A List of Responders
Virtual Manufacturing Background Project
Tony.Woo@um.cc.umich.edu T. C. Woo Industrial Engineering, FU-20 University of Washington Seattle, WA 98195
Research Project Summaries a. Visibility Algorithms in Design and Manufacturing Given a target geometry and a source with a given cone of visibility, we expose the target to the source optimally, which has applications in materials processing and imaging. Mathematically known as the Covering Problem, minimization of the number of re-positioning and re-orientations of the source does not lend to polynomial time solution. We are however encouraged by the aide of the Gaussian mapping and the discovery of its dual, the visibility map. For sources with a hemispherical cone, the visibility map of a target is always convex, if not empty, hence giving rise to fast algorithms. Work is progressing in a wide range of applications: in machining, measuring, scanning, etc. for different geometries of the source and the target (as in point, line, and surface), as well as for different types of lines of sight (as in circular, for robots with rotary joints, or parabolic, as for trajectories of particles in vapor deposition). b. Tolerancing of Flexible Components Sheet metal components are prevalent in automobiles and aircrafts. Because they are flexible, variations from the nominal dimensions come from two sources: those inherent in the manufacturing process such as stamping and those induced by handling, fixturing, and joining. Indeed, common sense suggests that accuracy in the assembly of flexible components may be difficult to maintain. By conceptualizing an assembly as in series or in parallel, we derive the resultant tolerances. That the tolerance in parallel assembly decreases as a function of the stiffness coefficient of the material is a pleasant, if not surprising, result. We also note that variations in flexible components are correctable -- by the very process of joining. Novel sequencing of the joints are investigated, in the spirit of "error correction": an ideal design being the "signal", and the manufacturing process being the "channel". c. Computational Metrology The qualitative assessment of a component relies on (1) the method for data sampling and (2) the algorithm for determining the tolerance "zone". Based on the work of a Fields medalist, we exhibit two sampling methods which maintain the same accuracy as that of the uniform or random, yet reduces the number of samples (hence time) almost quadratically. By the same token, given the same number of samples, the two methods improve the accuracy almost quadratically. The work has been done in (the fine grain domain of) determining surface roughness. When applied to (the course grain problem of ) tolerancing, however, the two sampling methods show a peculiar sensitivity to the surface topology. Investigations in singularity theory are under way. Algorithms for tolerancing have been ambiguous: there is no procedural specifications in the existential ANSI standards of Y14 (Dimensioning and Tolerancing) and B89 (Metrology). Collaboration with the Courant Institute of the New York University, Manufacturing Engineering Laboratory of the National Institute of Standards and Technology, Manufacturing Systems Department of IBM Research at Yorktown Heights, and the Computer Science Department at Johns Hopkins, and the Geometry Center and the Computer Science Department at the University of Minnesota may help pave the way to a new procedural standard. d. Geometric Dynamics Surfaces and geometries undergo changes, as in the machining of workpiece geometry, the growth of tissues in biological systems, and the breaking of waves in the ocean. Towards the understanding of a science of changes, and to capture the morphology, we begin with a 100 year old problem posed by J. C. Maxwell in his essay "On Hills and Dales"-- by computing an intrinsic "sea level" in a given set of contours. Morphogenesis is modelled by a family of parallel surfaces in differential geometry, in which singularities, folds, and cusps are of particular concern. (They, for example, represent collision of the machine tool which cause gouges, as well as the formation of caustics in the design of geometrical optics.) The notion of geometrical stability is then applied to mechanical designs, not in the classical sense of static equilibria, but to achieve robustness to design changes. e. Agile Manufacturing The complexity of manufacturing increases along the scale of: continuous (as in the production of newspaper or chemicals), flow line (as in automotive assembly), batch (as in copying services), and job shop (as in the kitchen of a restaurant). "Agile" manufacturing places further demands on the job shop manufacturing, not only in quality, cost, and delivery, but also in the ability to utilize excess capacity. This compression of scales leads us to various paradigms of phase changes in the physical sciences. We begin with the understanding of "work". As "heat transfer", we model data communication in an attempt to understand the basic currency in a transaction: information. The classical model due to Shannon, which places no weight on the "value" or the "quality" of information, is augmented by that of Kolmogorov-Chaitin, which leads to the notions of minimality (of program size) and optimization. Research though preliminary is far-reaching. f. Manufacturing of Software Software tools and systems are being built today, not unlike the cathedrals in the Renaissance era, line by line, stone by stone. As there appears to be a parallel between software engineering and the manufacturing of hard goods, we seek similarities and differences. We begin with the metrics for measuring complexity, in the hope of classifying components for the employment of "group technology" from manufacturing. While manufacturing manipulates materials based on their physics, software engineering is seen to be based on the logic of information. In this light, the two are "duals". Such linkages between information and physics promises pay-offs in two important areas: the automation of software production and the science of "digital physics".
A List of Responders
Virtual Manufacturing Background Project
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