details of this are discussed in a separate paper ‘*. To improve the image quality, we developed a three layer scheme, i.e. divided the voxel of the part into three different layers (refer to Figures 4 and 6 as examples). The skin layer contains voxels on the boundary of the part and is usually one or two voxels thick. The normals used to render the surfaces were inherited from the CAD model during the voxelization process. These voxels are assigned a gray colour, and a see-through opacity. The second layer, i.e. the highlighted layer, consists of the voxels with the characteristics of interest. Specifically, in the case of the heavy sections, it contains the voxels with a distance greater than the specified value; for the flow, it contains the voxels within the specified distance from the gate. These voxels are totally opaque, and have red color. To better perceive the shape and locations of the problem regions, contextual normal estimation was used to obtain the normals of the problem regions 12.All the other voxels constitute the intermediate layer, and they are totally transparent. This scheme was chosen for two main reasons. First, it will further expedite the ray casting process. Since the voxels in the intermediate layer can be skipped by the rays, no cornpositing or shading is required in this layer. In addition, comparisons of different rendering properties for voxels in the other two layers can be made to provide an effective depth cue.
Figure 5
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The presentation of the problem regions was further improved through theuse of animation. Animation provides another depth cue resulting in better perception of the geometry. In addition, a series of pictures with continuously varying distance thresholds help designers find the problems. For thermal-related problems, the highlighted regions can shrink/erode while the part surfaces remain semi-transparent to provide geometric perspective. The eroded red regions, where the core persists the longest, is the relatively thick section (Figure 4). Many problems can be observed by showing the core shrinking in on itself. First, the relative size of the core indicates the severity of the problem. Usually the breaks in the core pattern indicate non-uniformity in wall thickness. In the case of flow, the regions that do not become red the longest are the furthest regions from the gate (Figure 6). The scheme described above facilitates the visualization of the problem regions in the perspective of the overall part characteristics. In other words, the characteristics of the problem regions can be compared with those for the rest of the part to determine the severity of the problems. The attributes that are most important are the sizes of the highlighted regions, and the interactions among the various highlighted regions. Thus, the designer can easily conceive the locations of the problem regions relative to the part, and make design modifications accordingly.
Sectioned view of the numerical simulation-based temperature profile for the part obtained tram industry
A simple visualization
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RESULTS Based on the procedures described above, a prototype system has been created. Figure 4 shows the analysis results for a diecasting that was obtained from the industry. Because of porosity problems near its center, many parts failed in the field. The company had to use a special mechanism to increase the density of the metal in the problem region for pressure tightness. Besides the additional capital that had to be invested due to the special mechanism, there was an increased scrap rate. These problems were basically caused by the design not being compatible with the die casting process i.e. the presence of a region that was too heavy. Our system was able to find this incompatibility immediately. A comparison with the temperature profile obtained by numerical simulation (Figure 5) further illustrates that the thickest region identified by our system correspond well to the hottest region. For a more quantitative comparison, we have also sampled several points in the heaviest section of the example part shown Figure 4b and in the numerical simulaat those points. For the tion, placed “thermocouples” cooling curves obtained for those points, an intersection line can be drawn corresponding to the time at which approximately 95% of the metal has solidified (as shown in Figure 6). From this figure, we can see that the metal in the heaviest region of the part, is just starting to release the latent heat at that time. Therefore, the heaviest sections are located in the regions where the last 5% of the metal solidifies. By running this sytem on an IMB RS6000 37T workstation with 128 MB memory, the visualization
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system takes less than 1 minute to perform the analysis. On the other hand, the numerical simulation for the same part takes at least an hour, excluding the post processing time. To actually visualize the numerical results, the user has to slice through the object and usually requires much manipulation of the display to build an accurate mental model of the results. The simulation results, though, are quite similar to the wall thickness evaluation from our visualization tool. Therefore, our system has a significant advantage over conventional tools at the design stage. Figure 7 shows the how distance results for a hypothetical example part with a gate and overflows. Typically, the gate will not be designed prior to performing flow distance calculations. The results in Figure 7, however, are intended to illustrate the effect of geometry on the flow distance. The regions highlighted in red are closer to the end of the gate than the unhighlighted regions. Regions that could have fill problems because of long flow distances, i.e. that stay gray the longest in Figure 7, can be found through comparison with the results for the majority of the part.
CONCLUSIONS In this paper, we have presented a volume-based qualitative reasoning approach for die castability evaluation. Heavy mass causing solidification-related problems and flowdistance calculations are used as examples to demonstrate the idea, but the same philosphy can be applied to other problems as well. Part of the problems with conventional form feature oriented design rules in manufacturability
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Cooling curves for sample points in the heaviest region of the example part
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assessment are eliminated by identifying the underlying geometric characteristics in contrast to using the original rules themselves. Volumetric part representations and their associated processing techniques have proved to be very efficient to extract volume-related geometric characteristics. Volume visualization techniques are also adopted in this application to convey the results of die castability assessment in a nature and precise fashion. Based on these techniques, the geometric incompatibility of a design can be identified much faster than before and the results are directly linked to manufacturing problems. The system is also very intuitive, and it can be used interactively by designers as they create the geometry. The current effort is devoted to extending this method to cover more solidification-related issues. For example, another concern in die casting is the identification of relative hot regions in the die, which may cause heat checking and thermal fatigue-related defects. There are several design rules related to this concern, e.g. the distance between two ribs and the radius of holes. The approach described in this paper can be used to find whether the ribs are relatively too heavy; however; it can not tell the distance between them. For two closely spaced ribs, even though they can be appropriate in size. the part can still be poorly configured from the perspective of solidification. To extend our approach to cover this problem, other geometric data processing and reasoning methods are required.
