Elsevier

Computer-Aided Design

Volume 63, June 2015, Pages 1-11
Computer-Aided Design

Spiral and conformal cooling in plastic injection molding

https://doi.org/10.1016/j.cad.2014.11.012Get rights and content

Highlights

  • Spiral conformal cooling channels with high speed coolants.

  • An efficient algorithm to generate smooth spiral curves on free-form surfaces.

  • Spiral curves are governed by an approximated boundary-distance-map (BDM).

  • Region decomposition for covering by contours of BDM.

Abstract

Designing cooling channels for the thermoplastic injection process is a very important step in mold design. A conformal cooling channel can significantly improve the efficiency and the quality of production in plastic injection molding. This paper introduces an approach to generate spiral channels for conformal cooling. The cooling channels designed by our algorithms has very simple connectivity and can achieve effective conformal cooling for the models with complex shapes. The axial curves of cooling channels are constructed on a free-form surface conformal to the mold surface. With the help of boundary-distance maps, algorithms are investigated to generate evenly distributed spiral curves on the surface. The cooling channels derived from these spiral curves are conformal to the plastic part and introduce nearly no reduction at the rate of coolant flow. Therefore, the channels are able to achieve uniform mold cooling. Moreover, by having simple connectivity, these spiral channels can be fabricated by copper duct bending instead of expensive selective laser sintering.

Introduction

As a common manufacturing process, plastic injection molding has been widely used to fabricate a variety of products. During a plastic injection molding cycle, the plastic part and the mold must be cooled to room temperature so that the molded part can be solidified and with its shape maintained. A substantial portion of the total molding cycle (e.g., as much as 80%) could be required for cooling. To improve the efficiency, cooling channels are usually integrated into the mold. In general, conventional cooling channels in simple shapes are fabricated by drilling straight-line holes. These usually lead to non-uniform mold cooling (Ref.  [1]). Without attaining the uniformity of surface temperature in a mold, the quality of plastic parts must be impaired by undesired defects, such as part warpage, sink mark, and differential shrinkage. In addition, non-uniform cooling also increases the cooling time. In earlier studies  [2], [3], effective cooling by using the conformal cooling system has been proved on parts with relative simple shapes. However, these approaches cannot be used for the products with free-form shapes, even after applying a feature-decomposition technique as proposed in  [4].

The work presented in this paper is motivated by automating the design process of conformal cooling channels for products with free-form shapes. Recently, we presented an approach in  [5] to automatically generate circuit-like conformal cooling channels. The approach starts from offsetting the mold surface into a working surface, upon which a centroidal Voronoi diagram is used to help generate the cooling circuits. However, as the connectivity of a cooling circuit generated by  [5] is complicated, the flow rate of coolant and also the temperature in the channels are highly non-uniform. Pumping expenses will thus have to be drastically increased to improve the efficiency of heat transfer and assure uniform coolant temperature. Furthermore, the fabrication of such cooling system with complex connectivity must be conducted by the additive manufacturing technique such as selective laser sintering (SLS), which is very expensive. Our new approach proposed in this paper aims at solving these problems by designing spiral cooling channels.

A number of factors must be considered while designing cooling systems for plastic injection molding, such as layout and connections of channels, composition of coolant, and pressure drop of coolant and runner system. In this work, we focus on the 3D shapes of conformal cooling channels. Specifically, we investigate algorithms to generate spiral conformal cooling channels so that heat transfer in the cooling system is optimized and fabrication costs are reduced. Similar to our prior work in  [5], the axes of cooling channels are given on the working surface that is an offset of mold surface. Therefore, the shape of cooling channels is assured to be conformal to the mold surface. Uniform conformal cooling can be achieved as long as the temperature difference of the coolant between the inlet and the exit is small enough to be neglected. The efficiency of heat transfer is much higher in convention than conduction, and increases dramatically in turbulent flow. In particular, we focus on how to develop smooth spiral channels on the working surface conformal to the mold surface so that the turbulent flow is guaranteed.

Our design methodology of spiral and conformal cooling channels can be illustrated by Fig. 1. Given a cell-phone model to be fabricated by plastic injection molding (see Fig. 1(a)), offset surfaces are firstly constructed around it. The conformal cooling is accomplished by generating cooling channels on the offset surfaces. Part of the model’s offset surface falling in the upper mold is used as the working surface for generating cooling channels for the upper mold (see Fig. 1(b)). Taking this upper mold as an example, an enhanced Dijkstra algorithm is applied on the working surface to construct a piecewise linear approximation of the boundary-distance map (BDM) and its consequent iso-contours. Fig. 1(c) shows the color map of its BDM and the iso-contours in black curves. The iso-contours are all in a simple topology (i.e., forming only one loop at a fixed iso-value). Our idea is to transform this set of iso-contours into a spiral curve with approximately even spacing (as shown in Fig. 1(d)), in order to achieve uniform cooling. Finally, the spiral curves are served as axes to generate channels by sweeping a sphere along the curves (see Fig. 1(e)).

However, the contours of BDM on the working surface of the lower mold are in more complex topology—see Fig. 1(f), where some iso-contours have multiple loops. This brings in difficulty to generate a single spiral curve covering the whole working surface. To solve the problem, we develop an algorithm in this paper to first decompose the working surface into regions, such that each region is governed by a single spiral curve with nearly uniform space—see Fig. 1(g) for an example. As a result, three spiral channels are generated on the working surface in the lower mold (see Fig. 1(h)). In our approach, all the algorithms and computation are taken on the free-form surfaces represented by triangular meshes as shown in the middle of Fig. 1.

