Analysis of self-supporting conformal cooling channels additively manufactured by hybrid directed energy deposition for IM tooling

Abstract

Additive manufacturing (AM) of injection moulding (IM) tools has attracted significant interest in the polymer manufacturing industry for quite some time. However, hybrid manufacturing (HM) using directed energy deposition (DED), which involves concurrent additive and subtractive manufacture, has not been a commonly used process for IM tooling manufacture. This is apparent despite several advantages over the prevalent laser-powder bed fusion (L-PBF) alternative, including higher build rate, lower cost and integrated machining to directly achieve higher tolerances and surface finish. A key reason for this low utilisation is the limited ability of DED processes to produce circular channel profiles typically used in IM tooling, due to stricter constraints on the manufacturability of overhanging geometry. To address this, a range of self-supporting IM cooling channel profiles suited for hybrid laser and powder-based DED manufacture are proposed in this work. Numerical and experimental evaluations are conducted of the cooling performance of several non-circular conformal cooling channel (NCCC) profiles to identify a profile which achieves the maximum heat transfer for a constant cross-sectional area and coolant flow rate. Experimental studies included AM builds to evaluate the DED manufacturability of the selected NCCC profile on a conformally cooled HM benchmark model, followed by cooling performance characterisation, including a comparison against a reference L-PBF manufactured benchmark model. In conclusion, a shape correcting factor is obtained using response surfaces. This factor is used to convert thermal performance calculations for non-circular profiles to a conventional circular channel profile to simplify the DED manufacturing process for non-circular IM cooling channels.

1 Introduction

Injection moulding (IM) is one of the most common methods for volume manufacturing of plastic parts [1]. The application of additive manufacturing (AM) processes such as laser-powder bed fusion (L-PBF), electron beam—powder bed fusion and directed energy deposition (DED) has increased productivity in IM by enabling the manufacturability of tooling with conformal cooling channels (CCCs) with high cooling performance [2]. L-PBF has emerged as the predominant additive manufacturing process for IM tool production, owing to its capability to attain high resolution and construct cooling channels directly in various diameters and orientations [3]. Nevertheless, L-PBF processes typically exhibit slow build rates and relatively modest build volumes. Additionally, the L-PBF process faces limitations in achieving the required surface finish on crucial areas of IM tools directly. Consequently, L-PBF manufactured components often necessitate subsequent machining operations using separate subtractive manufacturing equipment. Due to the slow build rate and post-build machining requirements, L-PBF-manufactured IM tooling remains associated with elevated manufacturing cost. DED processes can have several embodiments that vary in the heat sources used (laser, arc or E-beam) or feedstock material form (powder or wire) [4]. They can achieve higher build rates and volumes but are limited by poor resolution, limited self-supporting build angles, and also require extensive post-build machining to achieve acceptable surface roughness [5, 6]. However, recently emerging hybrid manufacturing (HM) processes combining DED AM and in situ subtractive manufacturing technologies have the potential to address some of the shortcomings of standalone AM for IM tooling. HM machines allow for additive manufacture by material depositions, followed by concurrent in situ subtractive machining without the need to change equipment (Fig. 1). This is achieved with additive and subtractive end effectors positioned with 3- or 5-axis control, enabling the manufacture of complex geometries and surfaces with high accuracy. The result is higher build rates and resolution than those achieved with L-PBF or DED processes individually. HM systems have the potential for faster and cheaper additive manufacture of IM tooling, as well as the possibility of the application of coatings, repair of existing components and the manufacture of parts with two or more metals [7,8,9].

Fig. 1

Hybrid manufacturing process. a Additive process by direct energy deposition. b Subtractive process by milling (from [10])

However, the application of HM to the manufacture of IM tooling with conformal cooling channels is subject to key challenges. DED processes, like most AM techniques, have limits on the manufacture of unsupported surfaces inclined up from the horizontal, defined by the Minimum Manufacturable Overhang Angle (MMOA). Surfaces above the MMOA are typically self-supporting, while surfaces below the MMOA are not reliably manufacturable without support structures. The MMOA for laser and powder-based directed energy deposition process (LP-DED) is higher (typically 55°, ranging from 63° [11] to 30° [12]) than that for L-PBF (typically 30 ~ 40°) due to different process characteristics (such as the absence of an underlying powder bed in LP-DED). Conventionally, cooling channel profiles have mostly been circles [13] due to the associated ease of manufacture with drilling processes and relatively low-stress concentrations and pressure losses, or squares if the IM tool is manufactured using milled grooves [14]. The capability to consistently manufacture circular conformal cooling channels (CCCC) using DED can be limited, as the upper profile of the circular channel can exceed the process MMOA [15]. To overcome this issue, self-supporting alternative channel designs have become a necessity for manufacturing IM tools with CCCs via LP-DED.

