Generative design of conformal cooling channels for hybrid-manufactured injection moulding tools

Abstract

Effective cooling systems for injection moulding (IM) tools are critical to reducing manufacturing costs and cycle time for the polymer parts produced. This work presents a novel automated methodology for designing conformal cooling channels (CCCs) for IM tools via interlinking commercial moulding simulation tools with custom scripts. These scripts adjust CCC design in response to the spatial variability in global and local temperatures at the mould tool-part interface (MTPI) via generative design (GD). Four tool designs for manufacturing a simplified part were analysed numerically simulation and experimentally, including tools with either straight-drilled (non-conformal) cooling channels (tool steel), a manually designed CCC system (stainless steel or bronze alloy), or an automatically designed CCC system (stainless steel). While both manually designed CCC tools cool the part faster than the non-conformal tool (3–5% predicted vs. 40% measured for stainless steel and 9–12% predicted vs. 40% measured for bronze alloy), the GD-optimised CCC tool outperformed both (15–30% predicted faster cooling vs. 70% measured). The predicted MTPI temperature feature achieves reductions to both maximum and spatial variability in MTPI temperatures, which lead directly to significant reductions in manufacturing cycle time and polymer part warpage. These findings could have a major impact on the IM industry by reducing tool design costs and raw material waste via improving moulded part quality.

1 Introduction

1.1 Cooling channels for injection moulding tools—design and manufacture methods

The effectiveness of an injection moulding (IM) tool cooling system is critical to the cost and productivity of the moulding process, as cooling time typically dominates the moulding cycle’s duration [1]. Additionally, spatially uniform cooling, i.e. minimised $\Delta T$ across the mould tool-part interface (MTPI), is critical to moulded part quality as nonuniformity promotes thermal stresses that drive distortion (‘warpage’) [1]. Additively manufactured (AM) conformal cooling channels (CCCs) are considered the leading approach to improving mould cooling. However, their design is often conducted manually [2], which is challenging, time consuming, and prone to producing suboptimal designs, as it requires simultaneously satisfying numerous complex moulding and manufacturing process objectives and constraints. This research aims to automate the CCC design process using a custom generative design (GD) methodology that reduces design time, the likelihood of producing a suboptimal design, and manufacturing complexity.

The generative design (GD) process iteratively creates numerous design variants within user-defined design constraints and quality metrics [3]. These are shortlisted by either designers (‘artificial selection’) or computer programmes following some evaluation scheme (‘natural selection’); see Fig. 1, captioned ‘Generative design process’ in a study by Jia Cui and M X [4]. The user can customise the evaluation scheme to considerably narrow the scope of its output designs, streamlining the search process. This approach was applied here by (i) predefining CCC orientations, (ii) limiting CCC diameters based on operating pressures and profile conformity, and (iii) customising results postprocessing.

Fig. 1

a IM polymer part for which moulds have been developed, along with its dimensions.  b Internal surfaces of a conventional (straight-drilled) cooling channel design developed for this study (blue), with the simplified part’s near-cylindrical design shown in light grey and the runner and gate system delivering the molten polymer shown in purple. Channel dimensions, input, and output have also been labelled. Connecting hoses (green) link the two halves of the CCs. c Initial manual CC design for the mould tool with CCCs, along with the colour-respective parts labelled. d Mould tool design for conventional CC design—cavity (L) and core (R) moulds, with the external dimensions and surfaces being constant across all tools in the study.

Typically, cooling channels (CCs) are designed manually resulting in nonconformal cooling channels, most likely straight CCs associated with the manufacturing limits of the conventional machining methods used to create them (i.e. drilling [5]). This is unlikely to yield optimal cooling performance for complex mould tool and part designs. Conformal cooling channel (CCC) designs, whether developed manually or semi-autonomously, require (i) detection and rectification of interference between channels and mould tool features, (ii) estimation of spatiotemporally varying heat flux and/or temperature distributions across the MTPI, and (iii) final alterations to CCC routing within the constraints imposed by the mould tool’s manufacturing method. AM greatly improves IM design flexibility by enabling CCCs that follow the moulded part surface, thereby extracting heat evenly from the cooling part (reducing $\Delta T$ variation at the MTPI) [6]. AM thus increases the need for semi-autonomous design techniques such as GD to alleviate complex and repetitive manual design work by the toolmaker [1].

Numerous approaches have been presented to identify optimal CC and CCC designs for IM tools. Tang et al. [1] simultaneously optimise the channel diameter, location (of the channel axis within a 2D plane), and coolant flow rate. However, this approach focused on straight CC designs to permit machining via drilling, and is thus limited to simpler part geometries and cooling needs. Lam et al. [7]’s design method is based on an evolutionary algorithm that optimises CC design (channel diameter, offset distance, etc.) and IM process parameters (fill and pack pressures, times, etc.). However, defining design parameters based on the MTPI temperature variation is not possible, complicating minimisation of ΔT and moulding cycle time. Xu et al. [8]’s similar design methodology is suitable for CCCs (i.e. AM) but seems no longer publicly available. Finally, both Tang et al.’s and Xu et al.’s results are limited to static coolant temperatures and feature no selection process for initial CC and CCC design parameter values.

Saifullah et al. [9]’s design method places CCCs near the MTPI to increase heat transfer and minimise moulding cycle time, but is not automated. Luh et al. [6]’s automated method analyses temperature hotspots to refine positioning of non-equidistant CCCs with a uniform cross-section. However, temperature distributions are obtained from just one viewpoint, thus limiting efficacy for tool designs with high aspect ratios in the viewing direction.

Li [10]’s feature-based approach (i) decomposes a complex moulded part into simpler shape elements, and (ii) algorithmically generates CCCs by combining a predefined template generated for each shape element into a single CCC system. This initially works well for complex part geometries, but is not responsive to part-specific hotspots/coldspots. Torres-Alba et al. [11]’s similar method is based on a discrete multidimensional model of the moulded part. This suitably shortlists channel parameters (diameter, offset distance, pitch distance, etc.) via evolutionary algorithms based on the melt front temperature profile. However, it is limited by the sole use of melt front temperature (averaged into temperature clusters) to drive design development, i.e. temperature distributions at other locations in the mould cavity and at times after the mould filling stage are not considered. It does not, therefore, account for the dynamics of, e.g. coolant temperature and MTPI hotspots varying with the cooling system (i.e. changing the CCs is response to hotspots from each new design iteration until convergence). This issue is common to most methods described above.

Beyond performance-related CCC design challenges (described above) are manufacturing challenges. Tuteski and Kočov [12] review AM processes suitable for IM tool manufacture (e.g. powder bed fusion and direct metal deposition) and guidelines for designing CCCs for AM. These guidelines address (i) minimisation of cooling system stagnation points and plug stops to reduce debris accumulation and blockage, (ii) positioning CCCs to reduce cooling time and $\Delta T$ at the MTPI, and (iii) ensuring part solidity around the tool’s ejector pins prior to moulded part ejection (to reduce ejector pin marks and warpage). This was achieved using a ‘zigzag’ CCC layout with nonuniform channel offsets (to address (i) and (ii)) and using freezing time near the ejector pins as the estimate of cooling time (to address (iii).

1.2 Challenges in the design and manufacture of conformal cooling channels

Design requirements for CCC tools, in addition to reducing cooling time and $\Delta T$ at the MTPI, include mechanical and manufacturing aspects—(i) ensuring the in-service mechanical integrity of the tool; (ii) satisfying manufacturing constraints imposed by the tool’s manufacturing method—and coolant-related aspects; (iii) accommodating axial coolant temperature variation in the design process (to promote uniform heat flux); and (iv) complying with coolant supply constraints (e.g. maximum pressure drop possible from coolant pump); see Fig. 9, captioned ‘A conformal cooling design window defined by the cooling channel diameter and the cooling line length’ in the study conducted by Xu et. al [8].

Regarding manufacturing constraints, laser powder bed fusion is common in manufacturing IM tools with CCCs [13] due to its high resolution [14], with multi-material mould inserts being studied [15]. Directed energy deposition (DED), while offering higher deposition rates, has historically been less preferred for CCCs due to its lower resolution [14, 16], i.e. the cooling inserts themselves are still manufactured using laser-powder bed fusion [17]. In this study, DED’s capability at manufacturing conformal tools is further developed. Manufacturing constraints for DED further include an upper bound to the maximum manufacturable unsupported overhang angle, ranging from 63 [18] to 30° relative to the horizontal build substrate as reported by Nassar et al. [19]. Note that a similar overhang requirement exists for laser-powder bed fusion manufacturing; however, it can accommodate larger overhangs, typically 30–45° [20]. This permits smaller channels (microchannels with diameters of 500 μm) with multiple channel profiles [21]. A lower bound still arises though regarding accessibility for removal of excess powder from complex internal channels [20].

