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

Effective cooling systems for injection moulding (IM) tools are critical to reducing manufacturing costs & cycle time for the polymer parts that they produce. This work presents a novel automated methodology for designing conformal cooling channels (CCCs) for injection moulding (IM) tools. This is done through existing commercial moulding simulation tools interlinked with custom scripts that adjust CCC design in response to the spatial variability in global andlocal temperature at the mould tool-part interface (MTPI). Four mould tool designs for a hollow cylinder were developed and analysed via both numerical simulation and experiments. These include (i) conventional IM tool with straight-drilled cooling channels made of tool steel, (ii) a manually designed CCC system with stainless steel, (iii) copper-aluminium bronze ‘core’ andstainless steel ‘shell’ with CCCs identical to (ii), and (iv) stainless steel with a CCC system automatically designed using generative design (GD) driven by a genetic algorithm. Tool (ii) cooled the part faster than conventional tool with a manually designed CCC system (i) (3-5% predicted vs. 40% measured), as did tool (iii) with the bronze core (9-12% predicted vs. 40% measured). The GD-optimised CCC tool (iv) cooled fastest in both the predicted results (15-30%, 11-25% & 1.5-25% faster than (i), (ii) & (iii)) andmeasured results (70%, 50% & 50% for (i), (ii) & (iii)). The predicted MTPI temperatures were also lower for the GD-optimised tool (65%, 75% & 34% below (i), (ii) & (iii)). Therefore, the novel methodology proposed here for automatically designing IM tool CCCs achieves reduced (a) maximum andspatial variability in MTPI temperatures, (b) cooling time, and (c) warpage.

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 duration of the moulding cycle [1].
Alongside cooling time minimisation, spatially uniform cooling throughout the manufacturing cycle (i.e., that results in minimised across the mould tool-part interface (MTPI)) is critical to the quality of each moulded part, as nonuniformity promotes thermal stresses in the part that drives distortion (i.e., geometric errors AKA '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].This process is challenging, time consuming, and prone to producing suboptimal designs, as it requires simultaneously satisfying a range of 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.
Generative design (GD) is an iterative process used to generate a range of feasible design variants within user-speci ed design constraints and design quality metrics (Oh et al., 2019) (Oh et al., 2019).Generative design can be evaluated and selected by either designers or computer programs; see Fig. 1 [4].In the gure, arti cial selection refers to the users acting as design guides, while natural selection means that ΔT the process is guided by computers through mathematical or spatial constraints satisfying some evaluation scheme.Within custom GD systems, the designer re nes the GD process to narrow the scope of its output designs and thus streamline the search process.This approach was adopted in the current study by prede ning CCC orientations, providing different limits for channel diameters based on operating pressures and pro le conformity, and conducting customised postprocessing of results as de ned in section 2.3.
Manual channel design is typically used to generate nonconformal cooling channels (CCs), most likely straight CCs associated with the manufacturing limits of the conventional machining methods used to create them, i.e., drilling [5].Manual design is therefore unlikely to yield optimal cooling performance when faced with the geometric complexity of complex mould tool and part designs.The design of CCC mould tools, whether conducted manually or semi-autonomously with GD, requires (i) identi cation of interference between channels and mould tool features and implementation of routing alterations, (ii) estimation of the spatiotemporally varying heat ux and temperature distribution across the MTPI, and (iii) further alteration of CCC routing within the constraints imposed by the mould tool manufacturing method.The application of AM technology to IM has enabled much greater design exibility through the ability to manufacture CCCs with complex geometries that closely follow the moulded part surface, thereby extracting heat evenly from its interior and minimising variations at the MTPI [6].Semiautonomous techniques such as GD can be applied to nd optimal CCC designs with reduced designer input [1].
A range of approaches have previously been presented to identify optimal CC and CCC designs.Tang et al. [1] developed a numerical methodology for IM tools that simultaneously optimises the channel diameter, location (of the channel axis within a 2D plane), and coolant ow rate.This focused on producing designs with straight CCs due to their suitability for machining by drilling.This approach is thus limited to simpler part geometries comprising a series of straight channels only.
Lam et al. [7] proposed a design method based on an evolutionary algorithm to optimise both CC design (channel diameter, offset distance, etc.) & IM process parameters ( ll & pack pressures, times, etc.).
However, the approach is not capable of de ning design parameters based on the MTPI temperature variation, which does not allow for ΔT and moulding cycle time minimisation.Xu et al.
[8] developed a similar design methodology for producing CCC designs suited for AM; however, the resulting package seems no longer publicly available.Both Tang et al.'s and Xu et al.'s results were limited to static coolant temperatures, and no selection process was described for the CC and CCC parameters used to initialise their design algorithms.
Saifullah et al. [9] proposed a design method that places CCCs near the MTPI to increase heat transfer and minimise the moulding cycle time.However, this approach was not automated.Luh et al. [6] presented an automated method using hotspot analysis to re ne the positioning of (non-equidistant) CCCs with a uniform cross-section.However, while this approach does dynamically characterise hotspots and automatically produce a CCC design, temperature distributions are obtained by graphically observing ΔT hotspots from one view, thus limiting the achievable CCC optimisation for tool designs with high aspect ratios in the viewing direction.
Li [10] developed a feature-based approach that (i) decomposes a complex moulded part into simpler shape elements and (ii) algorithmically generates CCCs for the associated mould tool by combining a prede ned template generated for each simpler element into a single CCC system.Although this model works well for different geometries, it does not allow variation in cooling based on part-speci c cold and hotspots.Torres-Alba et al. [11] presented a similar method based on a discrete multidimensional model of the moulded part.This approach offered a good solution for acquiring channel parameters (diameter, offset distance, pitch distance, etc.) via evolutionary algorithms based on the melt front temperature pro le.However, the accuracy 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 lling stage were 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 cooling channel based on new hotspots and cold spots), possibly over multiple iterations until convergence is achieved.This is an issue common to most of the methods mentioned above.
Alongside the challenges to CCC design described above, there are further challenges associated with manufacturing CCC mould tools due to their complex internal geometry.Tuteski & Kočov [12] present an overview of AM processes relevant to IM tool manufacture (such as powder bed fusion and direct metal deposition) as well as guidelines for designing CCCs for AM.The guidelines addressed (i) minimisation of cooling system stagnation points and plug-stops to reduce debris accumulation and blockage, (ii) positioning CCCs to reduce cooling time and at the MTPI, and (iii) ensuring part solidity around the ejector pins prior to ejection to reduce ejector pin marks and deformation of the part.This was achieved using a 'zigzag' CCC layout with nonuniform channel offsets (to address (i) & (ii)) and freezing time near the ejector pins as the estimate of cooling time (to address (iii).

