Computational and C D R Theoretical Problems in Modern Rapid Prototyping Mark R. Cutkosky Stanford Center for Design Research http://cdr.stanford.edu/interface
Outline • Introduction to Layered Manufacturing C D R – 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 2 NAS Math. Modeling Forum 5/10/99 -mrc
Traditional manufacturing: a sequential process of C D R shaping and assembly 3 NAS Math. Modeling Forum 5/10/99 -mrc
Layered Manufacturing: commercial example C D R UV curable Laser liquid elevator Formed object Photolithography process Sample prototype (ME210 schematic power mirror for UT Auto) http://me210.stanford.edu 4 NAS Math. Modeling Forum 5/10/99 -mrc
Almost arbitrary 3D Geometries C D R Tilted frames (RPL) Loop Tile -- dense tiling of 3D space. (Carlo Sequin, U.C.B.) Minimum toroidal saddle surface (C. Sequin) 5 NAS Math. Modeling Forum 5/10/99 -mrc
From RP and CNC to . . . C D R RP CNC 1970 1990 Shape Deposition Manufacturing ( SDM) 2000 6 NAS Math. Modeling Forum 5/10/99 -mrc
Shape Deposition Manufacturing (CMU/SU) C D R ������������������ Part Support Deposit (part) Shape Shape Deposit (support) Embed 7 NAS Math. Modeling Forum 5/10/99 -mrc
SDM#1: Injection mold tooling (SU RPL) C D R 8 NAS Math. Modeling Forum 5/10/99 -mrc
SDM #2: Frogman (CMU) C D R • Example of polymer component with embedded electronics 9 NAS Math. Modeling Forum 5/10/99 -mrc
SDM #3: Ceramic parts (RPL) C D R Alumina vane Silicon nitride pitch shaft Alumina turbine wheels 10 NAS Math. Modeling Forum 5/10/99 -mrc
SDM for integrated assemblies C D R Shaft coupling Shaft Lift pot Body frame Motor Hip pot Leg links Abduct pressure Gears sensor Knee pot Motivation : Building small Actuators Lift pressure robots with prefabricated sensor Extend pressure sensor components is difficult... and results are not robust. 11 NAS Math. Modeling Forum 5/10/99 -mrc
SDM #4: Robot leg with embedded components (http:cdr.stanford.edu/biomimetics) C D R Steel leaf spring Designer Piston composes the design from library Part Primitive of primitives, including Outlet for valve embedded components Valve Primitive Circuit Primitive Inlet port primitive 12 NAS Math. Modeling Forum 5/10/99 -mrc
Robot Leg design (cont’d.) C D R Steel leaf-spring Internal Piston components are Sensor and circuit modeled in the 3D Spacer CAD environment. Valves Components are prepared with spacers, etc. to assure accurate placement. 13 NAS Math. Modeling Forum 5/10/99 -mrc
Robot Leg: compacts C D R The output of the software is a sequence of 3D shapes and toolpaths. Embedded components Part Support 14 NAS Math. Modeling Forum 5/10/99 -mrc
Robot Leg: embedded parts C D R Steel leaf-spring Piston Sensor and circuit Valves A snapshot just after valves and pistons were inserted. 15 NAS Math. Modeling Forum 5/10/99 -mrc
Robot Leg: completed C D R Finished parts ready for testing 16 NAS Math. Modeling Forum 5/10/99 -mrc
Layered Manufacturing: is it a new manufacturing paradigm? C D R Laminated manufacturing (1892-1940s) Photo-sculpture studio (1860) Laser-based photolithography (1977) [ Source: Beaman 1997] 17 NAS Math. Modeling Forum 5/10/99 -mrc
A process enabled by computing... C D R 3D solid model slicing material addition process trajectory planning ���� ������ �������� ������� ������ ������������ CAD process planner fabrication machine 18 NAS Math. Modeling Forum 5/10/99 -mrc
Summary of layered manufacturing processes C D R Commercial Research • Selective laser sintering • Photolithography (UT Austin) • Fused deposition • 3D printing (MIT) • Laser sintering • Shape deposition • Laminated paper manufacturing (CMU/Stanford) Engineering materials (metals, “Look and feel” prototype ceramics, strong polymers) Complex 3D shapes Graded materials direct from CAD model Embedded components Not quite direct from CAD model... 19 NAS Math. Modeling Forum 5/10/99 -mrc
