Robust Generation of 3-D Rolling Ball Offset

Many manufacturing processes, from CV Deposition in semiconductors to composite laminates, create geometries which are offsets based on the starting geometry. Processes of this type can be modeled as rolling ball offsets with either constant radius or a smoothly varying radius. Modeling the resulting shapes is mostly a trial and error process often requiring expensive prototypes to verify process interactions. Correctly modeling these processes in software is also a trial and error process as the theoretical prediction of the results is not a currently available operation in CAD systems.

Description

The current code correctly produces constant radius offsets for most geometries including those cases where topology changes occur. Failures occur when the projected surfaces cannot be represented by analytical surfaces, and the resulting spline surface intersects itself. Recognition and automated handling of such surfaces is an ongoing research topic. Correctly handled topology changes include solid self-intersection and creation of closed voids within the solid.

More difficult, and currently only partially functional, are variable radius offsets. Manufacturing processes are non-uniform for many reasons. The amount of material laid down can depend on many factors, including design intent, reactor flows, and process variability. Some way of automatically modeling the resulting geometry is required. This is particularly important as the scale of the parts is reduced, and the effects of process variability approach or exceed the scale of the features. To model this, a class specifying the amount of offset to be applied was implemented and is used to control the offset. Currently two versions exist: one for constant radius and one for deposition in MEMS fabrication. New rules can be implemented and passed to the offset library by the user.

Current Status

Limitations in variable radius offsets include:

• C2 continuous offset function – This limitation in the theory is not expected to constrain many uses of the code.
• Each surface must have constant offset at discontinuous interface with another face – Surfaces which are not tangent to adjacent faces and do not have a constant offset at that edge will require a spline surface to model the resulting edge’s offset. Funding ran out before this capability was implemented.
• Surfaces must be normal or tangent to adjacent surfaces – Surfaces in the offset model resulting from edges or vertices in the original solid must be tangent to adjacent surfaces. When the adjacent original surfaces are not perpendicular, the required offset surfaces are NURB surfaces of unique construction. Funding ran out before techniques for the automated construction of these surfaces were completed.
• Offset surfaces must not self-intersect – Unlike most analytical surfaces, it is possible for spline surfaces to intersect themselves. Since we know that offsets tend to create situations of this type, we need to automatically find these self-intersections and split the surface to eliminate any unneeded surface. Methods for finding spline surface self-intersections are under development but not yet implemented.

Blue Gear on Left is Before; Green Gear on Right is After