Designing and analyzing the conformal cooling channels for injection molding have been studied for many years (e.g.,  [1], [2], [3], [4], [5], [6], [7], [8], [9]). The systems developed in  [1], [2] involve a mathematical statement of the conformal cooling condition. Based on the criterion defined in  [2], we developed a method to approximate the typical dimensions of cooling channels in our prior work  [5]. This method will also be used to determine the dimensions of cooling channels in this paper. Many designers adopt the strategy introduced in  [4] to design the final cooling system by synthesizing the sub-systems defined on each of the recognized features of plastic parts. However, as the feature decomposition in general is a hard problem, this strategy is difficult to be realized on molds with freeform surfaces. Alternatively, Park and Pham  [3] proposes to decompose the regions according to the temperature distribution after the filling stage in molding simulation. Nevertheless, the computation of this approach may converge slowly on models with freeform shapes. Our region decomposition method presented in this paper is purely based on the geometric information—BDM, which can be computed efficiently. A recent effort to automate the design of cooling system is made in  [9]. However, the channels in their work are designed in the zigzag shape, which can significantly reduce the flow rate of coolants.

In our work, all the channel axes are created on the offset surface surrounding the given model. This offset surface is assigned as the working surface. The grown offset surface of a solid model can be computed according to the mathematical definition given in  [10]. Although the mathematical definition is compact, offsetting a freeform surface is not an easy job. We adopt the narrow-band signed distance-field (Refs.  [11], [12]) to generate the intersection-free offset surface for our cooling channels. Note that, the working surface must be intersection-free to prevent ill-topology on the axial curves of channels.

In the thread of research in CNC machining, spiral tool-path has been paid a lot of attention in the past (Refs.  [13], [14], [15], [16]). Bieterman and Sandstrom  [13] presented a method to use the solution of an elliptic partial differential equation (PDE) to morph a point (called center point) to the boundary of the shape. The spiral curves can only be generated on star-shaped polygons. In the work of Yao and Joneja  [14], deformed Archimedean spirals are placed on the medial axis, and a few contour parallel offset curves are added near the boundary to connect all elements to a single tool path. To solve the problem of self-intersection and the generalization of shape to be processed, Held and Spielberger  [15] investigated a method to generate spiral tool-path with the help of medial axis of a 2D polygon. None of these approaches consider the problem of generating spiral curves on free-form surfaces. Recently, a method is presented in  [16] to generate iso-parametric tool-paths on surfaces represented by point clouds. However, only direction parallel tool-paths and contour parallel tool-paths are considered. In summary, an approach involving region decomposition for generating nearly-equidistant spiral curves on free-form surfaces remains an open problem.

Our work has the following technical contributions.

  • An efficient algorithm is developed to generate smooth spiral curves on free-form surfaces, where the spiral curves are governed by an approximated boundary-distance map (BDM) and have approximately uniform spacing.

  • By analyzing BDM, a decomposition algorithm is investigated to segment free-form surfaces into regions that can be covered by contours of BDM with simple topology.

By incorporating the above two algorithms, a new design pipeline is investigated to generate spiral cooling channels for products with free-form shapes. Functionality of this approach will be demonstrated by experimental results and case studies.

Our paper is organized as follows. After introducing some preliminary terms in Section  2, Section  3 presents how to transform iso-contours of BDM into spiral cooling axes with even space. Section  4 describes BDM-based surface decomposition algorithm. Experimental results and case studies are shown in Section  5. Finally, the paper ends with the conclusion section.

Section snippets

Physical model

This section briefly describes a method to use the thermal dynamic model to determine the geometric parameters of conformal cooling channels. More details about this physical model can be found in our prior work  [5].

Considering a local cooling region in a cross-section of two adjacent cooling channels (as illustrated in Fig. 2), a simplified formula for evaluating the temperature difference of mold surface at points A and B can be derived as TmB¯TmA¯=ρpcplptcycleKm[(TmeltTeB)lB(TmeltTeA)lA]

BDM-based spiral channel generation

In this section, we present how to generate spiral curves from the iso-contours of BDM with equal distance—i.e., W for the generation of conformal cooling channels. The topology of surface region we are working on is assumed to be ω-simple.

Definition 5

For the BDM of a surface M, if all iso-contours generated by the stepwise threshold iω (iZ) have only one loop, the topology of surface M is named as ω-simple in terms of BDM.

BDM-based decomposition

Iso-contours of the BDM are generated on the working surface, M, to analyze whether M can be covered an intersection-free spiral curve with nearly even distances—the distance between neighboring spirals is expected to be a constant. If this cannot be satisfied, M must be decomposed into smaller regions to be covered by spiral curves. This section presents the methods for (1) analyzing iso-contours and (2) decomposing M by the topology information of iso-contours.

Results and discussion

The algorithms presented in this paper are implemented as a program in C++. The spiral curves can be generated efficiently on models represented by two-manifold triangular meshes. For example, spiral curves can be generated for the models shown in Fig. 9 with 31k triangles (the head model) and 53k triangles (the helmet model) in 344 ms and 314 ms respectively on a PC with Intel Core 2 Quad CPU Q6600 2.4 GHz. Moreover, the BDM-based decomposition can also be computed efficiently. The spiral

Conclusion

We present an approach in this paper to generate spiral and conformal cooling channels for plastic injection molding of parts with high-curved surfaces. This approach shows advantages in two aspects:

  • First, the cooling channels are generated on a working surface that is offset from the cavity surface of a mold. As a result, conformal cooling can be obtained. This is a characteristic that holds for our prior work on conformal cooling circuits  [5] but not for the conventional cooling channels 

Acknowledgments

The authors would like to thank the staff of the Digital Factory at the Hong Kong Polytechnic University for their technical support. The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong SAR, China (Project No.: PolyU 5368/09E).

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