Regarding in-service mechanical integrity, while minimising cooling channel spacing and depth reduces cooling time, a lower bound exists below which thermal and mechanical stress concentrations risk compromising tool integrity [20]. Recommended minimum tool wall thicknesses are $1\times d$ for steel, $1.5\times d$ for beryllium, and $2\times d$ for aluminium (Al), where $d$ is the CC’s diameter [22]. Regarding points (iii) and (iv), constraints due to coolant supply (i.e. pressure drops) and axial coolant temperature variation, the authors have found no studies in the literature discussing these extensively, and so these topics are studied in the current research and are accounted for in the current research outcomes.

1.3 Details of the current study

This study details a design methodology for IM tools with CCCs with the following novel aspects:

• Novelty I: Optimisation of mean CCC parameters such as channel diameter and offset distance from the MTPI using an evolutionary algorithm that includes their orientation with respect to the moulded part (to improved cooling efficacy and reduce coolant pressure drop).

• Novelty II: Automated processing of MTPI and coolant temperature distributions after each design iteration to continuously improve CCC positioning during CCC optimisation. Note that iteration progression employed the linear golden section search method (‘golden search’).

• Novelty III: Consideration of numerous tool manufacturing and operating constraints, i.e. unsupportable channel overhang angle for DED manufacturing, channel dimensions deliverable by DED, avoidance of interference between CCCs and the MTPI, and maximum deliverable coolant pressure.

As described in Sections 1.1–1.2, a single software tool that simultaneously optimises IM tool CCC design while still complying with the less-addressed design aspects (i–iv) described in Section 1.2 is currently unavailable (to the authors’ knowledge). Previous attempts at GD approaches fall short of capturing (or iteratively responding to) the temperature distribution in the cooling polymer [11]. However, this limitation may be addressed using custom scripts that combine the capabilities of disparate software tools each expert at particular aspects of the overall IM tool design problem. This approach is pursued here and employs three input datasets: (i) IM process parameters; (ii) material data for the mould tool, cooling fluid, and moulded material; and (iii) numerous constraints imposed by an IM tool’s design and manufacture. As expounded by Section 2, this novel approach sequentially performs the following:

• (i) development of an initial manual design for the IM tool’s CCCs, which incorporates high-level constraints on channel dimensions, tool size, and manufacturing method;

• (ii) multiphysics simulation of IM to predict part cooling time (defined here as time to reach ejection temperature) and surface temperature distribution at the MTPI;

• (iii) optimisation of the position of the (initially) manually designed CCCs to reduce both the mean temperature gradient along the MTPI across the two halves of the mould cavity (for reduced warpage) and the cooling time (novelty II described in Section 1.3).

In this study, steps (ii) and (iii) are automated, which are key novel advantages that significantly reduce design labour. These are achieved via a combination of multiphysics finite element analysis (FEA) and custom scripts that conduct computer-aided design (CAD) geometry preprocessing, postprocessing of results, and subsequent CAD model refinement. Experimental validation is conducted with CCC-equipped IM tools manufactured using a modern DED AM printer (Sections 2.1 and 2.5), thus testing its potential for rapid tooling manufacturing. Note that simulation validation studies applied to algorithmically generated IM tool designs equipped with CCCs have previously been reported, but never for DED. Finally, results from the CCC-equipped, GD-optimised, and AM-built IM tools built here are presented in Sections 3.2–3.5 and 3.8 and compared against a reference (manually designed and conventionally manufactured) IM tool design.

2 Materials and methodology

2.1 Initial design of moulding tool

For the current study, a simplified design of a moulded part was adopted to ease the physical interpretation of results. This test part is a thin-walled cylinder with 50 mm height, 60 mm base diameter, and 1° inward angle of the cylindrical wall towards its axis, i.e. a conical frustum, as seen in Fig. 1(a). The part is designed to be manufactured using polypropylene (Bormed 840, supplied by APN Plastics Pty Ltd, Melbourne, Australia) with physical properties tabulated in Appendix B4 (Table 13).

A conventionally cooled mould tool design is presented in Fig. 1(b) as an example of relevant IM tool designs manufacturable via conventional machining (drilling). The tool cooling system comprises a baffle and straight cooling channels. This simplified part geometry allows straight-drilled CCs to be placed close to the part’s surface, allowing for increased heat flux and thus faster cooling. Therefore, this design represents a ‘best-achievable’ conventional design to compare with the CCC designs developed later in this study. Both the straight-channel and CCC mould tool designs assume either tool steel (P20) for the conventional mould tool or stainless steel 316L (‘SS316L’) for the AM tools, with their properties provided in Appendices B1 and B2 (see material properties in Tables 10 and 11), respectively.

The initial design for the CCC mould tool was developed manually (as explained in Section 1.3) following two objectives: (i) prioritising the minimal distance between the coolant fluid (all results described in this study employed chlorinated water) and the MTPI, i.e. this purely geometric criterion was followed without the aid of multiphysics simulation, and (ii) suitability for additive manufacturing. These two objectives resulted in the unoptimised CCC design presented in Fig. 1(c). This was hybrid manufactured, with both additive and subtractive manufacturing (machining) stages occurring within the same 3D printer, using a five-axis Lasertec 65 3D hybrid printer (DMG Mori Co. Ltd, Pfronten, Germany), with an 1800-W laser, scanning speed of 1000 mm/min, powder feed rate of 12 g/min, argon gas flow of 5 L/min, layer height of 0.9 mm, and stepover width of 1.6 mm, with SS316L powder of size 45–106 μm (Höganäs, Sweden) used for deposition. Figure 1(d) illustrates the outer surfaces of the mould tool shown in Fig. 1 (b) and (c).

The major shortcoming to manually designing CCC mould tools such as Fig. 1(c), and thus the need for the current study, is the risk of spatially inhomogeneous removal of heat due to suboptimal channel placement or local stagnation of cooling fluid, resulting in hotspots within the cooling part. Over long timescales, stagnation may also cause secondary operating issues such as localised corrosion, causing weakening of the channel wall, and collection of corrosion products that further slow/block channel flow; this is discussed further in Section 3.9. Hotspots and coldspots can be reduced by using mould tool metals with higher thermal conductivity. For example, copper–aluminium bronze inserts with the initial conformal channel design (see Fig. 1(c)) were manufactured for this study using the hybrid printer described earlier from ‘Cu–Al bronze’ (Cu9.3Al1.3Fe weight percentages; henceforth abbreviated to ‘CuAl bronze’; see material properties in Appendix B3, Table 12) powder of size 45–125 μm (Metals for Printing (M4P), Magdeburg, Germany). However, the use of copper alloys in IM tooling may introduce compromises such as lower tool durability due to reduced strength and hardness, difficulties with laser processing, and increased costs.

2.2 Basic heat transfer analysis of injection moulding

To establish a baseline model, it is essential to analytically estimate channel parameters, ensuring thermodynamically optimal heat transfer (novelty I described at start of Section 1.3). Heat transfer during IM is described in detail by Xu et al. [8]. The energy required for extraction from the moulded material (i.e. moulding) during a single manufacturing cycle is that required to bring the part’s temperature from molten to that suitable for ejection, i.e. when a sufficient proportion of the material has solidified, the part’s rigidity can sustain ejection without appreciable warpage. The mould temperature (${T}_{{\text{mould}}}$) at the moulding ejection temperature (${T}_{{\text{eject}}}$) can be estimated from Eq. 2.1, which was derived by Turng and later numerically verified [23, 24].

$${T}_{{\text{mould}}}={T}_{\mathrm{ c}}+\frac{{\rho }_{{\text{p}}}{c}_{{\text{p}},{\text{p}}}h\left(2{K}_{{\text{m}}}W+H\pi D{l}_{{\text{m}}}\right)\left({T}_{{\text{melt}}}-{T}_{{\text{eject}}}\right)}{2H\pi D{K}_{{\text{m}}}{t}_{{\text{c}}}}$$

(2.1)

In Eq. 2.1, ${T}_{{\text{c}}}$ denotes the CC’s local coolant temperature and ${T}_{{\text{melt}}}$ denotes the polymer melt temperature. The polymer’s properties include ${\rho }_{{\text{p}}}$ (local density) and ${c}_{{\text{p}},{\text{p}}}$ (local specific heat capacity at constant pressure). The part’s properties include $h$ as the half-thickness of the polymer in the part, i.e. the maximum barrier through which conductive heat transfer occurs from the polymer to the MTPI. The mould tool’s properties include ${K}_{{\text{m}}}$ as the mould tool metal’s thermal conductivity. The CC properties include $D$ for the channels’ local hydraulic diameter, $W$ for the pitch distance between channels, and ${l}_{{\text{m}}}$ for the local offset distance between the CC’s surface and the MTPI. Finally, the coolant fluid’s properties include $H$ for the convective heat transfer coefficient between the laminarly flowing coolant near the CC surfaces and the turbulently well-mixed coolant occupying the CC bulk.

