Computer-Aided Design and Manufacturing Laboratory: Rotational Drainability Sara McMains UC...
-
Upload
cathleen-nicholson -
Category
Documents
-
view
221 -
download
0
Transcript of Computer-Aided Design and Manufacturing Laboratory: Rotational Drainability Sara McMains UC...
Computer-Aided Design and Manufacturing Laboratory: Rotational Drainability
Sara McMains
UC Berkeley
University of California, Berkeley
Drainability Testing a rotation axis for
drainability
2
University of California, Berkeley 3
Problem
Find an orientation relative to the horizontal rotation axis to drain trapped water Re-orientation is not allowed Can rotate either CW or CCW
gravity
Does not drain
Does drain
cross-section
rotation axis
trapped water
http://www.mtm-gmbh.com/
3
University of California, Berkeley 4
Motivation
Should run interactively Monitor/check design at any time
Feedback to designer if design is not drainable
Solve purely from geometric perspective Physics-based method such as CFD is too slow
Test a given orientation as a first step [Yasui, McMains
‘11] Assume force applied to water is gravity only
Rotation is slow enough
4
University of California, Berkeley 5
Geometric Analysis of Manufacturing Process Filling analysis in gravity casting [Bose et al. 98] Rolling a ball out of a polygon [Aloupis et al. 08] Tool accessibility analysis using visibility [Woo et al.
94] Find a rotation axis that minimizes number of
setups in planning for 4-axis NC machining [Tang et al. 98, Tang & Liu 03]
Related Work
5
University of California, Berkeley
Outline
Motivation and background Testing a rotation axis for drainability
Solution in 2D space Solution in 3D space
6
University of California, Berkeley 7
All water traps contain a concave vertex
Drain all concave vertices!
Trapped water
gravity
7
University of California, Berkeley 8
Consider...
One water particle approximates a water trap
gravity
8
University of California, Berkeley 9
Gravity directions that trap particle at vertex v:
Fix geometry, consider gravity rotating relative to geometry Describe gravity as a point on the Gaussian circle
v
2e1e
1H 2H
v v
vTCCWg CWg
}1,0)(|{ vpvpepH ii i
iv HT
1e 2e
CWgCCWg Gaussian circle
vT
9
CWCCW
University of California, Berkeley 10
Draining Graph
A
BC
D
EOUT
CWCCW
D
C B
AE
Draining graph
Particles trapped at concave vertices Capture transitions between concave vertices
10
University of California, Berkeley 11
Drainability Checking
A
BC
D
E
CWCCW
CW rotation
CCW rotation
ED A
C B
OUT
11
University of California, Berkeley
Outline
Motivation and background Testing a rotation axis for drainability
Solution in 2D space Solution in 3D space
Input is triangulated boundary representation
Results and conclusions
12
University of California, Berkeley 13
Construct Tv , find , in 3D
}1,0)(|{ vpvpepH ii
i
iv HT
1H 2H vT3H
2e1e
3e1e 2e 3e
v
Describe gravity as a point on the Gaussian Sphere.
CWg CCWg
13
University of California, Berkeley 14
Set rotation axis along z-axis Possible gravity direction where xy-plane intersects sphere
)plane()( xyTT vxyv )plane()( xyHH ixyi
ixyixyv HT )()( 14
Construct Tv , find , in 3DCWg CCWg
iCWg
iCCWg
University of California, Berkeley
1H 2H 3H
2e
1e
3e1e
2e 3e
v
15
i
xyixyv HT )()( )plane()( xyHH ixyi )plane()( xyTT vxyv
Incremental calculation of , CWg CCWg
2CWg
2CCWg
1CCWg1CWg
1CWg
1CCWg2CCWg
2CWg
3CWg3CCWg
CCWgCWg
3CCWg 3CWg
University of California, Berkeley
16
Cases for particle tracing in 3D From each concave vertex v
Trace along geometric features under / CWg CCWg
g
Construct 3D draining graph edges
Vertex cases
Ridge edge casesValley edge cases
16
University of California, Berkeley 17
Procedure Find concave vertices For each
Set as node in draining graph Calculate its , , and Under and , trace paths
Add directed edges according to the transitions
Check drainability by checking whether there is a path from each node to “out”
vT CWg CCWg
CWg CCWg
University of California, Berkeley
Outline
Motivation and background Testing a rotation axis for drainability
Solution in 2D space Solution in 3D space
Results and conclusions
18
University of California, Berkeley
Results
outlet
Not outlet
University of California, Berkeley 20
ResultsoutletNot outlet
202020
gravity
University of California, Berkeley 21
0.0
0.2
0.4
0.6
0.8
1.0
0 100,000 200,000 300,0000.0
0.2
0.4
0.6
0.8
1.0
0 20000 40000 60000
# of triangles # of concave vertices
Time (sec)Time (sec)
Performance: Avg. Testing Time
(2.66 GHz CPU, 4GB of RAM)
#triangles
3,572 120,004 160,312 289,956
University of California, Berkeley 22
Future Work
Relax simplifying assumptions Pauses required? Multiple rotations required? Consider initial filling state
Finding an orientation to
drain trapped water Estimating remaining water if not
completely drainable 22
University of California, Berkeley
Conclusions First formulation of solutions to
drainability feedback Concave vertex drainability graph Critical gravity directions for transitions Less than 1 second per orientation
23
University of California, Berkeley
Acknowledgements Yusuke Yasui Peter Cottle Daimler NSF
24