Challenges in the Design & Manufacture of Conformal Cooling Channels
Design requirements for CCC tools, in addition to reducing the cooling time and at the MTPI, include (i) ensuring mechanical integrity of the tool, (ii) satisfying constraints imposed by the mould tool manufacturing method, (iii) accommodating axial coolant temperature variation in the design process (to promote uniform heat ux), and (iv) complying with coolant supply constraints (e.g., maximum deliverable pressure drop from the coolant pump); see Fig. 2.
L-PBF is one of the most common processes for CCC IM tool manufacture [13] due to its high resolution [14], with multimaterial mould inserts with conformal channels being studied [15].Directed energy deposition (DED), while offering relatively high deposition rates, has historically not been preferred for manufacturing tools with complex geometries such as CCC mould tools due to low resolution [14,16] and even has cooling inserts manufactured using L-PBF within its bulk to incorporate complex cooling channels [17].However, the capability to manufacture conformal tools using DED (within limits) is developed using the ideology presented in this paper.

ΔT ΔT
Minimising channel spacing and depth increases heat removal, but a lower bound exists below which the resultant stress concentration can compromise the strength of the tool [18].Recommended minimum wall thickness values are for steel, for beryllium, and for aluminium (Al), where is the CC's diameter [19].With respect to (ii), manufacturing constraints for DED include an upper bound to the maximum manufacturable unsupported overhang angle, ranging from 63° [20] to 30° relative to the horizontal build substrate, as reported by Nassar et al. [21].A similar overhang requirement exists for LPBF manufacturing; however, L-PBF can accommodate larger overhangs, typically 30-45° relative to the horizontal build substrate [18].The printability of smaller channels (microchannels with diameters of 500 µm) with multiple channel pro les is made possible via LPBF [22].A lower bound, in this case, arises from the accessibility for powder removal of complex internal channels [18].