Alongside Eq. 2.1, Turng presents the cooling time (${t}_{{\text{c}}}$) at which ${T}_{{\text{eject}}}$ is reached; see Eq. 2.2 [23, 24].

$${t}_{{\text{c}}}=\frac{{h}^{2}}{{\alpha }_{{\text{p}}}{\pi }^{2}}{\text{ln}}\frac{8\left({T}_{{\text{melt}}}-{T}_{{\text{mould}}}\right)}{{\pi }^{2}\left({T}_{{\text{eject}}}- {T}_{{\text{mould}}}\right)}$$

(2.2)

where ${\alpha }_{{\text{p}}}=\frac{{K}_{{\text{p}}}}{{\rho }_{{\text{p}}}{c}_{{\text{p}},{\text{p}}}}$ denotes the local thermal diffusivity of the polymer and ${K}_{{\text{p}}}$ denotes the local thermal conductivity of the polymer. As expected, ${t}_{{\text{c}}}$ decreases with increasing ${\alpha }_{{\text{p}}}$, of which ${K}_{{\text{p}}}$ and ${c}_{{\text{p}},{\text{p}}}$ are likely to vary most easily to the manufacturer (via material selection for the finished part). The relationship between ${t}_{{\text{c}}}$ and ${K}_{{\text{p}}}$ is thus shown in Eq. 2.3,

$${t}_{{\text{c}}}=\frac{{h}^{2}{\rho }_{{\text{p}}}{c}_{{\text{p}},{\text{p}}}}{{K}_{{\text{p}}}{\pi }^{2}}{\text{ln}}\frac{8\left({T}_{{\text{melt}}}-{T}_{{\text{mould}}}\right)}{{\pi }^{2}\left({T}_{{\text{eject}}}- {T}_{{\text{mould}}}\right)}$$

$\therefore$ (if only ${K}_{p}$ varies)

$${t}_{{\text{c}}}\propto \frac{1}{{K}_{{\text{p}}}}$$

(2.3)

The critical overall process performance parameter ${t}_{{\text{c}}}$ thus appears to be mainly limited by the polymer’s thermal conductivity, ${T}_{{\text{melt}}}$, and ${T}_{{\text{eject}}}$, not the mould tool metal’s properties. However, mould tool metals with higher thermal conductivity affect ${t}_{{\text{c}}}$ implicitly via their reducing effect on ${T}_{{\text{mould}}}$. Equation 2.4 demonstrates that with increasing metal conductivity, the corresponding reduction in ${T}_{{\text{mould}}}$ becomes limited by polymer properties such as specific heat capacity and part half-thickness, which then become the rate-determining parameters for ${t}_{{\text{c}}}$:

$${T}_{{\text{mould}}, {\text{min}}}= \underset{{K}_{{\text{m}}}\to \infty }{{\text{lim}}}{T}_{{\text{c}}}+\frac{{\rho }_{{\text{p}}}{c}_{{\text{p}},{\text{p}}}h\left(2{K}_{{\text{m}}}W+H\pi D{l}_{{\text{m}}}\right)\left({T}_{{\text{melt}}}-{T}_{{\text{eject}}}\right)}{2H\pi D{K}_{{\text{m}}}{t}_{{\text{c}}}}$$

$$\therefore {T}_{{\text{mould}}, {\text{min}}}= {T}_{{\text{c}}}+\frac{{\rho }_{{\text{p}}}{c}_{{\text{p}},{\text{p}}}Wh\left({T}_{{\text{melt}}}-{T}_{{\text{eject}}}\right)}{H\pi D{t}_{{\text{c}}}}$$

(2.4)

Summarising the above, a low ${K}_{{\text{m}}}$ will increase ${t}_{{\text{c}}}$ per Eq. 2.2, leading to reduced cost-effectiveness of the process and possibly also increased surface temperature gradients at the MTPI that promote part warpage. However, a very high ${K}_{m}$ will not result in significant cooling time reduction in itself and needs to be coupled with a planned CCC design to impact cooling times.

2.3 Optimised tool design methodology overview

Following the initial manual CCC design process described in Section 2.1, an alternative optimised design was developed as described in Fig. 2. Ideally, this optimisation process would consider all geometric, thermomechanical, and economic aspects of the mould tool, polymer, coolant, and moulding process. In practice, channel geometry is likely the easiest to modify in a fine-scaled manner, whereas other process and material properties may be practically limited to a few discrete numerical values or qualitative choices. Thus, optimising CCC mould tool design often reduces to optimising CCC geometry. However, the end goal is unchanged, which is the minimisation of surface temperature gradients at the MTPI at the end of the cooling stage with the lowest possible cooling time. Figure 2 presents the resulting simplified workflow for the CCC geometry optimisation methodology developed here and the software implementation at each step.

Fig. 2

Workflow describing the generative design (GD) process described in this study. ΔT refers to the maximum temperature gradient across the MTPI

Step (a) in Fig. 2 describes initiation of the design optimisation process from the CAD file describing the intended geometry of the finished (moulded and ejected) part (novelty I described at start of Section 1.3). The designer specifies initial design features and input data in the form of part and mould tool CAD data, boundary conditions, tool design limits and constraints, polymer characteristics, and IM machine operational parameters. These data are variously stored in a spreadsheet, CAD model, and the injection moulding process simulation software used here ‘Moldex3D Studio 2022 R1’ (CoreTech System Co. Ltd., Zhubei City, Taiwan), and are accessed by Moldex3D Studio to simulate the IM process (Section 2.4), as well as by the CAD package Autodesk Fusion 360 (Autodesk, Inc., San Rafael, USA) to model the CCC (Section 2.4.2).

Step (b) involves developing an initial mould tool design to produce this part (novelty I described at start of Section 1.3), containing all the external surfaces such as ejector pins, inserts, injection gates, etc., and is performed manually here as several external factors (e.g., local parting planes, number of gates, etc.) that may influence the design are nontrivial to automate. This initial design includes emplacing internal mould tool divisions, i.e. virtual parting planes that subdivide the future CCCs into discrete groups of ‘circuits’, each of which lies between a neighbouring pair of mould tool divisions. For the simplified part geometry studied here, $N=1$ mould tool division was combined with $N+1$ independent CC circuits per resulting half-mould. Given the symmetry of the simplified part geometry (Fig. 1 (a)), the CCC design could be simplified to two CCC circuits, one for each half-mould and comprising single curvilinear serpentine channels.

In steps (c)–(i) in Fig. 2, the initial manual mould tool design is optimised for hybrid AM. For the serpentine CC, virtual parallel section planes spaced apart by the intended channel pitch distance were added to each mould half (Section 2.4.2), onto which the central axes of the CCs were aligned. Subsequently, in step (c), the mould tool geometry was converted to a surface mesh with cell aspect ratios near unity to aid the later computation of step (f) (novelty I described at start of Section 1.3). This mesh’s resolution has a lower bound as follows: (1) ‘control points’ are defined at the intersections of the parting surface mesh with the virtual section planes (Section 2.4.3), and (2) robust use of these control points requires their parent mesh’s cell size to be within 10%–50% of the CCCs’ mean predefined diametric range (presented in Table 2). These limit values arose as cell spacing < 10% led to prohibitive computational runtimes while cell sizes > 50% will generally increase the chances of the GD CCC designs interfering with a generic mould cavity’s web and flange feature, e.g. bosses, cut-outs, ejector pins, and fins around bends and sharp corners along the MTPI.

Following mesh creation in step (c) in Fig. 2, the GD design process then executes the genetic algorithm (GA) in step (d), setting up the initial mean CCC parameters, including the mean offset, CCC diameter, pitch distance, mean mould temperature, and analytically estimated cooling time (see Section 2.4.2) (novelty I described at start of Section 1.3). In step (e), the GD process sections the mould tool design according to the mean CCC pitch distance obtained from the GA results in step (d) (novelty I described at start of Section 1.3). Step (f) places control points in 3-D space using 1-D parameters where the surface meshes meet the section planes and then defines the initial offset values as per the GA output (novelty I described at start of Section 1.3). Step (g) generates the CAD geometry of the uniform conformal channel, as described in Section 2.4.3 (novelty I and novelty III described at start of Section 1.3).