2.
Beiter, K. A. and lahii. K., Grometry-Based Indexfi~r Predicting Sink in Pla.stic Parts, Technical Report, ERC/NSM-P-9 l-61. Engineering Research Center for Net Shape Manufacturing. The Ohio State University, Columbus. OH, 1991, Borgefora. G.. Distance transformations in arbitrary dimensions. Mark
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ACKNOWLEDGEMENTS The authors also wish to thank the North American Die Casting Association, US Department of Energy, Ford Motor Company, and the Center for Die Casting at the Ohio State University for their support. The center is funded by the National Science Foundation and industrial membership. REFERENCES I. Barton, H. K.,
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The Society of Die
13. Marks. P.. Process reengineering and the new manufacturing enterprise wheel: I.5 processes for competitive Advantage, published by The Computer and Automated Systems Association of the Society of Manufacturing Engineers (CASA/SME) Technical Forum. 1994. IS. NADCA DDC. Product Design for Die Casting, Diecasting Development Council of the North American Die Casting Association, 19X8. 16. Porter. W. A., Modern Foundations of .Twfrm Enginrerin~. Macmillan Company, New York, 1968. 17. Rosenfeld, A. and Pfaltz, J., Distance functions on digital pictures. Pottern Rrcognition, 1968, l(l). 33-61. IX. Verwer. B. J. H.. Local distances for Distance Transormations m Two and Three Dimensions. Thesis, Delft University of Technology. I99 I, pp.23-33. volume viewing. 19. Yagel. R. and Kaufman. A.. Template-based Proceedin,+\ of Eurograp1~ic.s. 1992. 11, I S3- 167.
A simple visualization tool to support concurrent engineering design: S C Lu et a/. 20
Zuiderveld, K. Z., Koning, A. H. J. and Viergever, M. A., Acceleration of ray casting using 3D distance transform. Proceedings of Visualizafion in Biomedicul Computing, Vol. 1808, ed. R. A. Rot&. SPIE, Chapel Hill, NC, pp. 324-335.
State University. ical Engineering
Shao-Chiung Lu is a principal development engineer working on the research and development qfDesign,for Munufucturing (DFM) and Visualization tools for various industrial applications at Ford Motor Co. His rrvearch and technical publications cover a varieq of topics in Computer Graphics, Corwrrrent Engineering, and CAE System Integration. He received his MS in 1992 and PhD in 1996, both from the Deportment qf Mechanical Engineering at the Ohio He received his BS.frorn the Department of Mechanut the Notional Taiwm UniverriQ in 1987.
Alexander Rebello is a PhD candidate in Industrial and Systems Engineering at The Ohio State Universin. His work as a part of the Center .for Die Casting involves development qf concurrent enginec’ring tools ,for use in design and manufacturing. He received his BSIE, BS in Computer Sciewe and Engineering Physics and BA in Mathemutics rrt St Ambrose University in 1988 and his MS degree from The Ohio State lJni~,er.,ity in 1991. He is (1 member of IlE
R. Allen Miller received the BME degree ,from Union College in 1966, the SM degree in Mechanical Engineering ,from the Mo.wachusett.s Institute of Technology in 1967, and the PhD degree in Control and Systems Engineering ,from Case Western Reserve Universin in 1971. He has been with Ohio State .since 1971, currently holding the rank of Prqfersor and Chair of the Department of lntluctrial, Welding and Systems Etlgineerin,y. His re.srnrch interests rare in the cueus design ,for munufactura, purticularly design for die casting and die casting die design. He is also interested in the development of design environments to support purr and die/mold design including CAD/ CAM/CAE integration, und technology support .for die costing and die/mold manufacturing jirms. He is the director of the Cerlter for Die Casting which is u consortium of academic reseurchers, the North American Die Casting Association. and several die casting corn ponies which jticuses on applied resmrch,for the die uxting industc. he i.c cl10 the director of the Practice-Oriented Mun~fncturing Engineering program. a College of Engineering musters pmqmm e.vtablished in 1994. Dr Miller M’(ISthe rec,ipirnt of the MwQuigg Award,for Excellent~e in Teaching in 1975, a College cj’Engmerring Research Award in 1982, and the IEEE Systems, Man, and Cybernetics SocieQ Franklin V. Ttrylor Award,for the outstanding paper prevented at the 1981 international Cocfereme on Cybernetics and So&~. He is a member of IEEE, HE, SME. ASME. ASEE, NADCA, the Auociation ,for Mamtfacturing E.xcellence. and The Humrrn Factor? cmd Ergonomic-s So&&.
Dr Kinzel is a professor in mechanical engineering and has worked in design, stress analysis, and CAD/CAM for more than 25 years. He received his BME and MS degrees from The Ohio State Vniversity in 1968 and 1969, respectively, and his PhD from Purdue in 1973. He joined the faculty of the mechanical engineering departments at Ohio State in 1978 and is currently teaching cour.yes in machine design, kinematics, and CAD/CAM. Prior to joining Ohio State. he was u principul research engineer at Batelle’s Columbus Luboratories. At Ohio State. Dr Kin:el has supervised more than 80 design and manufacturing oriented theses to completion. He has been u principal investigator on more thutt 40 research projects, and has publishedmore than 100 pulpers in the design and manufacturing areas. He is currently work&r: 011research issues in sheet-metal ,forming and CAD/CAM.
