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

2. C D R NAS Math. Modeling Forum 5/10/99 -mrc 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

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

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

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

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

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

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

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

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

11. C D R NAS Math. Modeling Forum 5/10/99 -mrc 11 SDM for integrated assemblies Motor Leg links Shaft Shaft coupling Motivation: Building small robots with prefabricated components is difficult... and results are not robust.

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

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

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

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

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

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

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

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

20. C D R NAS Math. Modeling Forum 5/10/99 -mrc 20 Layered manufacturing results in a huge space 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?

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

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

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

24. C D R NAS Math. Modeling Forum 5/10/99 -mrc 24 Design space with arbitrary geometry and heterogeneous materials (E 3  T m ) Shape + material optimization: Assume m possible materials, (including void) with a mixture resolution of r. B W 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  286 1000 designs! Rapid Prototyping Workshop 5/99 -mrc

25. C D R NAS Math. Modeling Forum 5/10/99 -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.

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

27. C D R NAS Math. Modeling Forum 5/10/99 -mrc 27 Decomposition into ‘compacts” and layers Complete Part CompactsLayersTool Path

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

29. C D R 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 Build Axis (c) OK (a) no good (b) OK z1z1 z2z2

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

31. C D R NAS Math. Modeling Forum 5/10/99 -mrc 31 Deposition Process Planning (RPL)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

32. C D R 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

33. C D R NAS Math. Modeling Forum 5/10/99 -mrc 33 Design by Composition (M. Binnard)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

34. C D R NAS Math. Modeling Forum 5/10/99 -mrc 34 Decomposed Features SFF/SDM VLSI Boxes, Circles, Polygons and Wires SFF/SDM Design Rules Mead-Conway Design Rules   Wc/ >= 2 Minimum gap/rib thickness dd dd (top view)a) Generalized 3D gap/rib d  (side view)b) d  Minimum feature thickness d(m1,m2,m3) (side view)e) m1m2m3 d(m1,m2,m3,  ) m1m2m3 Toward a mechanical MOSIS?

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

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

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

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

39. C D R 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 (E 3  T m ) –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

40. C D R NAS Math. Modeling Forum 5/10/99 -mrc 40 Acknowledgements Thanks to the members of the Center for Design Research and the Stanford Rapid Prototyping Lab forCenter for Design ResearchStanford Rapid Prototyping Lab 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)