Details of the Current Study
The major novel aspects of the proposed design methodology are (i) optimisation of mean CCC parameters such as channel diameter and channel offset distance from the geometry using evolutionary algorithms, including their orientation with respect to the moulded part (to improved cooling e cacy and minimised pressure drop), (ii) extraction and processing MTPI to position cooling channels using the linear search algorithm 'Golden Section Search Method' and (iii) consideration of numerous manufacturing objectives and constraints such as maximum operating pressures, unsupported channel pro les and dimensions based on manufacturing method (DED), and particularly an avoidance-ofinterference methodology for the CCCs.As described in sections 1.1-1.2, a single software tool that simultaneously optimises mould tool CCC design while complying with the less-addressed design aspects described in points (iiv) of section 1.2 is currently unavailable to the authors' knowledge.
Previous attempts made at generative design fall short of capturing the temperature pro le adequately (or at the right temperature) [11].However, this limitation may be addressed by using custom scripts to combine the capabilities of disparate software tools that are each expert at particular aspects of the overall CCC mould tool design problem.This approach is pursued here and employs three input datasets: (i) moulding process parameters, (ii) material data for the mould tool, cooling uid, and moulded material, and (iii) numerous common user-de ned constraints in the context of CCC mould tool design and manufacture.The order of events during execution of this methodology is described in section 2, but in brief, they involve the following: (i) Developing an initial manual design for the mould tool's CCCs that incorporates high-level constraints on CCC dimensions, tool size, and manufacturing method.
(ii) Multiphysics simulation of the IM process to predict part cooling time (de ned as time to reach ejection temperature) and surface temperature at the MTPI.
(iii) Optimisation of the position of the 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.For the current study, a simpli ed design of a moulded part was adopted to ease the physical interpretation of the results.The test part is a thin-walled cylinder with 50 mm height, 60 mm base diameter, and 1° inwards angle of the cylindrical wall towards its axis, i.e., a conical frustum.The part is designed to be manufactured using polypropylene (PP) (Bormed 840, supplied by APN Plastics Pty Ltd, Melbourne, Australia) with physical properties tabulated in Appendix B4.
A conventionally cooled mould tool design is presented in Fig. 3(a) as an example of IM tool designs manufacturable via conventional machining (drilling).The tool cooling system comprises a ba e and straight cooling channels.This simpli ed part geometry allows straight-drilled CCs to be placed close to the part's surface, allowing for increased heat ux 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 & B2, 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 uid (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 manufacture.These two objectives resulted in the unoptimised CCC design presented in Fig. 3(b).This was hybrid-manufactured, with both additive and subtractive manufacturing (machining) stages within the same 3D printer, using a veaxis Lasertec 65 3D hybrid printer (DMG Mori Co. Ltd, Pfronten, Germany), with an 1800 W laser, a scanning speed of 1000 mm/min, powder feed rate of 12 g/min, argon gas ow of 5 l/min, layer height of 0.9 mm and stepover width of 1.6 mm with stainless steel (SS316L) powder of size 45-106 µm (Höganäs, Sweden) used for deposition.Figure 3(c) illustrates the outer surfaces of the mould tool shown in Fig. 3 (a) & (b).
The major shortcoming to manually designing CCC mould tools such as Fig. 3(b), 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 uid, 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 ow; 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. 3(b)) were manufactured for this study using the hybrid printer described earlier from 'CuAl Bronze' (Cu9.3Al1.3Feweight percentages; henceforth abbreviated to 'CuAl Bronze') 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, di culties with laser processing, and increased costs.

Basic Heat Transfer Analysis of Injection Moulding
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 su cient proportion of the material has solidi ed, the part's rigidity can sustain ejection without appreciable warpage.The mould temperature ( ) at the moulding ejection temperature ( ) can be estimated from Eq. 2.1 [23], Eq. 2.1 where denotes the CC's local coolant temperature and denotes the polymer melt temperature.
The polymer's properties include (local density) and (local speci c heat capacity at constant pressure).The part's properties include 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 as the mould tool metal's thermal conductivity.The CC properties include for the channels' local hydraulic diameter, for the pitch distance between channels, and for the local offset distance between the CC's surface and the MTPI.Finally, the coolant uid's properties include for the convective heat transfer coe cient between the laminarly owing coolant near the CC surfaces and the turbulently well-mixed coolant occupying the CC bulk.Note that Eq. 2.1 was numerically veri ed by Himasekhar [24].Alongside Eq. 2.1, Turng [23] presents the cooling time ( ) at which is reached; see Eq. 2.2.This estimate was also numerically veri ed by Himasekhar [24] The critical overall process performance parameter thus appears to be mainly limited by the polymer's thermal conductivity, , and , not the mould tool metal's properties.However, mould tool metals with higher thermal conductivity affect implicitly via their reducing effect on .Eq. 2.4 demonstrates that with increasing metal conductivity, the corresponding reduction in becomes limited by polymer properties such as speci c heat capacity and part half-thickness.which then become the rate-determining parameters for : Eq. 2.4 Summarising the above, a low will increase 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 will not result in signi cant cooling time reduction in itself and needs to be coupled with a planned CCC design to impact cooling times.