Roni Yagel is an Associate Professor in the Department of Computer and Information Science and an Adjunct Associate Professor in the Advanced Computer Center,for Art and Design and the Biomedical Engineering Center at The Ohio State Vniversit). He headr the Volume Graphics Research Group which pursues research in computer graphics, volume graphics, scientiJic visualization, virtual reality, and image processing. Roni Yagel received his PhD in 1991 from the State University of New York at Stony Brook where he was also a re,yeurcher in the Department ofAnatomy und the Department qf Physiologv and Biophysics. He received his BSc Cum Laude trnd MSc Cum Lude,frorn the Department of Mathematics and Computer Science at Ben Guriorl University qf the Negev, Israel, in 1986 and 1987. respecti\,elv. His resenrch and technical publications deal with a varie@ of topics ii7 volume graphics and visualization. His research interests include nlgorithms,for graphics, imaging, and animation. error c,ontrol it) image generation. and visualization tools,% industrial rrnd scientific clpplic ation s. For more informutiorl see: htt~~://~~~~~~~..Ci.~.ohio-stat. rtlu/?‘trgel
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Desfgn. Vol 29, No 10, pp. 727-735,
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p 1997 Elsevier Science Ltd. All rights reserved Printed I” Great Britain 0010.4485/971$17.00+0.00
Applications A simple visualization tool to support concurrent engineering design S C Lut, A B Rebellot,
R A Millert, G L Kinzelt*
carefully combining selected processes, e.g. component design and manufacturing, to facilitate the decision making process. Design for manufacturability (DFM) is, therefore, a key factor in determining the success of concurrent engineering and the competitiveness of products. DFM is especially important in the domain of net shape manufacturing processes, where the part geometry restricts the die design which in turn significantly affects the producibility and the quality of the resulting part. However, most net shape parts are typically designed based on the functional requirements alone. The manufacturability is not considered until the design is nearly completed, or even worse, until die design is started. At this stage, usually only minor changes are made to the design to try to accommodate the process. The remaining incompatibilities with the process may require the use of special die mechanisms which make the die unnecessarily complex and costly, or may require compromise in the selection of processing conditions which always affects quality. Many times, even minor changes are not allowed due to time pressure, and the process engineers have to live with these poor designs. This greatly increases the costs and scrap rates, and decreases the die life and productivity. The key to success in DFM is the use of the right designsupport tools which promptly provide relevant manufacturing-related feedback at an appropriate level of detail. In this paper, we present a new geometry-driven approach based on a volumetric part representation for manufacturability evaluation. In contrast to evaluation using conventional form feature-oriented design rules, this approach provides more consistent and robust results based on the overall part geometry. It extracts the underlying geometric characteristics which actually affect part quality or increase manufacturing difficulties from the part model. It also provides a fast evaluation tool that can assist the designers in making decisions about die design. All the information is then presented to designers in a form which can be easily interpreted via visualization techniques. Thermal and flowrelated problems in die casting are used as examples to demonstrate this idea. It should be noted that the methodology developed in this study is general and can be applied to other net shape manufacturing processes, e.g. injection molding, equally well.
Due to the nature of the die cashng process, the part geometry restricts the die design significantly and hence affects the quality of the part. However, as is often the case in other manufacturing processes, the manufacturability of die castings is not considered until the design has been nearly completed and detailed. Primarily, this is due to the limited capability of current Computer-Aided Engineering (CAE) tools to support design evaluation, especially during preliminary design. In this paper, we present a new volumebased geometric reasoning and visualization approach to support this task. This system is very efficient in terms of computation time and can evaluate the whole range of designs regardless of their shape complexity. In addition, it is very simple-to-use and the results are self-evident. The current focus is on thermal- and flowrelated problems in die casting. Our approach, however, is general and can be applied to other manufacturing processes. 0 1997 Elsevier Science Ltd Keywords: design for manufacturability, visualization, geometric reasoning
die casting, volume
INTRODUCTION Concurrent engineering is a product management philosophy to increase competitiveness and reduce timeto-market. It strives to incorporate various life-cycle concerns into the early stages of design such that the resulting design will not only meet the functional requirements but also be manufacturable and profitable. However, a completely balanced cross-functional-team attempting to address simultaneously all the issues involved in a product development cycle is difficult to realize with the current state-of-the-art 4. In practice, it is best implemented by ‘To whom correspondence should be addressed at: Department of Mechanical Engineering, The Ohio State University, 206 West 18th Street. Columbus, OH 432 IO- I 107, USA tEngineering Research Center for Net Shape Manufacturing, The Ohio State University, Columbus, OH, USA ZDepartment of Computer and Information. The Ohio State University, Columbus, OH, USA Paper Received:
17 Fehrrrcr~~ 1996. Rcviwd:
and R Yagel*
23 Februar_v 1997
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PREVIOUS WORK Feature-oriented
approach
Form feature-oriented technology is a commonly used approach to support manufacturability evaluation. In this approach. high level manufacturing-related information is stored in a feature model in the form of feature names and parameters/attributes. The features’ names can then be matched with standard design rules, and their attributes can be used to determine producibilitys. Originally, this approach was used primarily in manufacturability assessment regarding process planning in the machining process where localized form features usually correspond quite well to the machining operations. Later on, a similar strategy was attempted for net shape manufacturing processes such as die casting and injection molding (e.g. Refs 4. 6 and 13). However. the same relationship simply does not exist in those processes. For net shape manufacturing, the processes are characterized by building a die/mold to form the shape of a component, tilling the die cavities with the molten metal, and cooling, packing. and ejecting. All the phenomena are related primarily to the whole part rather than being restricted to the local features. Therefore. the manufacturing concerns in these processes are related to the smoothness of wall thickness transition and the existence of flow obstructions. These are general geometric characteristics rather than regular form features. It is extremely difficult to derive them from a feature-dependent part representation, especially for complex shapes. In general. a feature-oriented evaluation can best be used to examine the manufacturability of individual features, and may be limited interactions among features. In net shape manufacturing processes where the overall geometry dominates the producibility, it is extremely difficult for this approach to guarantee problem coverage. Many specific problems of using features in the domain of net shape processes can be found in Refs 11 and 8.