In step (h), which represents the iterative optimisation phase of the GD process, FEA simulations of the moulding process are conducted (novelty II described at start of Section 1.3) on the polymer part using Moldex3D Studio with the process parameters detailed in Section 2.4.1. Results that are stored are stored at each control point. A conditional statement evaluates whether the MTPI temperatures are satisfactorily uniform while maintaining the minimised cooling time. The average MTPI temperature is calculated, and adjustments are made to the simulated cooling times to mathematically balance Eqs. 2.1 and 2.2. The GD process then iteratively improves upon the CCC design by modifying the offset distance of each channel at its control points (using a ‘golden search’; see Section 2.4.3) until the simulation results feature minimised MTPI surface temperature gradients (limited hot spots and cold spots) alongside minimised cooling time.

In addition to the above CCC offset optimisation, a second group of moulding process parameter optimisations are performed. This involves using an internal Moldex3D Design of Experiments (DOE) module (Section 2.4.4) to identify moulding process parameters (such as fill and pack pressures and times—see Section 2.4) until they result in an equal compromise between minimum cooling time and uniform surface temperature distribution at the MTPI at the end of the polymer filling [25]. The DOE is based on the Taguchi method [26] and is performed only during the first iteration of the pointwise offset optimisation (step (h)).

During the final postprocess (step (i)), the channel circuit designs are ‘edited’ for manufacturability as follows. Channels are first mirrored at the insert’s plane of symmetry and the CCC serpentines are merged to form full cylindrical serpentines. The two-channel circuits (inside and outside the cavity) are connected to their symmetrical counterparts via helical joints. Step (i) then ends with the designer postprocessing the optimised CCC design. This involves smoothing channel bends, connecting CCCs as mentioned earlier in this section, and checking the predicted coolant pressure drop and moulded part warpage (novelty III described at start of Section 1.3). The designer then converts the GD design model file into AM toolpaths for building the cavity-core inserts prior to assembly into the completed mould.

As illustrated in Fig. 2, the GD process developed here was implemented using a combination of pre-existing dedicated software packages and custom programming code:

• Moldex3D Studio was chosen for IM process simulation in step (h). This package performs multiphysics thermal and fluid flow simulations for a given CCC configuration and moulding process parameters. Moldex3D saves temperature distributions and coolant information (flowrate, Reynolds number, and CCC axis temperature) at the GD process’s control points defined in step (f). Moldex3D also optimises moulding manufacturing process parameters based on the DOE approach (step (h)). Moldex was selected due to being a widely used tool in industry and having extensive automation capabilities.

• Autodesk Fusion 360 (Autodesk, Inc., San Rafael, USA) is used for CAD geometry modelling of the mould tool (steps (b) and (c)) and CCC design based on control point information obtained in steps (g), (h), and (i). Similar to Moldex3D, extensive automation capabilities in its application programming interface and a large support community made Fusion 360 the ideal choice for this study.

• Python was used for exporting and analysing data from Moldex3D and Fusion using these software packages’ APIs. This programming language was chosen due to the compactness and legibility of the resulting code.

After creating an optimised CCC mould tool design, which involves going through steps (a)–(i) of Fig. 2 (inclusive), if its moulding simulation predicts high coolant pressure drop through the channels and/or moulded part warpage beyond user-specified limits, manual adjustments are made to the CCC design parameter’s allowable ranges as used by the GA in step (d). These, e.g. could increase the minimum allowable CCC diameter (to reduce head loss) or the minimum offset limit (to reduce warpage). The GD algorithm is then rerun from step (d) onwards as illustrated in Fig. 3. Future work will involve determining the direct influence of channel parameters on both head losses and part warpage to incorporate this manual step into the GD algorithm.

Fig. 3

Complete high-level workflow for GD process and manual postprocessing

To summarise the overall mould tool design process developed for this study, the designer first assembles the mould tool’s overall boundary and initial conditions and part geometry, as well as material and moulding process parameter data. These are input into Moldex3D Studio, which through a DOE process identifies process parameters that produce a uniform surface temperature profile at the MTPI and minimal cooling time at the end of the cooling stage. The first iteration of the CCC offset optimisation loop (step (h) in Fig. 2) is run using a Python programme under the guidance of Eqs. 2.1 and 2.2, after which the model parameters are refined in Fusion 360 using optimised values. The mould tool design can then be postprocessed manually to address any remaining external manufacturing, operational, and customer requirements before fabrication.

2.4 Implementation of optimised design

2.4.1 Overview

A constant set of moulding parameters was used for all three initial mould tool designs (conventional, manual conformal, and GD-optimised conformal) described in this study for the purposes of comparison of results; see Table 1.

Table 1 Moulding parameters used in Moldex3D for all simulations presented in this study

Parameters in italics were selected via the internal DoE module within Moldex3D in the first iteration of the step (h) loop in Fig. 2. All other parameters were selected by the designer based on prior experience, industry standards, or following material data from the material supplier.

After the above parameter values are set, an initial set of CCC design parameters is developed; this process entails optimisation through a genetic algorithm (GA) generating mean CCC properties (1-D optimisation of CCC parameters) represented in steps (d) in Fig. 2, and is described in Section 2.4.2 (novelty I). After CCC generation is complete and temperature data at MTPI are available, the iterative CCC pointwise offset optimisation process within step (h) in Fig. 2 is conducted as is also described in Section 2.4.3 (novelty II described at start of Section 1.3). The GD process’s controlling Python script interrogates the simulation results obtained at the end of each iteration of step (h) to extract results from Moldex3D at the control points where the surface mesh intersects with the mould’s virtual section planes (as described in Section 2.3); example control points are shown in Fig. 4. Extracted data include surface temperature at the MTPI and coolant temperature and velocity. These data are used by the GD process to optimise the CCC offset distance from the MTPI at individual control points (rather than their mean offset as in step (d)). Both the internal operations of this iteration process and its termination process are described in detail in Section 2.4.3.

Fig. 4

Example location of CCC control points for the optimisation process along the MTPI. The surface temperature distribution is at the MTPI and was predicted by Moldex3D’s multiphysics FEA simulation. The plane used to symmetrically cut the part into halves has also been highlighted in grey dotted boundary lines, along with the respective moulds to which the MTPI belong

Simulations predictions chosen for experimental validation include (i) pressure drop between the channel inlet and outlet, (ii) warpage of the moulded part at an arbitrary surface point after ejection, and (iii) surface temperatures to ensure the accuracy of the surface temperatures used by the GD process to guide CCC design optimisation. These results are presented in Section 3.3–3.5, respectively. Section 2.4.4 discusses the usage of DoE in Moldex3D for process parameter optimisation in step (h) of Fig. 2 after CCC generation, and Section 2.4.5 discusses a novel methodology for avoiding interference in features and channels (novelty III).

2.4.2 Conformal channel optimisation parameters (novelty I in Section 1.3)

GAs use optimisation techniques based on evolutionary processes, i.e. virtualised ‘crossovers’ and ‘mutations’ propagate through a GA’s iterations according to the principle of natural selection [27]. In the current study, genes in a chromosome represent CCC parameters, namely (i) channel diameter (kept fixed for the channel system throughout the rest of the GD process), (ii) channel pitch distance (also fixed for a channel system), and (iii) mean offset distance from the MTPI. Specifically, (i)–(iii) were optimised via GA in steps (d) of Fig. 2 to develop a basic CCC design using the fitness function developed for this study and defined in Eq. 2.5. The GA process involved initially formulating 10 virtual chromosomes with five genes each (these represent design aspects of the IM tool and are listed momentarily). The chromosomes were crossbred by the GA algorithm with genetic convergence (i.e. optimum fitness for purpose) being judged as reached once all 10 are passed on to their progeny 100 times consecutively without a mutation resulting in a higher fitness function value. The subsequent channel positioning optimisation in step (h) then makes further adjustments to the mean channel offset distance at each control point individually; see Section 2.4.3.

$$f={t}_{c}+ \sum\nolimits_{k=1}^{n= {\text{no}}.\mathrm{ of moulds}}\left|({T}_{{\text{mould}}, k}-\overline{T })\right|$$

(2.5)

The objective function ($f$) was set as the sum of the cooling time and the range ($n$) of MTPI temperatures (${T}_{{\text{mould}}, k}$) away from the mean ($\overline{T }$) predicted for each CCC as per Eq. 2.5. To ensure consistent dimensionality of all terms within this summation, the cooling time was nondimensionalised by the initial estimated cooling time for the same mould tool with conventional CCs (estimates may be supplied by the mould tool designer or customer), and the mould tool temperature was nondimensionalised by the midpoint of the supplied mean tool temperature limits (supplied by the mould tool designer; see Table 2). Pseudocodes for both the GA and its controlling programme are presented in Appendix A1.