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. 4. 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 ne-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 4 presents the resulting simpli ed work ow for the CCC geometry optimisation methodology developed here and the software implementation at each step.
Step (a) in Fig. 4 describes initiation of the design optimisation process from the CAD le describing the intended geometry of the nished (moulded & ejected) part.The designer speci es initial design features and input data in the form of part & mould tool CAD data, boundary conditions, tool design limits & constraints, polymer characteristics, and IM machine operational parameters.These data are variously stored in a spreadsheet, CAD model, and injection moulding process simulation software, Moldex3D Studio 2022 R1 (CoreTech System Co. Ltd., Zhubei City, Taiwan) and will be 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 (section2.4.2).
Step (b) involves developing an initial mould tool design to produce this part, 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 in uence 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 simpli ed part geometry studied here, mould tool division was combined with independent CC circuits per resulting half-mould.Given the symmetry of the simpli ed part geometry (Fig. 3), the CCC design could be simpli ed to two CCC circuits, one for each half-mould and comprising single curvilinear serpentine channels.
In Steps (c-i) in Fig. 4, 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).This mesh's resolution has a lower bound as follows: (1) 'control points' are de ned 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 prede ned 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 & ange feature, e.g., bosses, cut-outs, ejector pins, and ns around bends and sharp corners along the MTPI.
Following mesh creation in Step (c) in Fig. 4, 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).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).
Step (f) places control points in 3D space using 1-D parameters where the surface meshes meet the section planes and then de nes the initial offset values as per the GA output.Step (g) generates the CAD geometry of the uniform conformal channel, as described in section 2.4.3.In Step (h), the GD process runs FEA moulding process simulations.The GD process then iteratively improves upon the channel design by modifying the offset distance of the channel at control points until a converged solution is achieved that features optimised (minimised) surface temperature gradients at the MTPI (limited hot spots and cold spots) and a minimised cooling time.This iterative optimisation of the CCC offset value is performed at the control points using the 'Golden Section Search method' (section 2.4.3).
In addition to the above CCC offset optimisation, a second group of moulding process parameter optimisations are performed.This involves using an internal Modlex3D Design of Experiments (DoE) module (section 2.4.4) to identify moulding process parameters (such as ll & 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 lling [25].The DOE is based on the Taguchi method [26] and is performed only during the rst iteration of the pointwise offset optimisation (Step (h)).During the nal postprocess (Step (i)), the channel circuits are mirrored at the plane of symmetry, and the CCC serpentines are merged to form full cylindrical serpentines, with the two circuits (inside and outside the cavity) connected to their symmetrical halves via helical joints.These are then Boolean-subtracted from their respective cavity-core mould tool inserts to determine the completed moulds.
Step (i) ends with the designer postprocessing the optimised CCC design (smoothing bends, connecting CCCs as mentioned earlier in this section, and checking coolant pressures and part warpages) and proceeding to convert the GD design model into toolpaths ready for AM.
As illustrated in Fig. 4, the GD process developed here was implemented using a combination of preexisting dedicated software packages and custom programming code: • Moldex3D Studio was chosen for IM process simulation in Step (h).This package performs multiphysics thermal and uid ow simulations for a given CCC con guration and moulding process parameters.Moldex3D saves temperature distributions and coolant information ( owrate, Reynolds number, and CCC axis temperature) at the GD process's control points de ned 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 application programming interface (API) automation capabilities.
• Autodesk Fusion 360 (Autodesk, Inc., San Rafael, USA) is used for CAD geometry modelling of the mould tool (steps (b) & (c)) and CCC design based on control point information obtained in Steps (g), (h), and (i).The extensive API capabilities and a large support community made Fusion the ideal choice for the project.
• Python for exporting & analysing data from Moldex3D & Fusion using these software packages' APIs.This programming language was chosen due to the compactness and legibility of the resulting code.
Following the production of an optimised CCC mould tool design, which requires one traversal through Step (i) of Fig. 4, should the tool experience excessive operating coolant pressures and part warpage vs. externally speci ed tolerances, changes are made manually to the CCC parameter range, and the GD algorithm is rerun; see Fig. 5.
To summarise the overall mould tool design process developed for this study, the designer rst 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, identi es process parameters that produce a uniform surface temperature pro le at the MTPI and minimal cooling time at the end of the cooling stage.The rst iteration of the CCC offset optimisation loop (Step (h) in Fig. 3) is run using a Python program under the guidance of Eq. 2.1 & Eq.2.2, after which the model parameters are re ned in Fusion360 using optimised values.The mould tool design can then be postprocessed manually to address any remaining external manufacturing, operational, and customer requirements before fabrication.