Numerical simulation Numerical simulation of manufacturing processes based on finite element. finite difference, or boundary element methods are becoming more common. These approaches are in general very powerful, and have provided engineers much insight into the processes. However, many problems arise because those simulation tools were not developed to support part design. They rely heavily on the engineers’ expertise for preparation and interpretation of the results. Generally, the user must have strong numerical modeling skills and a deep understanding of the physics embedded in the numerical model to make the right decisions while building an input model and performing the simulation. They typically involve a large number of calculations, resulting in long run times. At the initial stage of a design, many “what if” questions need to be answered. Designers will want to explore many design alternatives to achieve a compromise. To support this, the evaluation tools in this stage should provide prompt feedback and should be simple to use. From this perspective. it is questionable whether the level of computation in typical numerical simulations is affordable and whether the accurate numerical results are really required in preliminary design. In fact. most decision-making in preliminary design relies primarly on qualitative information regarding the
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design: S C Lu et al. geometric compatibility of the design with the selected manufacturing process. For example, a qualitative judgement might be: the excessively heavy section of a die casting adversely affect cycle time and part quality, and hence should be identified and avoided’“. This is in contrast to a quantitative evaluation given by a detailed description of the temperature held inside the die and the casting. Besides, at the early stages of a design, many process parameters remain undertermined so the numerical solutions, based on speculative input, do not mean much. Furthermore, the assumptions behind the model are critical to the correct interpretation of the results. Even if problems can be intelligently identified, these types of tools do not provide any insight into how the problems can be fixed. All those problems inhibit designers in applying the numerical tools to assist interactive decision-making in preliminary design. Therefore, they are used only for post-development design verification by experienced process engineers and typically only on the most expensive projects or parts with known problems. Their impact on the design process is limited. Hence, there is a need for development of other tools to complement the numerical tools.
APPROACH In this paper, we present a new geometry-driven evaluation that can overcome many of the problems mentioned above. This approach is based on a “binary voxel model”” generated by voxelizing a CAD model. In the voxelization process, an object is decomposed into a collection of identical cubic units, called voxels. The digitized object is then embedded in a large 3-D Frame Buffer such that each voxel is associated with a value indicating whether it belongs to the die or to the part. Distance transformation is then applied to extract the geometric characteristics of interest from the voxelized object, ie. the heavy section and the flow distance. Volume rendering is then utilized to help the user visualize the results. This approach is discussed in more detail in the following sections.
APPLICATIONS The approach presented here is centered around specific manufacturing problems and the current focus is on thermaland how-related problems in die casting. For thermalrelated problems, the task is to improve the geometrical compatibility of a design with the die casting. In the case of flow, the focus is to provide a design-aid that can determine roughly the suitability of potential gate locations.
Thermal-related problems: Geometric characteristics identification Most thermal-related problems in die casting are caused by the presence of relatively large thermal masses. Thermal masses are those regions of a part that take a relatively long time to solidify. Their presence is often accompanied by shrinkage voids in the part, and soldering and oxide deposits on the cavity surface. According to experienced die casters and die casting design handbooks, the geometric characteristic which should be eliminated to prevent the aforementioned thermal-related defects is the heavy regions of the part 15.‘.‘.
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Naturally, geometry is not the only factor that cause these defects. In die casting, the control of process parameters and other die design factors, including cooling line design, length and distribution of spray, and gating system design have a substantial effect on the solidification of castings Is. Even though adjustment of these factors can improve the solidification, the most economical way to avoid thermalrelated part defect is to design a part geometry without these problem-related characteristics. In fact, most of the other design decisions, except part geometry, remain undetermined in the preliminary design stage. The main benefit of geometry-based evaluation is that it can make the specification of the other design factors easier, the die less expensive. the lead time shorter, and the quality better.
Gate design support In the die casting process, metal is injected into the die cavities through small apertures called gates to form the part. Gate placement has a dominant effect on the filling pattern, which in turn significantly affects part quality. A good starting point with regard to gate design is to have the gates placed so that there are no extremely remote regions from the gates and the part filling is balanced in terms of flow distance. Measuring the flow distance involves finding the distance traversed through the casting from any point in the casting to the gate. This information will help the designer determine the number and potential locations of the gates. This will help eliminate some poor gate designs which would cause flow-related defects like incomplete fill. Currently diecasters estimate this distance using their experience and visual inspection. This is a tedious and error-prone task to say the least, and depends greatly on the experience of the diecaster. Thus, a program that can calculate the flow distance automatically and consistently will be valuable.
Part representation One of the most critical issues in this application is the identification of an appropriate representational scheme to support the manufacturability evaluation. Conventional CAD models, such as B-Rep and CSG, provide a reasonably robust environment in terms of geometric modeling and manipulation. However, it is quite difficult to derive diecastability-relevant geometric characteristics, e.g. wall thickness, consistently and efficiently from these models. In our application, the binary voxel-based model is used to support diecastability evalution. It has many advantages over conventional CAD models, especially for this type of application. Based on this representation, some volumetric geometric characteristics, such as total volume and surface area, though approximate, are readily available. Since solidification and filling of diecastings are volumetric phenomenon, the geometric characteristics which dominate these phenomena are volumetric in nature. The voxel model lends itself to the identification of those geometric properties affecting part solidification and filling. Since manufacturability evaluation is performed on the collection of uniform cells, the reasoning algorithms is not sensitive to the shape complexity. Furthermore, the uniformity of voxel representations enables us to model and control their behavior easily during reasoning. Lastly, the generation of the voxel model (e.g. Ref. 10) is substantially easier and required much less user intervention than complex meshes
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used in numerical tools. The above reasons choice of voxel models for our application.
