Automated Design of Multi-Piece Molds for Making Geometrically
Complex Objects
Main Participants:
Satyandra K. Gupta,
Savinder Dhaliwal, Jun Huang, Malay Kumar, and
Alok K. Priyadarshi
Sponsor: This project was sponsored by the Office of Naval
Research. We also received in-kind support from Spatial Technologies
and Protoform
North America.
Keywords: Mold Design, Multi-Piece Molds, and Geometric
Reasoning.
Motivation
Conventional molds, usually referred to as two-piece molds have only
one primary parting surface and consist of two major pieces: core
and
cavity. These two pieces are separated along a single parting
direction
to eject the molded part. Since the mold pieces are constrained to move
in
a single direction, several undercuts are encountered in case of
complex
industrial parts. A number of side cores are required to form these
undercuts.
The side cores, apart from being very costly complicate and slow down
the
molding operation. Some very complex parts may not even be producible
using
a two-piece mold.
Multi-piece molds overcome the restrictions imposed by traditional
molds by having many parting directions. These molds have more than one
primary parting surface and consist of more than two mold pieces or
subassemblies. Each of these mold pieces has a different parting
direction. This freedom to remove the mold pieces from many different
directions eliminates the
undercuts produced by two-piece molds. A multi-piece mold can be
visualized
as a 3D jigsaw puzzle, where all the mold pieces fit together to form a
cavity
and then can be disassembled to eject the molded part. Moreover, since
there are no actuated side cores in multi-piece molds, the tooling cost
is significantly low. This makes multi-piece molding technology an
ideal candidate for making geometrically complex ceramic objects. The
ability to manufacture geometrically complex objects economically will
significantly expand the design space and will allow development of new
products in many different areas.
Currently, multi-piece molds are not widely used because of lack of
knowledge and required expertise to design these molds. The complete
automation of mold
design will radically reduce the cost and lead-time associated with the
deployment
of multi-piece molds and hence make them a viable candidate. Therefore,
in this project we have focused on automated design and fabrication of
multi-piece
molds.
Main Results and Their Anticipated Impact
We have developed the following three different approaches to the
design of multi-piece molds.
Feature-Based Approach for Designing Multi-Piece Sacrificial
Molds: We have developed a feature-based algorithm for
automated design of multi-piece sacrificial molds. For those class of
parts that can be modeled using our feature-based representation, the
feature-based decomposition and concave edge-based decomposition steps
ensure accessibility of mold components and therefore circumvent the
need for explicit global accessibility computations. The main
benefits of our algorithm are enumerated below.
- Our algorithm tends to create mold partitions in which parting
planes contain natural edges of the object. In case of ceramic parts,
such partitioning is preferred over partitioning in which the parting
plane passes through
the middle of a face of the object due to reduction in number of
secondary
operations.
- This approach allows us to manufacture parts that could not be
produced earlier using two-piece molds. Thus it expands the design
space for parts that can be produced using casting processes such as
gelcasting and polyurethane manufacturing.
- Since this approach automatically produces solid models of mold
components, it can be integrated with CAM systems to generate the
cutter path plans
for manufacturing the individual mold components. Thus an integrated
system
can be developed that can simultaneously design and generate the cutter
path plans for manufacturing the individual mold components in a mold
assembly.
Accessibility-Based Spatial Partitioning to Generate Multi-Piece
Sacrificial Molds: We have developed an algorithm based on
accessibility-driven partitioning approach to automate the design of
sacrificial multi-piece
molds. Sacrificial multi-piece molds are used for producing
geometrically
complex gelcast ceramic parts. The algorithm presented in this paper
analyzes
the accessibility of the gross mold shape and partitions it using
accessibility information. Each partitioning step improves
accessibility of decomposed
mold pieces. By performing successive decomposition, this algorithm
finally
produces a set of mold components that are accessible and therefore can
be
manufactured using milling and drilling operations. We have developed a
hybrid
approach to finding feasible partitioning planes for solving the
accessibility
problems on the gross mold shape. We first generate and evaluate a set
of
a finite number of partitioning planes using enumerative method. Then
we
improve the quality of the set by locating addition feasible
partitioning
planes in the vicinity of near-miss planes in the set through
analytical
method. Finally we determine the near-optimal set of partitioning
planes
using set-covering techniques. We have tested this approach on the
automated
mold design for several geometrically complex parts. 1 to 3-cut
solutions
were generated for the molds of these parts. Our accessibility-based
decomposition
presents an improvement over previous approaches in the following
aspects:
- It uses global accessibility information and therefore can find
solutions that cannot be found by using local information such as
undercuts and curvature. Use of local information usually results in
local optima. The spatial partitioning approach is capable of locating
partitioning planes using analytical formulations in the vicinity of
promising regions and therefore it can construct more
complete search space compared to previous approaches that use
heuristic
techniques.
