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Computational and Theoretical Problems in Modern Rapid Prototyping

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  1. Computational and Theoretical Problems in Modern Rapid Prototyping Mark R. Cutkosky Stanford Center for Design Research http://cdr.stanford.edu/interface

  2. Outline • Introduction to Layered Manufacturing • Commercial and research processes • Enabling factors (why now) • Capabilities and opportunities • (Almost) arbitrary geometry • Functionally graded materials • Integrated assemblies, “smart parts” • Computational challenges • Huge design space • Analysis • Process planning and control • Summary NAS Math. Modeling Forum 5/10/99 -mrc

  3. Traditional manufacturing:a sequential process of shaping and assembly NAS Math. Modeling Forum 5/10/99 -mrc

  4. Layered Manufacturing: commercial example UV curable liquid Laser elevator Formed object Photolithography process schematic Sample prototype (ME210 power mirror for UT Auto) http://me210.stanford.edu NAS Math. Modeling Forum 5/10/99 -mrc

  5. Almost arbitrary 3D Geometries Tilted frames (RPL) Loop Tile -- dense tiling of 3D space. (Carlo Sequin, U.C.B.) Minimum toroidal saddle surface (C. Sequin) NAS Math. Modeling Forum 5/10/99 -mrc

  6. Shape Deposition Manufacturing ( SDM) From RP and CNC to . . . RP CNC 1970 1990 2000 NAS Math. Modeling Forum 5/10/99 -mrc

  7. Shape Deposition Manufacturing (CMU/SU) Embedded Component Part Support Deposit (part) Shape Shape Deposit (support) Embed NAS Math. Modeling Forum 5/10/99 -mrc

  8. SDM#1: Injection mold tooling (SU RPL) NAS Math. Modeling Forum 5/10/99 -mrc

  9. SDM #2: Frogman (CMU) • Example of polymer component with embedded electronics NAS Math. Modeling Forum 5/10/99 -mrc

  10. Alumina vane SDM #3: Ceramic parts (RPL) Silicon nitride pitch shaft Alumina turbine wheels NAS Math. Modeling Forum 5/10/99 -mrc

  11. Shaft coupling Shaft Motor Leg links SDM for integrated assemblies Motivation: Building smallrobots with prefabricatedcomponents is difficult...and results are not robust. NAS Math. Modeling Forum 5/10/99 -mrc

  12. SDM #4: Robot leg with embedded components (http:cdr.stanford.edu/biomimetics) Steel leaf spring Designer composes the design from library of primitives, including embedded components Piston Part Primitive Outlet for valve Valve Primitive Circuit Primitive Inlet port primitive NAS Math. Modeling Forum 5/10/99 -mrc

  13. Robot Leg design (cont’d.) Steel leaf-spring Internal components are modeled in the 3D CAD environment. Piston Sensor and circuit Spacer Valves Components are prepared with spacers, etc. to assure accurate placement. NAS Math. Modeling Forum 5/10/99 -mrc

  14. Robot Leg: compacts The output of the software is a sequence of 3D shapes and toolpaths. Embedded components Part Support NAS Math. Modeling Forum 5/10/99 -mrc

  15. Robot Leg: embedded parts Steel leaf-spring Piston Sensor and circuit Valves A snapshot just after valves and pistons were inserted. NAS Math. Modeling Forum 5/10/99 -mrc

  16. Robot Leg: completed Finished parts ready for testing NAS Math. Modeling Forum 5/10/99 -mrc

  17. Layered Manufacturing: is it a new manufacturing paradigm? Laminated manufacturing (1892-1940s) Photo-sculpture studio (1860) Laser-based photolithography (1977) [Source:Beaman 1997] NAS Math. Modeling Forum 5/10/99 -mrc

  18. A process enabled by computing... 3D solid model slicing trajectory planning material addition process data exchange format motion control trajectories CAD process planner fabrication machine NAS Math. Modeling Forum 5/10/99 -mrc

  19. Commercial Photolithography Fused deposition Laser sintering Laminated paper Research Selective laser sintering (UT Austin) 3D printing (MIT) Shape deposition manufacturing (CMU/Stanford) Engineering materials (metals, ceramics, strong polymers) Graded materials Embedded components Not quite direct from CAD model... “Look and feel” prototype Complex 3D shapes direct from CAD model Summary of layered manufacturing processes NAS Math. Modeling Forum 5/10/99 -mrc

  20. Layered manufacturing results in a hugespace of possible designs: • Ability to create arbitrary 3D structures with internal voids • Ability to vary material composition throughout the structure • Ability to embed components such as sensors, microprocessors, structural elements. What kind of design environment will help designers to understand and exploit the potential of layered manufacturing? NAS Math. Modeling Forum 5/10/99 -mrc

  21. Ability to create arbitrary 3D structures with internal voids (homogeneous materials) W Shape optimization example: Find the minimum-weight shelf structure, bounded by box B, that supports load W without failing. B Space within B is divided into N cells, each of which can be filled or empty. Number of unique designs  2N NAS Math. Modeling Forum 5/10/99 -mrc Rapid Prototyping Workshop 5/99 -mrc

  22. Ability to vary material composition Deposition heads can be controlled to deposit varying amounts of each material* as the part is built. Total material composition varies throughout the part. deposition heads Support structure Volume fractions always add to unity* *void, or empty space, is treated as a special case of material NAS Math. Modeling Forum 5/10/99 -mrc