GEOMETRIC
justify
the
REASONING
All the thermal-related geometric characteristics identified above are based on the concept of thickness. Unfortunately, thickness is an everyday term that is difficult to define precisely in die casting. In practice, experienced die casters visually check the wall thickness on engineering drawings, perhaps with the help of a ruler. The evaluation is totally experience-based, and hence there can be no guarantee of consistency. To systematically model wall thickness, Cocks’ suggested the use of the diameters of maximum inscribed spheres as a presentation of wall thickness for diecastability evaluation. The same idea has been adopted in applications for injection molding*. Basically, it requires the computation of the diameters of many inscribed spheres which just touch the part boundary. Based on this, local mass concentration can be identified by comparing the diameter of the spheres, as shown in Figure 1. This approach provides die casting engineers with a systematic means to model thickness. However, manual computation of inscribed spheres is very cumbersome. Even with the help of CAD systems, the calculation of inscribed spheres is a tough task for a polygon model, not to mention the various surface definitions in a regular B-Rep model. A voxel model is used because it provides us with a limited number of points from which the inscribed spheres can be approximated through the use of the distance transformation. The details are discussed in the following.
Heavy section The distance transform (DT) is a tool used in image processing. Basically, it computes in each voxel of an object the shortest distance to the so called “designated” voxels. In the case of wall thickness calculation, the “designated” voxels are specified to be those voxels on the boundary. In this case, the DT represents the radius of the inscribed spheres. i.e. the shortest distance to the part boundary. Based on this transform, heavy sections can be identified by extracting voxels with relatively large distance values because they are farther away from the part boundary, as illustrated in Figure 2.
Heavy Section Figure I Identification inscribed spheres
of local
mass
concentration
through
use of
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design: S C Lu et al. whose individual lengths are a and b. For 5 X 5 neighborhoods there are 3 types of prime vectors whose individual lengths are a, b, and c. These prime vectors are not necessarily linearly independent, but they are not integer multiples of any other prime vector. By varying the local processing window and the length of the prime vectors, we can define many different metrics. For example, for a 3 X 3 case we can at least define 3 types of metrics: city block (a = 1 b = 2 or x), chessboard (a = 1 b = l), and 3-4 chamfer metric (a = 3 b = 4). It should be noted that a and b must be selected such that 2a 2 b and b 2 a to meet the triangular inequality rule. If defined this way, the general chamfer distance between two discrete points p(x,.y,) and q(x2,y2) is: D(p,q)=b*m+a*n
Figure 2 2-D example showing the procedure to extract the heavy section using the Voxel model and distance transform
is defined in terms of metrics. Euclidean distance is commonly used in continuous space and the every day world. However, the computation of this “true” distance is in fact a global operation. Even in voxel models, computing the Euclidean distance from a voxel to its closest “designated” voxel(s) requires knowledge of the whole image, and thus is computationally prohibitive. To obtain a DT efficiently, many other metrics have been introduced in the discrete world to approximate the Euclidean distance (e.g. Refs 3,17). The computation of distance based on these discrete metrics is performed locally in a small neighborhood, a limited number of voxels at a time. In principle, the discrete distance between two points is calculated by accumulating the local distance along the shortest discrete path between them. Consider two points p and q in the space Z defined by a uniform grid. A discrete path Sk is a series of distinct points p =pl ,p2.. .pIl = q in Z such that pi and pI-l are connected by one of the prime vectors vi defined for a given metric 18. Each prime vector is associated with a length, i.e. the local distance, which when summed along the path, constitutes the total length of the path L(SJ. That is
X OXI -4,
Distance
Sk=S(WI,W2,.......W,},W;
E
{Vj}
.i
The distance between two points p and q is then the minimum length of all possible paths between them, i.e. D@, q) = min(L(&))
V& E S
where S is the set of all possible paths between p and q. Figure 3 shows 2-D examples of two classes of metrics defined in 3 X 3 and 5 X 5 neighborhoods. In the case of 3 X 3 neighborhoods, there are two types of prime vectors
RI-4 I
I
1 -_)I
I
I
=a
I--+I=b I---I
=c
Figure 3 2-D examples of two classes of metrics defined in 3 X 3 and 5 X 5 neighborhoods
730
andn=abs(y,
Yl -Yz
-y2
1
-xl
-x2)
When a = 1 and b = 1, we obtain the chess board distance, i.e. D@,q)=Max(x, -x2, yl - y2). On the other hand, for the case of city block, no diagonal steps will be made, so the distance defined in this metric is simplyD(p,q)= yI - y2 + xl -x2. In general, a more accurate distance can be obtained by expanding the processing window. In the extreme case, if the processing window is expanded to cover the whole object, a true Euclidean distance can be obtained. In the design of diecastings, the most important concern is to keep the thickness of the walls uniform. Therefore, evaluation tools should indicate the relatively thick and thin sections of a casting. From this perspective, the cityblock metric can be used because it is a valid metric, i.e. (a) D,h(P, , P2) 2 0 VP,, P2 E Z (b)D,,(P,P2)=0
M P, =P2
(C)DdPIPd
=
Dc/,(P2f’1)
(d)Dcb(P1Pz)
+
Dcb(p2p3)
2
D,,(plp3)
Ref. 16). On the other hand, depending on the size of the machine a company prossesses, there are different ranges of wall thicknesses that are preferred for different die casting alloys. A part can be manufactured most economically with die casting standard practice if its walls are within these ranges. Actually, there are no hard and fast rules governing the maximum and minimum wall thickness of a diecasting, and besides, this quantitative range is only a rough guideline. Still, quantitative approximation to the wall thickness can provide designers with insight in many cases. For a more accurate distance measure, integer-based chamfer metrics are usually used along with the corresponding scale factor. This type of metric has the advantage of being both computationally efficient and accurate. The integer value is chosen by scaling the theoretical optimum local distance to whole numbers, and a scalar is then used to obtain the calculated distance. In this application, we use the 3-4-5 chamfer metric defined on a 3 X 3 X 3 local window. Based on previous work, even with this integer approximation, the relative error of the chamfer distance can be easily kept under 1O%.3.‘” Borgerfors’ proposed an efficient 2-pass algorithm for computation of DT with several discrete metrics, including city-block and the chamfer metrics. This algorithm requires (see
2 wj
L(S,)=
wherem=Min
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that the volume be traversed only twice to calculate distance to the boundary for each voxel.