Overview
A constant set of moulding parameters was used for all three initial mould tool designs (conventional, manual conformal & 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.Note that values in italics were all selected via the internal DoE module within Moldex3D in the rst iteration of Step (h) in Fig. 4. All other parameters were selected by the designer based on prior experience, industry standards, or given by the materials supplier.

Parameter
Value  4 is conducted as is also described in section 2.4.3.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. 6.
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.
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 sections 3.2.23.5, respectively.Section 2.4.4 discusses the usage of DoE in Moldex3D for process parameter optimisation in Step (h) of Fig. 4 after CCC generation, and section 2.4.5 discusses a novel methodology for avoiding interference in features and channels.

Conformal Channel Optimisation parameters
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 xed for the channel system throughout the rest of the GD process), (ii) channel pitch distance (also xed for a channel system), and (iii) mean offset distance from the MTPI.Speci cally, (iiii) were optimised via GA in Steps (d) of Fig. 4 to develop a basic CCC design using the tness function developed for this study and de ned in Eq. 2.5.The subsequent GD process in Step (h) makes further adjustments to the mean channel offset distance at each control point individually, as explained in section 2.4.3.
Eq. 2.5 The objective function ( ) was set as the sum of the cooling time and the range ( ) of MTPI temperatures ( ) away from the mean ( ) 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 program are presented in Appendix A1.
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), (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 ow into all parts of the cavity) and an upper bound (above which the part is insu ciently 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. 4 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.

Further Optimisation in Step (f) of Initial Channel Offset Distances Calculated by Steps (d) using Golden Section Search Method
The current study makes use of the Golden Section Search Method (GSSM) in Step (h) in Fig. 4, 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 GSSM refers to this method's use of the golden ratio to determine the search parameters [28] by searching for an optimised solution value using proportionally equal search intervals [29].The choice of GSSM is due to its availability in the optimisation libraries prebuilt into Python and the simplicity of its fundamental concepts and application [30].For some applications, it is also more accurate and faster to converge than Newton's method [30].
Step (f) in Fig. 4 is coded using a Python script that rst generates control points from the mould's mesh le (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 de ne 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. 4) signi cantly without appreciably increasing the spatial re nement of the CCCs created.For the simpli ed 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 7 shows the control points relative to the entire part's surface.
Option 1: Initial CCC design taking place in Steps (d & e) in Fig. 4 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 3D space from a 1D channel pro le.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 re nement in a control pointwise manner.
Option 2: GD of CCC offsets taking place in Step (h) in Fig. 4 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 GSSM 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.

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 rst iteration of Step (h) of Fig. 4 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 [31], such as injection pressure, mould closing speed, mould pressure, backpressure, screw speed, barrel temperature, and melt temperature [32].

Avoidance of Interference between Conformal Channels & MTPI Features in Step (h)
Control point de nition and usage to compute the optimal CCC offset distances requires 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. 8(a).In this study, constraints are de ned within the GD process on the allowed mean offset to the CCCs produced by Step (g) in Fig. 4.
The section planes are made parallel so that the CCCs cannot interfere with each other in the direction perpendicular to the section planes.A nal 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 & channel-channel), a detection module was introduced, which operates following the pseudocode presented in Appendix A5.The result is eliminated interference; see Fig. 8(b).

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 nonAM tool manufacturing methods.
2. Initial CCC mould tool design made from SS316L, i.e., validating simulations of a complex but nonoptimised 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 breglass-insulated Type K thermocouple (Hales Australia Pty Ltd, Braeside, Australia) placed within the inserts and surrounded by thermal paste.
With regards 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 are 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 (thermo uidic) simulation was run for each mould tool design using a large (upper bound to the) speci ed cooling time; see Table 3.This was decremented in steps of 0.5 s, and the simulation was 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 (de ned in section 2.2 and stated by the supplier).These analyses yield two cooling times for comparison of the four simulated mould tool designs, with the results presented in section 3.7.3 Results