Table 2 The five genetic algorithm (GA) input and output parameters used as genetic values (genes in a chromosome) and their constraints. Genetic values are assigned at random during the GA initialisation step, a population of 10 chromosomes maintained and optimised via crossbreeding under the guidance of the chosen fitness function (cooling time)

Constraints on input parameters include (i) geometrical limits for the mould bolster (AKA frame plates, which are the housings used to host multiple mould cavities within the same IM assembly), and (ii) minimum part wall thickness for mechanical integrity (Section 1.2), and the manufacturable CCC cross-sectional shape. Constraints on output parameters are mean mould tool temperature lower bound (below which the molten polymer will not flow into all parts of the cavity) and upper bound (above which the part is insufficiently frozen to eject without excessive warpage), and the boiling point of the coolant. Table 2 presents the input and output parameters used by the GA in step (d) in Fig. 2 and their constraint values used in this study.

In general, the CCC design optimisation problem is constrained but not limited to a single optimum and furthermore does not depend linearly on all its input variables. Thus, linear optimisation techniques are not useful for exploring the solution space. Hence, the use of GAs is a reasonable alternative for optimising the highly interdependent variables listed above.

2.4.3 Further optimisation in step (f) of initial channel offset distances calculated by steps (d) using golden search method (novelty II in Section 1.3)

The current study makes use of golden search in step (h) in Fig. 2, based on the output of step (g), i.e. optimising further the initial mean offset/distance between the CCCs and the MTPI calculated in step (d) to maintain the desired mould tool temperature. ‘Golden’ in golden search refers to this method’s use of the golden ratio to determine the search parameters [30] by searching for an optimised solution value using proportionally equal search intervals [31]. The rationale behind the use of golden search lies in its integration within the prebuilt Python optimisation libraries and the simplicity of its fundamental concepts and application [32]. For some applications, it is also more accurate and faster to converge than Newton’s method [32].

Step (f) in Fig. 2 is coded using a Python script that first generates control points from the mould’s mesh file (made in step (b)) to permit checking for parting planes, sliding cores, ejector pins, etc., which might prohibit CCC placement through or around them. Using the part geometry to define control points does not allow such adaptability. The pseudocode for this detection method is presented in Appendix A2. The control point spacing was set at 1 mm for the present mould tool geometry, as having closer control points increased the computational time of the CCC pointwise offset optimisation algorithm (step (h) in Fig. 2) significantly without appreciably increasing the spatial refinement of the CCCs created. For the simplified part geometry described in Section 2.1, the mould tool design was restricted to half the part to (i) reduce the computational runtime and (ii) enforce symmetry of the resulting mould tool design. Figure 5 shows the control points relative to the entire part’s surface.

Fig. 5

Control point placement over half the simplified part geometry described in Section 2.1, thereby allowing the internal contours to be traced by the algorithm. Only half the part is considered by the control points, as described in Section 2.3, placed on both MTPIs in the core and cavity moulds. The points inside the part, that form the outline of the half-part model, are only virtual and do not control any channel placement for the complete mould design (Fig. 2 i). The plane used to symmetrically cut the part into halves has also been highlighted in grey dotted boundary lines

Option 1: initial CCC design taking place in steps (d) and (e) in Fig. 2

After placement of the control points along the MTPI, initial CCC offset distances were set such that the CCCs were fully conformal to the MTPI without consideration of coolant properties and MTPI temperature distribution. The control points, along with the offsets obtained in the GA, allow channel creation in 3-D space from a 1-D channel profile. This design process is obviously rapid and simple but leads to an MTPI temperature distribution that is strongly dependent on the geometry, e.g. local part thickness and coolant temperature (which increases along the CCC), and leads to hotspots and coldspots. Thus, this approach is effective only at producing an initial CCC design for later refinement in a control pointwise manner.

Option 2: GD of CCC offsets taking place in step (h) in Fig. 2

CCC design was performed by adjusting the CCC offset distance at each control point (instead of the mean offset) under the guidance of results from the Moldex3D multiphysics simulations of the IM process. These results were extracted at the control points following the pseudocode presented in Appendix A3. Adjustment of offset distances at the individual control points continues iteratively until step (h) converges. The sizes of individual adjustments are calculated based on the golden search algorithm with the objective of reducing nonuniformities in the mould tool temperature at the control points. The pseudocode for this offset calculation is given in Appendix A4.

2.4.4 Implementation within Moldex3D Studio of the DoE module in step (h)

As described in Section 2.3, the Moldex software package’s DoE process during the first iteration of step (h) of Fig. 2 is initiated by the mould tool designer by conducting simulations for a range of IM process parameters (listed in Table 1) as control factors according to the Taguchi method-based DoE (Section 2.3). Taguchi’s method of DoE determines the minimum number of experiments according to Taguchi arrays, within the permissible limits of the process parameters, which are adjusted to deliver an objective and complete analysis of their effects. For IM, the Taguchi method adjusts process parameters with a critical effect on process times and part quality [33], such as injection pressure, mould closing speed, mould pressure, backpressure, screw speed, barrel temperature, and melt temperature [34].

2.4.5 Avoidance of interference between conformal channels and MTPI features in step (h) (novelty III in Section 1.3)

Control point definition and usage to compute the optimal CCC offset distances require knowledge of the mould tool’s surface to avoid interference between surface features and the adjusted positions of the CCCs at the control points; see Fig. 6(a). In this study, constraints are defined within the GD process on the allowed mean offset to the CCCs produced by step (g) in Fig. 2.

Fig. 6

Example of interference between an adjusted CCC and a mould’s geometric features. (a) Interference of the channel with features such as extrusions and ejector pins, and (b) the same design after the interference detection and avoidance module is applied. Control points responsible for these channel segments were ignored as they were subjected to the interference rules, thereby rerouting the channels to avoid interference

The section planes are made parallel so that the CCCs cannot interfere with each other in the direction perpendicular to the section planes. A final source of channel-channel interference occurs when the parting plane is nonuniform, which may lead to CCCs intersecting with each other.

To prevent both sources of interference (channel-part feature and channel-channel), a detection module was introduced that operates following the pseudocode presented in Appendix A5. The result is eliminated interference; see Fig. 6(b).

2.5 Comparison of different CCC designs with FEA simulation equivalents

The reasoning behind the four mould tool designs studied here is as follows:

• 1. Conventional mould tool design (straight-drilled CCs) manufactured from P20 tool steel (a conventional mould tool material), i.e. validating simulations of a ‘baseline’ CC-equipped mould tool designed for easy manufacturing from a material well established for use with non-AM tool manufacturing methods.

• 2. Initial CCC mould tool design made from SS316L, i.e. validating simulations of a complex but non-optimised CCC geometry relative to ‘1’ (above). The change of material to SS316L refers to its common use with AM tool manufacturing methods (DED used in this study).

• 3. Initial CCC mould tool design made from CuAl bronze, i.e. validating simulations of the same complex CCC geometry as ‘2’ (above) but with a high-conductivity mould tool material to study its impact on heat transfer.

• 4. GD-optimised mould tool design made from SS316L, i.e. validating simulations of an AM-built mould tool (DED used in this study) with an optimised CCC layout relative to ‘2’ (above).

As described in Section 1.3, experimental mould tools were 3D printed for validation of their corresponding FEA simulations, which serve numerous purposes for both research and industrial practice. Variables used for validation are listed in Section 2.4 and include (i) coolant pressure drop between the inlet and outlet of the mould bolster, (ii) part warpage during and after ejection, and (iii) temperature close to the MTPI, with the results presented in Sections 3.3–3.5, respectively. Warpage was measured using a linear variable differential transformer (LVDT) with a ± 2.5 mm range (model D6/02500A, RDPE, Wolverhampton, UK). Coolant pressure at the entry to the CC system for the four mould tool designs was measured using a differential pressure transducer 629C (Dwyer Instruments Inc., Michigan City, USA). Temperature within the mould tool (near the MTPI) was measured using a 3-mm fibre-glass-insulated type K thermocouple (Hales Australia Pty Ltd, Braeside, Australia) placed within the inserts and surrounded by thermal paste.

