Institute for Systems Research

In multi-stage molding process, the desired multi-material object is produced by carrying out multiple molding operations in a sequence, adding one material in the target object in each mold-stage.

We model multi-material objects as an assembly of single-material components. Each mold-stage can only add one type of material. Therefore, we need a sequence of mold-stages such that (1) each mold-stage only adds one single-material component either fully or partially, and (2) the molding sequence completely produces the desired object.

In order to find a feasible mold-stage sequence, our algorithm decomposes the multi-material object into a number of homogeneous components to find a feasible sequence of homogeneous components that can be added in sequence to produce the desired multi-material object.

Our algorithm starts with the final object assembly and considers removing one component either completely or partially from the object one-at-a-time such that it results in the previous state of the object assembly. If the component can be removed from the target object leaving the previous state of the object assembly a connected solid then we consider such decomposition a valid step in the stage sequence. This step is recursively repeated on new states of the object assembly, until the object assembly reaches a state where it only consists of one component.

When an object-decomposition has been found that leads to a feasible stage sequence, the gross mold for each stage is computed and decomposed into two or more pieces to facilitate the molding operation. We expect that our algorithm will provide the necessary foundations for automating the design of multi-stage molds and therefore will help in significantly reducing the mold design lead-time for multi-stage molds.

In this paper, we propose the idea of process planning for small batch manufacturing, i.e., we simultaneously consider multiple parts and exploit opportunities for sharing manufacturing resources such that the process plan will be optimized over the entire set of parts. In particular, we discuss a geometric algorithm for multiple part cutter selection in 2-1/2D milling operations.

We define the 2-1/2D milling operations as covering the target region without intersecting with the obstruction region. This definition allows us to handle the open edge problem. Based on this definition, we first discuss the lower and upper bond of cutter sizes that are feasible for given parts. Then we introduce the geometric algorithm to find the coverable area for a given cutter. Following that, we discuss the approach of considering cutter loading time and changing time in multiple cutter selection for multiple parts. We represent the cutter selection problem as shortest path problem and use Dijkstra's algorithm to solve it. By using this algorithm, a set of cutters is selected to achieve the optimum machining cost for multiple parts.

Our research illustrates the multiple parts process planning approach that is suitable for small batch manufacturing. At the same time, the algorithm given in this paper clarifies the 2-1/2D milling problem and can also help in cutter path planning problem.

In this paper, we give a geometric algorithm to find the optimal cutters for 2-1/2D milling operations. We define the 2-1/2D milling operations as covering the target region without intersecting with the obstruction region. This definition allows us to handle the open edge problem. Based on this definition, we introduced the offsetting and inverse-offsetting algorithm to find the coverable area for a given cutter. Following that, we represent the cutter selection problem as shortest path problem and discuss the lower and upper bond of cutter sizes that are feasible for given parts. The Dijkstra's algorithm is used to solve the problem and thus a set of cutters is selected in order to achieve the optimum machining cost.

We believe the selection of optimum cutter combination can not only save manufacturing time but also help automatic process planning.

1. We give a general definition of the problem as the task of covering a target region without interfering with anobstruction region. This definition encompasses the task of milling a general 2-D profile that includes bothopen and closed edges.

2. We discuss three alternative definitions of what it means for a cutter to be feasible, and explain which of thesedefinitions is most appropriate for the above problem.

3. We present a geometric algorithm for finding the maximal cutter for 2-D milling operations, and we show thatour algorithm is correct.

Our methodology has the following three benefits over the state-of-the-art. First, by using multi-piece molds we can create complex 3D objects that are impossible to create using traditional two piece molds. Second, we make use of sacrificial molds. Therefore, using multi-piece sacrificial molds, we can create parts that pose disassembly problems for permanent molds. Third, mold design steps are significantly automated in our methodology. Therefore, we can create the functional part from the CAD model of the part in a matter of hours and so our approach can be used in small batch manufacturing environments.

The basic idea behind our mold design algorithm is as follows. We first form the desired gross mold shape based on the feature-based description of the part geometry. If the desired gross mold shape is not manufacturable as a single piece, we decompose the gross mold shape into simpler shapes to make sure that each component is manufacturable using CNC machining. During the decomposition step, we account for tool accessibility to make sure that (1) each component is manufacturable, and (2) components can be assembled together to form the gross mold shape. Finally, we add assembly features to mold component shapes to facilitate easy assembly of mold components and eliminate unnecessary degree of freedoms from the final mold assembly.