  23. Material composition: product space m = number of materials (including void) vi= volume fraction of each material r = deposition mixture resolution Product Space: Example: urethane, glass fibers, teflon, and void, controlled to a resolution of 10% volume fraction  286 unique mixtures possible. NAS Math. Modeling Forum 5/10/99 -mrc

  24. Design space with arbitrary geometry and heterogeneous materials (E3 Tm) W Shape + material optimization: Assume m possible materials, (including void) with a mixture resolution of r. B Space within B is discretized into N cells, each of which can be filled with a unique mixture of materials. Number of unique designs  N Example: 101010 cells, 4 materials, 10% mixture resolution  2861000designs! NAS Math. Modeling Forum 5/10/99 -mrc Rapid Prototyping Workshop 5/99 -mrc

  25. Toward a design environment for layered manufacturing • The design space is huge. • But there are significant constraints associated with the manufacturing processes. • Therefore, provide an environment that combines manufacturing analysis, design rules, and design libraries to help designers explore the full potential of layered manufacturing. NAS Math. Modeling Forum 5/10/99 -mrc

  26. Computational issues #1:Process Planning Decompose Input Deposit Machine Decompose Deposit Machine • Process constraints • Manufacturability • Support structures • Deposition method • Deposition parameters • Path planning • Machining method • Tool selection • Machining parameters • Path planning (source:J.S. Kao SU RPL) NAS Math. Modeling Forum 5/10/99 -mrc

  27. Decomposition into ‘compacts” and layers Complete Part Compacts Layers Tool Path NAS Math. Modeling Forum 5/10/99 -mrc

  28. Decomposition based on process sequence (5) (6) (7) (8) NAS Math. Modeling Forum 5/10/99 -mrc

  29. Definitions: Compact[Merz et al 94] • 3-D volume with no overhanging features • Rays in growth direction enter only once • Compacts correspond to SDM cycles z2 z1 Build Axis (a) no good (b) OK (c) OK NAS Math. Modeling Forum 5/10/99 -mrc

  30. Decomposition algorithms Locate silhouette edges, split surfaces Merge compacts Extrude concave loops (source:J.S. Kao SU RPL) NAS Math. Modeling Forum 5/10/99 -mrc

  31. Deposition Process Planning (RPL) • Thermal Stresses Develop due to: • Temperature gradients • Differences in expansion coefficient • Thermal Stresses Cause: • Part inaccuracy • Delamination • Solutions • Develop optimal deposition path and process parameters to minimize thermal stresses • Tailor alloy to maintain desirable properties while minimize thermal expansion coefficient NAS Math. Modeling Forum 5/10/99 -mrc

  32. Problems with automated process planning • finite thickness of support material • finish on unmachined surfaces • warping and internal stresses • decomposition depends on geometry,not on intended function NAS Math. Modeling Forum 5/10/99 -mrc

  33. Design by Composition(M. Binnard) Users build designs by combining primitives with Boolean operations • Primitives have high-level manufacturing plans • Embed components and shapes as needed Primitives merged by designer Manufacturing plans merged by algorithm NAS Math. Modeling Forum 5/10/99 -mrc

  34. a) (top view) b) (side view) d d d(a1,a2) d(a1,a2) l 2l Dd Minimum gap/rib thickness Generalized 3D gap/rib e) (side view) 2l l d(m1,m2,m3) d(m1,m2,m3,a1,a2) Wc/l >= 2 m1 m2 m3 m1 m2 m3 Minimum feature thickness Toward a mechanical MOSIS? SFF/SDM VLSI Boxes, Circles, Polygons and Wires Decomposed Features SFF/SDM Design Rules Mead-Conway Design Rules NAS Math. Modeling Forum 5/10/99 -mrc

  35. Primitive = Compact Set + Precedence Graph Primitive Compact set Compact precedence graph • Set of valid compacts • No intersections • Fills the primitive’s projected volume • Acyclic directed graph • Link for every non-vertical surface

  36. A B Merging Algorithm Example + = A B C=A È B intersection compacts non-intersecting compacts NAS Math. Modeling Forum 5/10/99 -mrc

  37. Combining composition and decomposition CAD MODEL re-analysis (if needed) DESIGN DECOMPOSITION DESIGN BY COMPOSITION LIBRARY: Decomposed Designs & primitives COMPACT SET CPG SEQUENCE & TOOL PATH PLANNING NAS Math. Modeling Forum 5/10/99 -mrc

  38. A need for integrated mechanical, thermal and electrical analysis VuMan (CMU) mechanical, thermal analysis NAS Math. Modeling Forum 5/10/99 -mrc

  39. Summary Emerging layered manufacturing processes such as SDM: • are made feasible by recent advances in desktop computing and solids modeling • afford a huge design space (E3 Tm) • provide a rich area for geometric reasoning and process planning • present formidable challenges in analysis, process planning and control to achieve consistent, high-quality parts NAS Math. Modeling Forum 5/10/99 -mrc

  40. Acknowledgements Thanks to the members of the Center for Design Researchand the Stanford Rapid Prototyping Lab for their work in generating the results and ideas described in this presentation. This work has been supported by the National Science Foundation (MIP-9617994) and by the Office of Naval Research (N00014-98-1-0669) NAS Math. Modeling Forum 5/10/99 -mrc