Preamble
The results presented here begin with presentation and experimental validation of FEA multiphysics simulation predictions for the four mould tool sets -conventional in P20 Tool Steel (Fig. 3 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 is able to overcome them.While measuring the cooling times for the four mould tool inserts studied here (Tool Steel conventional, SS316L preliminary conformal, bronze preliminary conformal, and SS316L optimised conformal), differences were observed in the failure modes during ejection of the moulded plastic parts.The failure mode is described in sections 1.2 & 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 reduced from a 'safe' upper estimate for all four mould tool designs (50 s for the current study) until the parts produced from each mould tool fractured during ejection.This value of cooling time for each mould tool was then taken to be the limiting cooling time for that design.The failure modes observed during part ejection for each mould tool design were as follows: • Conventional mould tool in P20 Tool Steel: part failure occurred over one of the mould tool's ve ejector pins (the pin at the sprue; see Fig. 3) • Initial CCC mould tool in SS316L: part tearing occurred at the part gate (see Fig. 3), 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 observations, it was hypothesised that the cause of failure was generally the presence of partially molten polymer near the ejector pins causing distortion and rupture of the plastic melt when force from the ejector pins was applied during part ejection.This led to the notion that simple observation of surface temperature data is insu cient to de ne a practically robust cooling time for a given mould tool design.In other words, it is vital to allow for complete solidi cation 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.

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

Simulation Validation Results for Coolant Pressure Drop
Within the Channels

Preamble
Validation of the multiphysics simulation predictions from Moldex3D for coolant ow through the CCCs was determined by comparing the predicted and measured coolant pressure drop along them, which was performed for the GD-optimised mould tool in SS316L.This variable was chosen instead of sensorrecorded temperature, 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).This similarity may be 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 owrate, as the coolant owrate was kept constant in both experiments and simulations.
The CCC coolant pressure drop in the channels predicted by the FEA simulation of the GD-optimised CCC mould tool and the measured experimental data using its hybrid-manufactured equivalent CC con guration for both the cavity and core inserts are shown in Table 4.Note that the CCC coolant pressure (when relatively high) drop indicates the likelihood of coolant stagnation, which, as described in section 2.1, constitutes a critical long-term operational risk.

Predicted Coolant Pressure Drop Validation Error for GD-Optimised Conformal Mould Tool in SS316L
Table 4 demonstrates that the predicted coolant pressure drops in 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 di cult to measure experimentally within the internal CCs) than the value assumed by the multiphysics FEA solver (5 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 in 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 μ further experimental pressure losses that are not accounted for in the simulation, which therefore underpredicts the measured coolant pressure drop.Quanti cation of these real-world losses requires several further pressure sensors to be placed inline along the cool path.However, this would require signi cant redesign of the coolant path to accommodate these further sensors, which was beyond the scope of this work.

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 produced by the conventional mould tool design (see Fig. 3(a)) in P20 Tool Steel.Quanti cation of warpage by Moldex3D is limited to a steady-state prediction of shrinkage after cooling at room temperature for 24 hours.The corresponding measurement by LVDT (section 2.5) was in-mould shrinkage.The difference is the out-of-mould shrinkage, including cooling and curing, which was measured with Vernier callipers after ejection.

Predicted Part Warpage Validation Error for Conventional Mould Tool Design in P20 Tool Steel
Table 5 shows the measured and predicted values of warpage.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-ofmould shrinkage; hence, inaccuracies in positioning the tips at the probe location could arise.
2. De ection from back pressure: The injection and holding pressure caused the plastic melt to ow into the ori ce housing the LVDT actuator, which slightly increased the thickness of the plastic being measured.Even with controls in place, this de ection 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 it is measured using Vernier callipers in an unconstrained position, i.e., in a different state.
4. Miscellaneous factors include data logging delays, electrical interference, calibration errors, etc., which may cause further errors in measured warpage.

Simulation Validation Results for Temperature at
Locations of Mould Tool Probes

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 the readings for the polymer-proximate sensor are presented here for brevity; see Fig. 10.These temperature pro les represent the cyclic steady-state evolution of temperature near the MTPI, which was achieved after 5-10 moulding cycles for all mould tool designs (20-30 cycles were completed for each design to con rm this).

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 between measured and predicted temperatures in Fig. 10 over the cooling stage of a single, steady-state manufacturing cycle.Data were taken from the thermocouple probe's location near the MTPI.The percentage error is the root mean square (RMSE) temperature difference recorded relative to the absolute baseline coolant temperature of 35°C.GDoptimised conformal (Fig. 11 (d)) Tool material: SS316L 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 nearMTPI temperature pro les in Fig. 10.