Layered manufacturing results in a huge space of possible designs: C D R • 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? 20 NAS Math. Modeling Forum 5/10/99 -mrc
Ability to create arbitrary 3D structures with internal voids (homogeneous materials) C D R W Shape optimization example: Find the minimum-weight shelf structure, bounded by box B , B that supports load W without failing. Space within B is divided into N cells, each of which can be filled or empty. Number of unique designs ≈ 2 N 21 NAS Math. Modeling Forum 5/10/99 -mrc Rapid Prototyping Workshop 5/99 -mrc
Ability to vary material composition C D R Deposition heads can be deposition controlled to deposit heads varying amounts of each material* as the part is built. Total material composition varies throughout the part. Support structure Volume fractions always add to unity* *void, or empty space, is treated as a special case of material 22 NAS Math. Modeling Forum 5/10/99 -mrc
Material composition: product space C D R m = number of materials (including void) v i = volume fraction of each material m ∑ 1 = v i 1 i = r = deposition mixture resolution urethane 1 glass + − r m ( 1 )! + − r m Product Space: = C void 1 − ! ( − 1 )! m r m teflon Example: urethane, glass fibers, teflon, and void, controlled to a resolution of 10% volume fraction ⇒ 286 unique mixtures possible. 23 NAS Math. Modeling Forum 5/10/99 -mrc
Design space with arbitrary geometry and heterogeneous materials ( E 3 × T m ) C D R 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. N 1 + − r m Number of unique designs ≈ C 1 − m Example: 10 × 10 × 10 cells, 4 materials, 10% mixture resolution ⇒ 286 1000 designs! 24 NAS Math. Modeling Forum 5/10/99 -mrc Rapid Prototyping Workshop 5/99 -mrc
Toward a design environment for layered manufacturing C D R • 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. 25 NAS Math. Modeling Forum 5/10/99 -mrc
Computational issues #1: Process Planning C D R Decompose Input Deposit Machine Decompose Deposit Machine • Process constraints • Deposition method • Machining method • Manufacturability • Deposition parameters • Tool selection • Support structures • Path planning • Machining parameters • Path planning ( source: J.S. Kao SU RPL) 26 NAS Math. Modeling Forum 5/10/99 -mrc
Decomposition into ‘compacts” and layers C D R �������� �������� ������ ��������� ���� 27 NAS Math. Modeling Forum 5/10/99 -mrc
Decomposition based on process sequence C D R primary material (5) (1) (2) (6) support material (3) (7) (4) (8) 28 NAS Math. Modeling Forum 5/10/99 -mrc
Definitions: Compact [Merz et al 94] C D R • 3-D volume with no overhanging features • Rays in growth direction enter only once • Compacts correspond to SDM cycles [ ] ( ) , , ∀ ∀ ∀ ∃ ∃ ∈ ↔ ≤ ≤ x y z z z x y z a z z z 1 2 1 2 z 2 z 1 (b) OK (c) OK ���������� ����������� 29 NAS Math. Modeling Forum 5/10/99 -mrc
Decomposition algorithms C D R Locate silhouette edges, split surfaces Merge compacts Extrude concave loops �D� �E� �F� ( source: J.S. Kao SU RPL) 30 NAS Math. Modeling Forum 5/10/99 -mrc
Deposition Process Planning (RPL) C D R laser beam •Thermal Stresses Develop due to: metal powder •Temperature gradients 3/8” •Differences in expansion coefficient 6” •Thermal Stresses Cause: cooling •Part inaccuracy •Delamination deflection •Solutions •Develop optimal deposition path and process parameters to minimize thermal stresses •Tailor alloy to maintain desirable properties while minimize thermal expansion coefficient 31 NAS Math. Modeling Forum 5/10/99 -mrc
Problems with automated process planning C D R • finite thickness of support material • finish on unmachined surfaces • warping and internal stresses • decomposition depends on geometry, not on intended function 32 NAS Math. Modeling Forum 5/10/99 -mrc
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