With regard to warpage, due to the differences in the observed failure mode of parts produced from two of the three mould tool metals (SS316L vs. CuAl Bronze as mentioned in Section 2.1), the measured cooling times (which as explained in Section 1.3 represent the time until safe ejection of the moulded part) for these two mould tool metals are not directly comparable. This difference in failure mode occurs due to minor manufacturing differences that cause the ejector pin location to move slightly closer to the part centre, exposing it to a warmer centreline temperature of the part rather than a cooler near-wall section; more discussion is presented in Section 3.2. For comparison of experimental cooling times between mould tool designs, a more comparable criterion is therefore needed than the time needed to reach the supplier-stated ejection temperature for the polymer.

Two alternatives were chosen here: (i) the measured time required for the polymer melt to freeze at the ejector pin locations (results in Section 3.8) and (ii) using simulation-predicted cooling times for comparison rather than measured cooling times. Calculation of (ii) was pursued as follows. A multiphysics (thermofluidic) simulation was run for each mould tool design using a large (upper bound to the) specified cooling time; see Table 3. This was decremented in steps of 0.5 s and the simulation rerun each time until the part was predicted to be no longer fully frozen (cooled throughout to below its glass transition temperature) at the end of the cooling cycle. This time was then the predicted ‘freezing time’ for the part, to be contrasted with the part’s ‘ejection time’, which is that required for the part to reach throughout a maximum of the polymer’s ejection temperature (defined in Sect. 2.2 and stated by the supplier). These analyses yielded two cooling times for comparison of the four simulated mould tool designs, with the results presented in Section 3.7.

Table 3 Moulding cycle input parameters for the four mould tool designs studied here, which differ with both CC geometry and construction material. Material data are presented in Appendix B1 (Table 10), B2 (Table 11), and B3 (Table 12)

3 Results

3.1 Preamble

We begin with presentation and experimental validation of FEA multiphysics simulation predictions for the four mould tool sets—conventional design in P20 tool steel (Fig. 1(b)), initial conformal design in SS316L (Fig. 1(c)), initial conformal design in CuAl bronze (Fig. 1(c)), and optimised conformal design in SS316L (Fig. 2 subpanel for step (i)). The results are organised by validated data type, i.e. coolant pressure drop (Section 3.2.2—optimised conformal in SS316L simulation is validated), warpage (Section 3.4—conventional in P20 tool steel simulations is validated), and temperature at the locations of the experimental sensors (Section 3.5—all four mould tool design simulations are validated). Section 3.6 presents multiple CCC designs arising from the GD process from different input parameters. Following this is a performance comparison of the CCC mould tool designs via simulation (Section 3.7) and experiment (Section 3.8). Section 3.9 describes the major remaining issues surrounding manual conformal cooling channel generation and how the process in the current study overcomes them.

3.2 Introduction to simulation validation

3.2.1 Modes of failure of plastic parts during ejection for different experimental mould tools

While measuring the cooling times for the four mould tool inserts studied here, differences were observed in the failure modes during ejection of the moulded plastic parts. The failure mode is described in Sections 1.2 and 2.5 as referring to the manner of distortion or (in extreme cases) fracture of the part. Experimental trials were conducted during which the cooling time of the plastic part was progressively reduced from a ‘safe’ upper estimate for all four mould tool designs (50 s for the current study) until the parts fractured during ejection. This value of cooling time was then taken to be the limiting cooling time for that mould tool design. The failure modes observed during part ejection were the following:

• Conventional mould tool in P20 tool steel: part failure occurred over one of the mould tool’s five ejector pins (the pin at the sprue; see Fig. 1 (c));

• Initial CCC mould tool in SS316L: part tearing occurred at the part gate (see Fig. 1 (c)), causing the part to warp;

• Initial SS316L CCC mould tool in CuAl bronze: part failure occurred over ≥ 1 of the mould tool’s four ejector pins, with penetration of the pin/s into the base of the part;

• Optimised CCC mould tool in SS316L: part failure occurred over ≥ 1 of the ejector pins in the mould tool at the base of the part, causing excessive distortion near the ejector pin

From the above, it was hypothesised that the cause of failure is the presence of partially molten polymer near the ejector pins causing distortion and rupture of the plastic melt when force from the ejector pins is applied during part ejection. This led to the notion that simple observation of surface temperature data is insufficient to define a practically robust cooling time for a given mould tool design. In other words, it is vital to allow for complete solidification of the polymer near the ejector pin locations before ejection. Thus, all simulation results presented in this study feature this criterion within all statements of cooling time.

3.2.2 Validation of coolant pressure drop

Differences in the geometry of the four mould tool sets as manufactured can arise due to potential machining errors. Therefore, any validation-related comparisons of performance characteristics such as coolant pressure drop between the inlet and outlet of the mould bolster, cooling time, and warpage during and after ejection are unavoidably subject to slight noise.

3.3 Simulation validation results for coolant pressure drop within the channels

3.3.1 Preamble

Validation of the multiphysics simulation predictions from Moldex3D for coolant flow through the CCCs was determined by comparing the predicted and measured coolant pressure drops. This was performed for the GD-optimised mould tool in SS316L. This process variable was chosen for validation instead of coolant temperatures, as the deviation in recorded temperature for coolants (± 0.5 °C) is close to the difference in inlet and outlet CCC temperatures (0.7 °C increase). This similarity is likely due to the generally high thermal diffusivity of the mould tool materials, which tends to reduce temperature gradients during the cooling stage. The CCC pressure drop was chosen over the CCC flowrate as the coolant flowrate was kept constant during both experiments and simulations.

3.3.2 Predicted coolant pressure drop validation error for GD-optimised conformal mould tool in SS316L

The CCC coolant pressure drop predicted by FEA simulation of the GD-optimised CCC mould tool and its measured equivalent for the hybrid-manufactured tool are shown in Table 4. Note that the CCC coolant pressure drop when high indicates a likelihood of coolant stagnation, which, as described in Section 2.1, constitutes a critical long-term operational risk.

Table 4 Comparison of measured and predicted coolant pressure drop in the CCCs for the GD-optimised mould tool design

Table 4 demonstrates that the predicted coolant pressure drops along the cavity and core CCCs underpredict the measured values. This is attributed to two factors:

• 1. The average wall roughness is likely higher in the experimental tools manufactured by DED (and is difficult to measure experimentally within the internal CCs) than the value assumed by the multiphysics FEA solver (5 $\upmu$ m). The roughness is fundamentally due to the manufacturing method used, and therefore, pressure loss due to roughness is likely underestimated in the simulation.

• 2. The internal connections of pipes to the CCs in the inserts create pressure losses not accounted for in the simulation, particularly along the sharp bends involved in the transfer of coolant from the mould bolster to the insert. Changes in hydraulic diameters, particularly in the coolant couplings (or connectors), cause further experimental pressure losses that are not accounted for in the simulation. Quantification of these real-world losses requires several further pressure sensors to be placed inline along the coolant’s path. However, this would require significant tool redesign, which was beyond the scope of this work.

3.4 Simulation validation results for warpage of the ejected moulded part

3.4.1 Preamble

Validation of the FEA multiphysics simulation predictions for warpage of the plastic part during ejection involved comparing the predicted and measured shrinkage, both in mould and out of mould, of the plastic part. This was performed for the conventional mould tool design (see Fig. 1(b)) manufactured in P20 tool steel. Prediction of warpage by Moldex3D is limited to a steady-state prediction of shrinkage after cooling at room temperature for 24 h. The closest corresponding measurement (Section 2.5) was in-mould shrinkage measured using the LVDT. The difference between these metrics is then the out-of-mould shrinkage, including cooling and curing, which was measured with a digital Vernier calliper after ejection.

3.4.2 Predicted part warpage validation error for conventional mould tool design in P20 tool steel

Table 5 shows the measured and predicted values of warpage. Figure 7(a) shows the experimental jig for measuring in-mould part shrinkage and Fig. 7(b) depicts the response of the measuring device over 3 cycles.

Table 5 Comparison of measured and predicted warpage measured from the cavity wall (prior to shrinkage) to the cooled and shrunken plastic at the end of the cooling stage (measured via LVDT), plus the out-of-mould shrinkage (measured using a Vernier calliper)

Fig. 7

A Location and shape of the warpage probe (grey) shown alongside the FEA-simulated part. The predicted displacement (inset) includes both in-mould and post-moulding shrinkage of 0.46 mm. b LVDT-measured in-mould shrinkage of 0.26 mm above the LVDT’s baseline value

The simulation validation error is relatively small and is considered here to occur due to the following:

• 1. Inaccurate measurement of out-of-mould shrinkage: a Vernier calliper was used to measure out-of-mould shrinkage; hence, inaccuracies in positioning the tips at the probe location could arise.