- It uses hybrid problem solving strategy. It first tries to find
an optimal solution. If an optimal solution with the user-specified
characteristics does not exist, then it uses state-space search to find
the best possible solution in the given amount of computation time.
Algorithm for Generating Multi-Piece Permanent Molds: We
have developed a multi-piece mold design algorithm to automate several
important mold-design steps: finding parting directions, locating
parting lines, creating parting surfaces, and constructing mold pieces.
This algorithm constructs mold pieces based on global accessibility
analysis results of the part and therefore guarantees the disassembly
of the mold pieces. We have also developed a software system, which has
been successfully tested on several complex industrial
parts. Our approach is a significant improvement over the previous
approaches
with respect to the following characteristics:
- The previous mold splitting algorithms were either limited to
two-piece molds or planar parting surfaces. A disassembly-based
algorithm was developed that guarantees the disassembly of the mold
assembly. The algorithm can
create parting surfaces for non-planar parting lines also.
- The previous algorithms found parting directions using a local
approach. Our algorithm locates the parting direction of a face is in
the global accessibility cone of the face. Global accessibility is
important because it ensures that the mold can be disassembled. This
fact also enables the design of multi-piece multi-cavity molds. Also,
in contrast to the Z-buffer approach that gives approximate solution in
the image space, our algorithm determines exact accessibility in the
object space. It is also capable of robustly handling near-vertical
faces by compensating for the surface tolerance of the part.
- In contrast to approaches that sample parting directions, our
algorithm performs global accessibility analysis of the part to find
the candidate
parting directions. This ensures that the candidate parting direction
set
is complete.
- For efficient implementation of the algorithm, conditions based
on polyhedral part properties were developed to prune unnecessary
obstruction tests. Our algorithm successfully designed valid
multi-piece molds for representative parts from industry within 5
minutes.
- A hybrid approach combining breadth-first and depth-first search
was developed to find a near-optimal solution within a user-specified
time
limit. Our algorithm, within a reasonable time, always returns an
optimal
solution when the numbers of sets in the solution is small (2-4). On
more
complex parts it is capable of finding feasible solution; however,
optimality
cannot be guaranteed in such cases.
Limited volume production is increasingly becoming a common
industrial
practice in the era of mass customization. Prototyping is also almost
always
done to eliminate errors in a design before finalizing it. Since molds
are
constantly changed in prototyping and limited volume production, it is
required
that the tooling cost is low. Since multi-piece molds can be produced
cheaply, this technology is an ideal candidate for limited volume
production and prototyping. By making polyurethane prototypes using
urethane molds, the costs can be further
brought down. Some rapid prototyping technologies would cost
approximately ten times the cost of urethane-molded parts. Multi-piece
molds are also capable of producing very complex parts. Some parts that
cannot be produced by traditional molds can easily be produced by
multi-piece molds. Space puzzle molding is a popular multi-piece
molding technology, which has been successfully used for the last 10
years to produce quality parts. It can produce very complex parts and
the tooling cost is also significantly less than that of conventional
molds.
Related Publications
The following papers provide more details on the above-described
results.
- S. Dhaliwal, S.K. Gupta, J. Huang, and M. Kumar. A feature based
approach to automated design of multi-piece sacrificial molds. Journal
of Computing and Information Science in Engineering, 1(3):225-234,
September 2001.
- J. Huang, S. K. Gupta, and K. Stoppel. Generating sacrificial
multi-piece molds using accessibility driven spatial partitioning. Computer
Aided
Design, 35(13):1147-1160, 2003.
- S. Dhaliwal, S.K. Gupta, J. Huang, and A. Priyadarshi.
Algorithms for computing global accessibility cones. Journal of
Computing and Information Science In Engineering, 3(3):200-209,
September 2003.
- A.K. Priyadarshi and S.K. Gupta. Geometric algorithms for
automated design of multi-piece permanent molds. Computer Aided
Design, 36(3):241-260, 2004.
- A.G. Banerjee and S.K. Gupta. Geometric algorithms for automated
design of side actions in injection molding of complex parts. Computer Aided Design,
39(10):882-897, 2007.
Some of these papers are available at the publications
section of the website.
Contact
For additional information and to obtain copies of the above papers
please contact:
Dr. Satyandra K. Gupta
Department of Mechanical Engineering and Institute for Systems Research
University of Maryland
College Park, Md-20742
Phone: 301-405-5306
FAX: 301-314-9477
WWW: http://www.glue.umd.edu/~skgupta/