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
Viterbi School of Engineering
University of Southern California
Los Angeles, California 90089-1453
Phone: 213-740-0491
Email: guptask [AT] usc [DOT] edu