• 2. Deflection from back pressure: the injection and holding pressure caused the plastic melt to flow into the orifice housing the LVDT actuator, which slightly increased the thickness of the plastic being measured. Even with controls in place, this deflection was still able to increase the (apparent) measured warpage.

• 3. Constrained vs. unconstrained measurements: in-mould shrinkage is measured when the part is constrained by the core, whereas when measured using Vernier callipers it is in an unconstrained position, i.e. in a different state.

• 4. Miscellaneous factors: these include data logging delays, electrical interference, calibration errors, etc., which may cause further errors in measured warpage.

3.5 Simulation validation results for temperature at locations of mould tool probes

3.5.1 Preamble

Validation of the FEA multiphysics predictions for temperature was conducted at the location of the experimental temperature probe placed closest to the MTPI, which was in the same location for all four mould tool designs (P20 tool steel conventional, SS316L preliminary conformal, CuAl bronze preliminary conformal, and SS316L GD-optimised conformal). Note that measuring temperature within the moulded part itself is challenging due to (i) disruption of the part’s integrity due to the presence of the sensor and (ii) part shrinkage/separation from the sensor tip leading to inaccuracy or loss of recorded data. Therefore, simulation validation was conducted using a temperature value measured within the bulk of the mould tool as close to the MTPI as possible. While multiple locations within each mould tool were experimentally probed, the sensor placed closest to the MTPI showed the largest simulation validation error for all four mould tool designs studied. Thus, only these readings are presented here for brevity; see Fig. 8. These temperature profiles represent the cyclic steady-state evolution of temperature near the MTPI, which was achieved after 5–10 moulding cycles for all mould tool designs (note that 20–30 cycles were completed for each design to confirm these stabilisation cycle numbers).

Fig. 8

FEA multiphysics simulation validation of temperature near the MTPI for a conventional, b SS316L conformal, c CuAl bronze conformal, and d GD-optimised SS316L conformal mould tool designs. Note that these traces represent the cyclic steady state evolution of temperature over a single moulding cycle, which includes a temperature rise (filling and packing stages) and fall (cooling and ejection)

3.5.2 Potential causes of predicted temperature validation error for the four mould tool designs

Differences in the measured and predicted temperature at the probe’s location near the MTPI presented in Table 6 may be due to the following:

• 1. Loss of contact due to in-mould shrinkage: an air gap may develop between the polymer and MTPI (tool wall) surrounding the sensor.

• 2. Slow/low resolution of the thermocouple: a relatively durable thermocouple was used due to the harsh operating environment, which necessitated a compromise on both its precision (± 4 °C) and response time (likely a few seconds).

• 3. Conduction through the thermocouple stem: this issue is endemic to thermocouples and tends to increase the sensor response time as well as introduce error into measurements.

Table 6 Absolute difference $\left|\mathrm{\delta T}\right|$ between measured and predicted temperatures in Fig. 8 over the cooling stage of a single steady-state manufacturing cycle. Data were taken from the thermocouple probe tip’s location near the MTPI. The percentage error is the root mean square temperature difference recorded relative to the absolute baseline coolant temperature of 35 °C

Fig. 9

A High-coolant-pressure parallel CCC design, b low-coolant-pressure parallel CCC design, c perpendicular CCC design, and d helical CCC design. All four mould tool design variants are compatible with the part geometry manufactured by the mould tool designs in Fig. 1(b, c). In the panels, channels (blue) were locally shifted (by moving their control points, i.e. red dots in Figs. 4 and 5) at numerous points along their length to minimise MTPI variation in the moulded part

The error between the predicted and measured temperatures is within the thermocouple precision window (± 4 °C), so the FEA multiphysics model developed here is considered experimentally validated with respect to the predicted near-MTPI temperature profiles in Fig. 8.

3.6 Outcomes of the generative design process (novelty I in Section 1.3)

Validation of the simulation results from the FEA multiphysics simulations described in Sections 3.3–3.5 permits their predictions, particularly those for GD-optimised designs, to be assumed representative of real-world results. Therefore, this section expands upon the above validation studies to model multiple scenarios of real-world interest, i.e. different outputs from the GD tool design optimisation process originating from different guidance sets input by the tool designer. Note that the below changes to inputs would ideally be explored automatically; however, as explained in Section 2.3, this more complex layer of design automation has been left to future work. Figure 9 presents the different GD-optimised outcomes based on different input design criteria, whether in terms of operating limits to channel diameters in Table 2 or the way the temporary mould inserts were designed in step (h) in Fig. 2.

Figure 9(a) presents a mould tool CCC design developed here, but with a low diameter (4 mm) and pitch (8 mm), in a two-part mould with a parting plane across the flat faces of the cylinder shown in Fig. 1(a). Its CCCs are relatively longer and constricted, thereby incurring major and minor coolant pressure drops an order of magnitude above others. For example, a lower pressure drop was observed in the corresponding design with increased CCC diameter (6 mm) and pitch (14 mm); see Fig. 9(b) design developed here. CCCs in both tool designs run parallel in both halves of their mould inserts.

Figure 9(c) presents a mould tool CCC design developed here with similar dimensions as Fig. 9(b) but with CCCs running perpendicular in both tool halves, which results in a more uniform temperature distribution at the MTPI (results not shown for brevity).

Figure 9(d) presents a mould tool CCC design developed by combining two identical halves of the half-mould tool setup shown in step (h) in Fig. 2. The two-part mould is now parted vertically from the centre of the cylinder to develop helical configurations in both the cavity and core. This design gives the best cooling efficacy in terms of uniform cooling circumferentially and results in a lower MTPI surface temperature gradient (by ~ 1 °C) and shorter cooling times (~ 2 s or ~ 7% shorter ejection time). It thus demonstrates the benefits of the GD process developed in this study, over manual design processes or automated designs that do not account for warpage and/or MTPI temperature uniformity. These one-part and two-part core designs are also manufacturable via DED, highlighting the complex CCC designs available via this blown-powder AM process. The results for this final GD-optimised mould tool design are contrasted with the other three mould tool designs developed for this study (Section 2.5) in Section 3.7 (comparison of simulation data across all four tool designs) and Section 3.8 (comparison of experimental data across all four designs).

3.7 Comparison of simulation datasets

Table 7 compares key design metrics for the GD-optimised mould tool design with those from the three other designs developed for this study. The GD-optimised design is predicted to outperform those with shorter cooling times at comparable, but more consistent, warpage (quality).

Table 7 Comparison of the four mould tool designs developed for this study based on results from multiphysics FEA simulations

3.8 Comparison of experimental datasets

Following Table 7, Table 8 compares key design metrics for the physical GD-optimised mould tool design with those from the three other physical designs 3D printed for this study. The GD-optimised design again demonstrates the lowest cooling time and joint lowest ejection time, but only an intermediate maximum temperature over the moulding cycle.

Table 8 Comparison of the four mould tool designs developed for this study based on experimental measurements

3.9 Challenges for manual conformal channel design

Experimental validation of the multiphysics FEA simulation predictions of coolant flow through the CCs (Section 3.2.2) focused on the coolant pressure drop, which was achieved within 5% for the cavity-side CCCs. This permits some confidence in the predicted velocity field within the CCs, which is predicted to be generally inhomogeneous for both flow speed (mean 55 cm/s and standard deviation 50 cm/s; see Fig. 10(a)) and direction. These inhomogeneities are strongly promoted by the presence of the aerofoil-shaped ‘winglets’ designed into the CC geometry, as shown in Fig. 10(b), which failed in their intended purpose of dividing coolant flow evenly among the vertical sections of the cavity-side CCs; see Fig. 11.

Fig. 10

A Coolant speed distribution for SS316L/CuAl bronze CCs (high speed flow, 232 cm/s, is red and low speed, close to 0 cm/s, is blue). b ‘Winglets’ designed to distribute flow evenly among the multiple vertical sections of the cavity-side CCCs; note that these were employed only in the two initial conformal mould tool designs presented in Fig. 1(c)

Fig. 11

Velocity streamlines for the coolant in the SS316L/CuAl bronze CCs. Sparse, dark blue streamlines represent slow-moving coolant

The uneven coolant flow in the cavity-side CCs in Fig. 11 results in uneven part cooling, i.e. wide temperature range present along the MTPI. This is particularly noticeable for the SS316L mould tool; see Fig. 12. This is significantly reduced using the more thermally conductive CuAl bronze as the mould tool material; see Table 7.