Outcomes of the Generative Design Process
The validation of results from the multiphysics FEA simulations in sections 3.3 3.5 permits their predictions, particularly those for GDoptimised designs, to be assumed to be reasonably representative of real-world results.Therefore, this section describes multiple outputs from the GD tool design optimisation process originating from different guidance from 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 automation has been left to future work.Figure 11 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. 4.
Figure 11(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 a at face of the cylinder shown in Fig. 3(a), meaning that its CCCs are longer and relatively constricted, thereby incurring major and minor coolant pressure drops an order of magnitude above those for the corresponding design with increased CCC diameter (6 mm) and pitch (14 mm); see Fig. 11(b) design developed here.CCCs in both designs run parallel in both halves of the mould insert.demonstrates the bene ts 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.This one-part and two-part core design is also manufacturable via DED, highlighting the complex CCC designs available via this blown-powder process.The results for this nal GDoptimised 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 designs) and section 3.8 (comparison of experimental data across all four designs).CCCs.This permits some con dence in the predicted velocity eld within the CCs.This is predicted to be generally inhomogeneous for both ow speed (mean 55 cm/s & standard deviation 50 cm/s; see Fig. 12(a)) and direction.These inhomogeneities are promoted strongly by the aerofoil-shaped 'winglets' designed within the CCs, as shown in Fig. 12(b), which failed in their intended purpose of dividing coolant ow evenly among the vertical sections of the cavity-side CCs; see Fig. 13.

Comparison of Simulation
The uneven coolant ow in the cavity-side CCs in Fig. 13 results in uneven part cooling, i.e., high temperature range along the MTPI.This is particularly noticeable for the SS316L mould tool; see Fig. 14.This is signi cantly reduced using more thermally conductive CuAl Bronze as the mould tool material; see Table 7.
Variations in CC geometry in response to the thermo uidic simulation results observed cannot be performed quickly and reliably, e.g., manual recon guration of the CCC geometry to deliver a uniform coolant owrate among the channels must be pursued through multiple manual design iterations involving manual monitoring of the resulting MTPI temperature gradients and warpage.Instead, the use of control points described in this study (Fig. 7 & 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, signi cantly reducing the designer's labour and oncosts.

Discussion
This section begins with a description of the effect of polymer part thickness on cooling time for the simpli ed cylindrical part geometry studied here, following which the results are generalised to reveal their implications for cooling parts with complex geometry.Per Eq. 2.2, the part cooling time is expected to be proportional to the square of the part thickness.Multiphysics simulation results for fully frozen cooling times at different part thicknesses agree closely with this expectation (R 2 > 0.99 in Fig. 15), which are considered reasonably representative of reality given the qualitative of the multiphysics FEA simulations presented in this study.However, for the range of part thicknesses tested, the linear term in the quadratic polynomial t to the cooling time vs. part thickness predictions is instead predicted to be of a similar magnitude to the quadratic term, and thus, the effect of part thickness on cooling time is only weakly quadratic for 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 GDoptimised mould tool designs decreases with increasing part thickness.
The multiphysics simulation results in Fig. 15 have two further consequences.First, parts with varying thicknesses will demonstrate spatially variable 'local' cooling times.However, conventional CC designs in general will be unable to cool these regions at the same rate as thinner regions of the part, leading to the thickest regions of the part becoming the rate-determining step for part cooling.This simply reveals the already-known rationale for conformal cooling of polymer parts.
Second, for relatively thin parts with complex geometry that are expected to cool rapidly, conventional CCs will be unable to conform to all their surfaces.Thus, the thickness of the tool material between these conventional CCs and the MTPI will be spatially highly variable, leading to a highly variable barrier to heat transfer presented by the mould tool metal and thus a spatially highly variable 'local' cooling time.Thus, mould tools designed for thin and geometrically complex parts are expected to bene t signi cantly from being designed with CCCs rather than conventional CCs, meaning that their automated design becomes critical to developing tool designs rapidly and with optimal performance, i.e., with low capital expense (tool design time) and operating expense (manufacturing time).
We note that thin and geometrically complex parts correspond to most use cases for polymer IM, as shown by the part thicknesses recommended by a common supplier of polymers for injection moulding (Appendix C1, Table 13).The GD-optimised mould tool design is demonstrated to reduce cooling time by > 15% for a part < 4 mm thickness even with simple cylindrical geometry (Appendix C2, Fig. 16), while resulting in arguably only marginal changes to warpage (Appendix C2, Fig. 17).The prediction of cooling time reduction mentioned above compares favourably with the measured reduction in minimum cooling time, i.e., 70% (30 s cooling time down to 9 s; see Table 8).This large reduction is mainly due to the conventional CC mould tool suffering from delayed freezing at the sprue locations (Fig. 3) relative to the optimised CCC mould tool, which delays 'safe' ejection of the part from the conventional mould tool design.
achieved even for geometrically simple parts, for which conventional CCs would be expected to be a competitive with CCCs.