tool to support concurrent
the
Flow-distance To help the designer make decisions about the gate design, an evaluation tool based on the voxel model has been developed. It provides the designer with an accurate and systematic means of finding the flow distance for userspecified potential gate locations. Based on the candidate gate locations, it computes the flow distance from every discrete point in the part (represented by the voxels) to these locations. The algorithm is based on calculation of the 3-D DT of a point to the potential gate location. In this case, the 3-D DT computes for each voxel of the diecasting. the shortest distance to the region specified as the gate. It behaves approximately like a line of sight algorithm from the voxel through the space occupied by the diecasting to the region specified as the gate. The user can specify the gates by selecting points on the surfaces of the parts that define the gate cross-section. The qualitative flow distance provided is ordinal in nature. This facilitates comparison of the various regions of the part allowing the user to find regions of comparatively long flow distances.
Visualization After the identification of the geometric characteristics, another challenge in this application is to appropriately present this to the designer. Visualization techniques play an important role here. In typical numerical tools, designers have to use slicing/sectioning to visualize the analysis results. This is in contrast to looking at the results directly in a 3-D perspective. To envision the overall spatial distribution of the variables. users have to build a mental picture of the results by remembering the 2-D pictures in previous sections. Obviously, this is not desirable.
Figure 4
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For better perception and comprehension, the results should be displayed directly in 3-D. In this application, we developed visualization tools that allow designers to view the problem regions, e.g. thickest sections, inside a semi-transparent object (like an X-ray film). This not only lets the designers view the regions of interest in perspective with the rest of the results but also helps them find the locations of these regions relative to the 3-D geometry. This goal is achieved through the use of volume ray casting. In this approach. a series of rays, which are either parallel to the viewing direction (parallel projection) or passing through the eye (perspective projection), are shot from each pixel on the screen window to the objects in the world space. For each ray, the algorithm calculates the point ir enters the volume and the point it leaves the volume. It then calculates the form of the ray based on these two points. As a ray passes through the volume,the voxel values are sampled along its length to obtain the color and intensity. This compositing process is continued until the ray accumulates enough opacity, hits an opaque voxel, or leaves the volume. casting supports volume semi-transparency; Ray however, it is relatively slow in its basic form. In addition, a typical semi-transparent volume rendering is amorphous and blocky. This is especially true for binary models. For our application, rendering speed and image quality are important issues that have to be addressed. In addition, it is more useful for the presentation of the information to be such that the problem regions stand out. In this following, we briefly discuss how these problems are addressed. To improve the speed of display, a new, efficient, volume rendering algorithm was developed by combing the template-based raycasting ” and distance-based space leaping2”. A 26 connected integer-based ray was used because of its speed, ability to perform uniform sampling, and the binary nature of our voxel model. A conversion table was used to account for the incompatibility between this ray (26-connected) and the DT used in this application
Heavy section analysis results for the example part provided by an industrial partner
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(6-distance or 3,4,5 chamfer distance). The details of this are discussed in a separate paper ‘*. To improve the image quality, we developed a three layer scheme, i.e. divided the voxel of the part into three different layers (refer to Figures 4 and 6 as examples). The skin layer contains voxels on the boundary of the part and is usually one or two voxels thick. The normals used to render the surfaces were inherited from the CAD model during the voxelization process. These voxels are assigned a gray colour, and a see-through opacity. The second layer, i.e. the highlighted layer, consists of the voxels with the characteristics of interest. Specifically, in the case of the heavy sections, it contains the voxels with a distance greater than the specified value; for the flow, it contains the voxels within the specified distance from the gate. These voxels are totally opaque, and have red color. To better perceive the shape and locations of the problem regions, contextual normal estimation was used to obtain the normals of the problem regions 12.All the other voxels constitute the intermediate layer, and they are totally transparent. This scheme was chosen for two main reasons. First, it will further expedite the ray casting process. Since the voxels in the intermediate layer can be skipped by the rays, no cornpositing or shading is required in this layer. In addition, comparisons of different rendering properties for voxels in the other two layers can be made to provide an effective depth cue.
Figure 5
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The presentation of the problem regions was further improved through theuse of animation. Animation provides another depth cue resulting in better perception of the geometry. In addition, a series of pictures with continuously varying distance thresholds help designers find the problems. For thermal-related problems, the highlighted regions can shrink/erode while the part surfaces remain semi-transparent to provide geometric perspective. The eroded red regions, where the core persists the longest, is the relatively thick section (Figure 4). Many problems can be observed by showing the core shrinking in on itself. First, the relative size of the core indicates the severity of the problem. Usually the breaks in the core pattern indicate non-uniformity in wall thickness. In the case of flow, the regions that do not become red the longest are the furthest regions from the gate (Figure 6). The scheme described above facilitates the visualization of the problem regions in the perspective of the overall part characteristics. In other words, the characteristics of the problem regions can be compared with those for the rest of the part to determine the severity of the problems. The attributes that are most important are the sizes of the highlighted regions, and the interactions among the various highlighted regions. Thus, the designer can easily conceive the locations of the problem regions relative to the part, and make design modifications accordingly.