Fig. 12

Predicted temperature distribution at the MTPI of the SS316L mould tool at the end of cooling. Red (dark grey in B/W publishing) indicates a high temperature near stagnation zones in SS316L CCCs highlighted in Fig. 10(a). Blue (also dark grey in B/W publishing) spots correspond to cooler sections that are excessively cooled by their neighbouring CCCs

In response to the observed thermofluidic simulation results, variations in CC geometry cannot be performed quickly and reliably. Historically, manual reconfiguration of the CCC geometry to deliver a uniform coolant flowrate among the channels has been pursued through multiple manual design iterations involving manual monitoring of the resulting MTPI temperature gradients and warpage. Instead, the use of control points as described in this study (Fig. 5 and Section 2.4.3) allows the CCC optimisation process to proceed largely via unattended running while also delivering a closer-to-optimally performing cooling system. These aspects significantly reduce the designer’s labour cost and tool operating cost, respectively.

4 Discussion

The design process for conformal cooling channels (CCCs) in injection moulding (IM) tools must consider the extent of conformation to the moulded part’s shape, the distribution of part mass (thickness), the surface area of the mould tool-part interface (MTPI), and the CCC’s hydraulic design, which collectively control the homogeneity of temperature in the cooling part. This can require CCCs with inhomogeneous flowrate and pressure gradient along and between channel segments, which carries the long-term challenge of flow stagnation, blockage, and reversal caused by corrosion products resulting from aqueous coolants. Manual design of branched CCC networks does not guarantee equal flow distribution, which promotes inhomogeneous shrinkage of the part (warpage) and reduced part quality. Thus, rapidly designing IM tools with robustly performing CCC networks requires multiphysics analyses that simultaneously account for heat transfer, fluid mechanics, and polymer thermomechanics (warpage), and must also be geometrically resolved, i.e. 1D models are useful only as a guide to performance and only when supported by 3D transient multiphysics analyses such as the GD process described in this paper. 3D analyses are obviously also required for the design of bimetal IM tools. Given the complex design space described above, the novel and useful aspects of the four IM tools described by this study using different design methods are summarised in Table 9. It was observed that although the GD optimised design is favoured for its lower cycle times and improved parts, there are still practical use cases for the conventional and manually designed conformal channels.

Table 9 Advantages, disadvantages, and example practical use cases for the four different IM tool designs described in this study

Within the broad comparison of tool design approaches described in Table 9 is a necessary comparison of how the advantages of a GD-optimised design scale with part complexity. This comparison is conducted here using the effect of polymer part thickness on cooling time, which is the major element of design complexity for the simplified cylindrical part geometry studied here. Following this, the results are generalised to reveal their implications for cooling parts with more complex geometry.

Per Eq. 2.2, part cooling time is expected to be proportional to the square of part thickness. Multiphysics simulation results for fully frozen cooling times at different part thicknesses agree closely with this expectation (R² > 0.99 in the modelling study in Fig. 13); note that these results are considered reasonably representative of reality given their qualitative experimental validation presented in Sections 3.3 to 3.5. For the range of part thicknesses modelled in Fig. 13, the linear term in the quadratic fit of cooling time vs. part thickness predictions is predicted to be of similar magnitude to the quadratic term, which is a particularly applicable result for moulded parts that are (i) spatially uniform in thickness, (ii) similarly accessible to CCCs across their surfaces, and (iii) a few mm thick. Thus, the relative difference in cooling performance between conventional and GD-optimised mould tool designs decreases significantly with increasing part thickness.

Fig. 13

Numerically predicted cooling time and cycle time savings for various moulded part thicknesses in conventional and GD-optimised (‘Opt’) CC mould tool designs. ‘Gain’ represents the percentage cooling time reduction in opting for CCC over the conventional CC for a particular thickness

The multiphysics simulation results in Fig. 13 have two further consequences. Firstly, given that moulded parts with varying thickness will demonstrate a spatially variable ‘local’ cooling time, conventional CC designs in general cannot be designed responsively to this need due to their limitations in routing complexity, leading to the thickest regions of the part becoming the rate-determining step for part cooling. Secondly, for relatively thin parts with complex geometry that are expected to cool rapidly, conventional CCs will be unable to conform equally to all their surfaces, leading to a highly variable local cooling time throughout the part. Thus, mould tools designed for thin and geometrically complex parts that are generatively designed with CCCs will be more economical both to design (low capital expenses) and run (low operating expenses) than conventional IM tool designs. Relevant to this is the fact that thin and geometrically complex parts correspond to most use cases for polymer IM, as demonstrated by the part thicknesses recommended by a common supplier of polymers for IM uses (Appendix C1, Table 14).

Aside from cooling time, part warpage is an essential moulded part quality concern. This does not increase significantly between the conventional CC to CCC mould tool designs, even at the lower cycle times achieved by the GD-optimised design (mean warpage 0.64 mm vs. 0.66 mm, respectively). However, the standard deviation of warpage decreases noticeably from 0.13 to 0.11 mm.

5 Conclusions

The innovative design methodology for CCC injection moulding (IM) tools presented here improves significantly on current approaches to achieving optimal performance of injection moulding (IM) tools. By employing evolutionary algorithms, the baseline ‘1-D channel system’ is established (novelty I described at start of Section 1.3). The ‘golden search’ algorithm strategically positions cooling channels by extracting and processing temperature distributions at the MTPI (novelty II). Finally, the conformal cooling channels are set up for hybrid DED manufacturing after consideration of operational and geometrical constraints (novelty III). The above approach combines the strengths of individual industry standard software tools through custom automated scripts that consider IM process parameters, material data, and user-defined constraints. Experimental validation was performed for the first time for four IM tool designs built using a modern DED HM printer. The performance of the four tool design approaches is as follows:

• The GD processes proposed in this paper present a good solution even for a simplified hollow cylindrical part geometry, i.e. for which conventional (non-CCC) channel geometries are expected to be similar in cooling time performance as CCCs.

• Manually designed CCCs may result in poor flow through channel branches that reduce cooling time (relative to a non-conformal design) but increase MTPI spatial temperature variation (relative to the GD process’s result) and thus warpage, costing redesign time and prohibitively increasing IM tool capital operating expenditures.

• The reduction in cooling time by using GD-designed CCCs increases with decreasing part thickness and increasing geometrical complexity of the part geometry. However, increasing geometrical complexity could potentially also cause build problems for some additive/hybrid manufacturing process, and accounting for these represents an area for future improvement of the GD process described in this study.

• Increased tool metal conductivity improves the MTPI temperature, which is preferable for moulded parts with thin sections. This has been shown to be the case with the CuAl bronze preliminary conformal tool having reduced gradients in predicted MTPI temperature compared to the preliminary SS316L conformal tool. Bimetallic tools (built using graded powder composition from two carefully selected metal powders) are a key method of achieving this, and potentially superior for the current study to as-layered bi-metallic composite tool builds have potential to develop delamination defects due to the large difference in coefficient of thermal expansion between CuAl bronze and SS316L.

With regard to future work, the GD process presented here is currently programmed to pursue a single minimised output (cooling time). However, we note that the method is fundamentally capable of hierarchically pursuing multiple design target criteria, and thus a parametric study that features different balances of multiple design criteria is of practical use. Automatic design of gating is another avenue which dictates a large section of cooling cycle performance and moulded part quality However, the immediate focus ahead lies in incorporating the number of parting plane number and their geometry, the number of CCC systems, the choice of mould tool metal, and the manufacturing method (and its constraints) into the GD process described here. These aspects are prioritised as we consider them be more time consuming to explore manually than optimisation of CCC distance from the MTPI. Thus, the capital and operating expenditure margin between automatically and manually designed future IM tools are anticipated to be larger than achieved here for a limited number of design variables.

Appendices

Appendix A: Python pseudo-code

1.1 Pseudo-code for genetic algorithm implementation

Appendix B: Material properties

2.1 Tool steel properties

Table 10 Tool steel (P20) material characteristics [29]

2.2 Stainless steel properties

Table 11 Stainless steel (SS316L) material characteristics [29]

2.3 Copper–aluminium bronze properties

Table 12 ‘CuAl bronze’ material data (obtained from Metals for Printing (M4P), Magdeburg, Germany)

2.4 Polypropylene properties

Table 13 Bormed polypropylene (HF840MO) material characteristics [29]