Conclusions
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 in uence the homogeneity of temperature in the cooling part.This can require CCCs with inhomogeneous owrate and pressure gradient along and between channel segments, which carries the long-term challenge of ow stagnation, blockage, and reversal caused by corrosion products resulting from aqueous coolants.Manual design of branched CCC networks does not guarantee equal ow 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, uid mechanics, and polymer thermomechanics (warpage) and must 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 revealed by this study are as follows: • The GD processes proposed in this paper present a good solution even for a simpli ed hollow cylindrical part geometry, i.e., for which conventional (nonCCC) channel geometries are expected to be similar in cooling time performance as CCCs • Manually designed CCC designs may result in poor ow through channel branches that reduce cooling time but increase MTPI spatial temperature variation and thus warpage, costing redesign time and prohibitively increasing IM tool capital expenditure (CAPEX) & operating expenditure (OPEX).GD or similar design tools are quantitatively demonstrated here to avoid this problem.
• The reduction in cooling time by using GD-designed CCCs increases with decreasing part thickness and increasing geometrical complexity of the part geometry, with increasing geometrical complexity potentially also causing build problems depending on the additive/hybrid manufacturing process used.
• Increased tool metal conductivity improves the MTPI temperature, which is preferable for moulded parts with thin sections.Bimetallic tools (built using graded powder composition from two carefully selected metal powders) are a key method of achieving this.
The GD process presented here is 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 a parametric study features different balances of these criteria, i.e., producing multiple Work ow describing the generative design (GD) process described in this study.ΔT refers to the maximum temperature gradient across the MTPI.
Channels for Injection Moulding Tools -Design & Manufacture Methods (a)), initial conformal in SS316L (Fig.3(b)), initial conformal in CuAl Bronze (Fig.3(b)), and optimised conformal in SS316L (Fig.4subpanel 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

3. 2
Introduction to Simulation Validation 3.2.1 Modes of Failure of Plastic Parts during Ejection for Different Experimental Mould Tools

Figure 9 (
a) shows the experimental jig for measuring in-mould part shrinkage, and Fig. 9(b) depicts the response over 3 cycles of the measuring device.

Figure 11 (
Figure 11(c) presents a mould tool CCC design developed here with similar dimensions as Fig. 11(b) but with CCCs running perpendicular in both tool halves, which results in a more uniform temperature distribution at the MTPI (results not shown).

Figure presents a mould
Figure presents a mould tool CCC design developed here made by combining two identical halves of the half-mould tool setup shown in Step (h) in Fig. 4. The two-part mould is now parted vertically from the centre of the cylinder to develop helical con gurations in both the cavity and core.This design gives the best cooling e cacy in terms of uniform cooling circumferentially resulting in a lower MTPI surface temperature gradient (by ~ 1°C) and cooling times (~ 2 s or ~ 7% shorter ejection time) and thus

Figure 2 Design
Figure 2

Figure 5 Complete
Figure 5

Figure 7 Control
Figure 7

Figure 14 Predicted
Figure 14 Steps (ii) & (iii) above are automated, which are key novel advantages of the methodology proposed here and signi cantly reduce the labour required to achieve a high performing, additively manufacturable, conformally cooled IM tool.Steps (ii)(iii) are achieved via a combination of multiphysics nite element analysis (FEA) simulations and custom code that conducts computer aided design (CAD) geometry preprocessing, postprocessing of results and subsequent CAD model re nement. .

Table 2 :
Genetic algorithm (GA) input and output parameters used as genetic values and their constraints.Genetic values are assigned at random during the GA initialisation step and then automatically optimised under the guidance of the chosen tness function (cooling time).

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

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

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

Table 7
compares key design metrics for the GDoptimised mould tool design with those from the three other designs developed for this study.The GDoptimised 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.

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

Table 9
Experimental of the multiphysics FEA simulation predictions of coolant ow through the CCs (section 3.2.2) focused on the coolant pressure drop, which was achieved within 5% for the cavity-side