Sectioned view of the numerical simulation-based temperature profile for the part obtained tram industry
A simple visualization
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RESULTS Based on the procedures described above, a prototype system has been created. Figure 4 shows the analysis results for a diecasting that was obtained from the industry. Because of porosity problems near its center, many parts failed in the field. The company had to use a special mechanism to increase the density of the metal in the problem region for pressure tightness. Besides the additional capital that had to be invested due to the special mechanism, there was an increased scrap rate. These problems were basically caused by the design not being compatible with the die casting process i.e. the presence of a region that was too heavy. Our system was able to find this incompatibility immediately. A comparison with the temperature profile obtained by numerical simulation (Figure 5) further illustrates that the thickest region identified by our system correspond well to the hottest region. For a more quantitative comparison, we have also sampled several points in the heaviest section of the example part shown Figure 4b and in the numerical simulaat those points. For the tion, placed “thermocouples” cooling curves obtained for those points, an intersection line can be drawn corresponding to the time at which approximately 95% of the metal has solidified (as shown in Figure 6). From this figure, we can see that the metal in the heaviest region of the part, is just starting to release the latent heat at that time. Therefore, the heaviest sections are located in the regions where the last 5% of the metal solidifies. By running this sytem on an IMB RS6000 37T workstation with 128 MB memory, the visualization
II j
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system takes less than 1 minute to perform the analysis. On the other hand, the numerical simulation for the same part takes at least an hour, excluding the post processing time. To actually visualize the numerical results, the user has to slice through the object and usually requires much manipulation of the display to build an accurate mental model of the results. The simulation results, though, are quite similar to the wall thickness evaluation from our visualization tool. Therefore, our system has a significant advantage over conventional tools at the design stage. Figure 7 shows the how distance results for a hypothetical example part with a gate and overflows. Typically, the gate will not be designed prior to performing flow distance calculations. The results in Figure 7, however, are intended to illustrate the effect of geometry on the flow distance. The regions highlighted in red are closer to the end of the gate than the unhighlighted regions. Regions that could have fill problems because of long flow distances, i.e. that stay gray the longest in Figure 7, can be found through comparison with the results for the majority of the part.
CONCLUSIONS In this paper, we have presented a volume-based qualitative reasoning approach for die castability evaluation. Heavy mass causing solidification-related problems and flowdistance calculations are used as examples to demonstrate the idea, but the same philosphy can be applied to other problems as well. Part of the problems with conventional form feature oriented design rules in manufacturability
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assessment are eliminated by identifying the underlying geometric characteristics in contrast to using the original rules themselves. Volumetric part representations and their associated processing techniques have proved to be very efficient to extract volume-related geometric characteristics. Volume visualization techniques are also adopted in this application to convey the results of die castability assessment in a nature and precise fashion. Based on these techniques, the geometric incompatibility of a design can be identified much faster than before and the results are directly linked to manufacturing problems. The system is also very intuitive, and it can be used interactively by designers as they create the geometry. The current effort is devoted to extending this method to cover more solidification-related issues. For example, another concern in die casting is the identification of relative hot regions in the die, which may cause heat checking and thermal fatigue-related defects. There are several design rules related to this concern, e.g. the distance between two ribs and the radius of holes. The approach described in this paper can be used to find whether the ribs are relatively too heavy; however; it can not tell the distance between them. For two closely spaced ribs, even though they can be appropriate in size. the part can still be poorly configured from the perspective of solidification. To extend our approach to cover this problem, other geometric data processing and reasoning methods are required.
2.
Beiter, K. A. and lahii. K., Grometry-Based Indexfi~r Predicting Sink in Pla.stic Parts, Technical Report, ERC/NSM-P-9 l-61. Engineering Research Center for Net Shape Manufacturing. The Ohio State University, Columbus. OH, 1991, Borgefora. G.. Distance transformations in arbitrary dimensions. Mark
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Kaufman, A.. Volumr Graphic\. Academic Press, 1990. Kaufman, A. and Shimony. E.. 3D scan-conversion algorithms for voxel-based graphics. Proceedings ACM Workshop ON Interactive 30 Grtrphia. 1986, pp. 45-75. Lu, S. C.. Rebello, A. B., Miller. R. A.. Kinzel. G. L. and Yagel, R., A volume-baaed geometric reasoning approach for diecastability evaluation. ASME Computrr.c in Engineering. 1995, 65-74. Lu. S. C.. Rebello, A. B., Cui. D. H.. Yagel. R., Miller, R. A. and Kinzel, G. L., A 3-D contextual shading method for visualization of diecaating defects. Procrrdingr of Visucdizution ‘96. San Francisco, CA. September 1996, pp. 40 I-404. Luby. S. C.. Dixon, J. R. and Simmons, M. K.. Designing tiith features: Creating and using a features database for evaluation of the manufacturability of castings. ASME Comprtrrc in Figinreriq. 1986. 2X.5-292.
ACKNOWLEDGEMENTS The authors also wish to thank the North American Die Casting Association, US Department of Energy, Ford Motor Company, and the Center for Die Casting at the Ohio State University for their support. The center is funded by the National Science Foundation and industrial membership. REFERENCES I. Barton, H. K.,
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13. Marks. P.. Process reengineering and the new manufacturing enterprise wheel: I.5 processes for competitive Advantage, published by The Computer and Automated Systems Association of the Society of Manufacturing Engineers (CASA/SME) Technical Forum. 1994. IS. NADCA DDC. Product Design for Die Casting, Diecasting Development Council of the North American Die Casting Association, 19X8. 16. Porter. W. A., Modern Foundations of .Twfrm Enginrerin~. Macmillan Company, New York, 1968. 17. Rosenfeld, A. and Pfaltz, J., Distance functions on digital pictures. Pottern Rrcognition, 1968, l(l). 33-61. IX. Verwer. B. J. H.. Local distances for Distance Transormations m Two and Three Dimensions. Thesis, Delft University of Technology. I99 I, pp.23-33. volume viewing. 19. Yagel. R. and Kaufman. A.. Template-based Proceedin,+\ of Eurograp1~ic.s. 1992. 11, I S3- 167.
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Zuiderveld, K. Z., Koning, A. H. J. and Viergever, M. A., Acceleration of ray casting using 3D distance transform. Proceedings of Visualizafion in Biomedicul Computing, Vol. 1808, ed. R. A. Rot&. SPIE, Chapel Hill, NC, pp. 324-335.
State University. ical Engineering
Shao-Chiung Lu is a principal development engineer working on the research and development qfDesign,for Munufucturing (DFM) and Visualization tools for various industrial applications at Ford Motor Co. His rrvearch and technical publications cover a varieq of topics in Computer Graphics, Corwrrrent Engineering, and CAE System Integration. He received his MS in 1992 and PhD in 1996, both from the Deportment qf Mechanical Engineering at the Ohio He received his BS.frorn the Department of Mechanut the Notional Taiwm UniverriQ in 1987.
Alexander Rebello is a PhD candidate in Industrial and Systems Engineering at The Ohio State Universin. His work as a part of the Center .for Die Casting involves development qf concurrent enginec’ring tools ,for use in design and manufacturing. He received his BSIE, BS in Computer Sciewe and Engineering Physics and BA in Mathemutics rrt St Ambrose University in 1988 and his MS degree from The Ohio State lJni~,er.,ity in 1991. He is (1 member of IlE
R. Allen Miller received the BME degree ,from Union College in 1966, the SM degree in Mechanical Engineering ,from the Mo.wachusett.s Institute of Technology in 1967, and the PhD degree in Control and Systems Engineering ,from Case Western Reserve Universin in 1971. He has been with Ohio State .since 1971, currently holding the rank of Prqfersor and Chair of the Department of lntluctrial, Welding and Systems Etlgineerin,y. His re.srnrch interests rare in the cueus design ,for munufactura, purticularly design for die casting and die casting die design. He is also interested in the development of design environments to support purr and die/mold design including CAD/ CAM/CAE integration, und technology support .for die costing and die/mold manufacturing jirms. He is the director of the Cerlter for Die Casting which is u consortium of academic reseurchers, the North American Die Casting Association. and several die casting corn ponies which jticuses on applied resmrch,for the die uxting industc. he i.c cl10 the director of the Practice-Oriented Mun~fncturing Engineering program. a College of Engineering musters pmqmm e.vtablished in 1994. Dr Miller M’(ISthe rec,ipirnt of the MwQuigg Award,for Excellent~e in Teaching in 1975, a College cj’Engmerring Research Award in 1982, and the IEEE Systems, Man, and Cybernetics SocieQ Franklin V. Ttrylor Award,for the outstanding paper prevented at the 1981 international Cocfereme on Cybernetics and So&~. He is a member of IEEE, HE, SME. ASME. ASEE, NADCA, the Auociation ,for Mamtfacturing E.xcellence. and The Humrrn Factor? cmd Ergonomic-s So&&.
Dr Kinzel is a professor in mechanical engineering and has worked in design, stress analysis, and CAD/CAM for more than 25 years. He received his BME and MS degrees from The Ohio State Vniversity in 1968 and 1969, respectively, and his PhD from Purdue in 1973. He joined the faculty of the mechanical engineering departments at Ohio State in 1978 and is currently teaching cour.yes in machine design, kinematics, and CAD/CAM. Prior to joining Ohio State. he was u principul research engineer at Batelle’s Columbus Luboratories. At Ohio State. Dr Kin:el has supervised more than 80 design and manufacturing oriented theses to completion. He has been u principal investigator on more thutt 40 research projects, and has publishedmore than 100 pulpers in the design and manufacturing areas. He is currently work&r: 011research issues in sheet-metal ,forming and CAD/CAM.
Roni Yagel is an Associate Professor in the Department of Computer and Information Science and an Adjunct Associate Professor in the Advanced Computer Center,for Art and Design and the Biomedical Engineering Center at The Ohio State Vniversit). He headr the Volume Graphics Research Group which pursues research in computer graphics, volume graphics, scientiJic visualization, virtual reality, and image processing. Roni Yagel received his PhD in 1991 from the State University of New York at Stony Brook where he was also a re,yeurcher in the Department ofAnatomy und the Department qf Physiologv and Biophysics. He received his BSc Cum Laude trnd MSc Cum Lude,frorn the Department of Mathematics and Computer Science at Ben Guriorl University qf the Negev, Israel, in 1986 and 1987. respecti\,elv. His resenrch and technical publications deal with a varie@ of topics ii7 volume graphics and visualization. His research interests include nlgorithms,for graphics, imaging, and animation. error c,ontrol it) image generation. and visualization tools,% industrial rrnd scientific clpplic ation s. For more informutiorl see: htt~~://~~~~~~~..Ci.~.ohio-stat. rtlu/?‘trgel
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