These self-supporting, non-circular conformal cooling channels (NCCCs) can be manufactured in one of two ways—through AM on a 3-axis DED bed with overhangs where necessary or using a 5-axis DED machine with part articulation [16]. The former reduces the process planning complexity to a large extent, as well as the machine-related costs. The latter, however, retains a laser nozzle perpendicular to the build plane, significantly enhancing build quality, and in some instances, permitting lower ‘MMOAs’ depending on collision allowances.

An additional challenge lies in the complexity of process planning for HM, a task that often demands considerable expertise and time [17]. Critical steps in process planning are the decomposition of the part into additively and subtractively manufactured features, sequencing the manufacture of features to generate a single (serialised) additive and subtractive toolpath for the HM printer, and avoiding tool-workpiece interference. Further considerations regarding the cleaning of coolant and debris between subtractive and additive sequences also need to be addressed [18]. The most recent advancements in the computer-aided process planning software tools, such as in the case of Siemens PLM NX, display incorporation of feature-based recognition to identify individual shapes from their database and determine the optimal process for their manufacturing [19]. They, however, fail to make cost comparisons, as well as identification of free-form shapes [20]. A set of research proposals discussing a feature-free method of milling was offered by Nelaturi et al. [21], which later extended for additive builds [22]. This was then combined as an all-inclusive HM process planner more recently [20]. The process, however, can be quite complex for an IM tool, and it uses an FDM/SLA/SLS approach to manufacture the AM sections, as opposed to a CNC-integrated LP-DED setup [22]. An inherent design for manufacturing solution for IM tools becomes necessary to minimise manual effort in the manufacturing stage.

Additional challenges in employing LP-DED for IM tooling include inconsistent deposition rates in bends and sharp corners [23], high as-built surface roughness vales which increase pressure loss [24, 25], potential high-stress concentrations in smaller channels and distortion due to thermomechanical stress [26]. These challenges can be addressed by using CCCs with alternative non-circular, self-supporting profiles and by developing effective methods for extending the manufacturability of overhanging features by using the 5-axis control ability of HM to articulate the part during manufacture. This capability has the potential to enhance productivity and reduce the final cost of machining IM tooling to specified tolerances (also known as net-shape costs).

Various studies have been performed in literature surrounding the use of alternative non-circular cross sections for CCCs in AM tools. Most studies are limited to L-PBF, for example Kuo et al. [27] and Mayer [28] focused on IM tools manufactured using L-PBF. In studies where the benefits of NCCCs were highlighted, no relations were made between circular channels and equivalent non-circular to streamline the transition from one to the other [29]. Analytical thermal performance estimates were conducted using the hydraulic diameter of the channel for comparison with a conventional circular channel counterpart [30]. However, the hydraulic diameter, while useful for uniform boundary conditions, cannot be used as-is for IM tooling as the channel walls do not experience uniform heat flux when placed close to the heat source (mould tool-part interface (MTPI)), as seen in Fig. 2. The channel walls closer to the interface will experience higher heat flux than the walls on the opposite end. Due to the associated increased problem complexity, numerical or experimental analyses are required to accurately characterise the heat transfer performance of such non-circular channels. However, the heat transfer performance of non-circular cooling channels and identification of high-performing profiles suitable for hybrid manufacture has not been well established in the literature with comprehensive numerical and experimental studies.

Fig. 2

Non-uniform temperature contours across the cooling channel and MTPI [31]

To summarise, the current research status highlighted in the literature surrounding conformal cooling channels is limited in manufacturing options (namely L-PBF) due to the more popular choice of circular cross-section channels. This limitation is inherently placed due to MMOAs of other manufacturing methods, unable to form closed tops of CCCCs. Conversely, in studies where NCCCs are discussed, no proper design and manufacturing strategy is discussed. For design, most refer to the use of hydraulic diameters to relate the NCCCs and CCCCs, which is an incorrect assumption for heat transfer. There is also no discussion on which NCCC design is more suitable for IM tools. For manufacturing, no clear manufacturing strategies are discussed, especially for the highly advantageous HM to make consistent depositions with the option of integrated subtractive machining to reduce pressure drop where necessary.

To address these research gaps, the present research aims to analyse the design and manufacturing strategies of NCCCs, in place of CCCCs, more suited for HM in an LP-DED machine. In doing so, the use of self-supporting NCCCs also allows the designer to overcome an LP-DED’s MMOA limitations. For the determination of preferred NCCC cross-sectional shape, the current work evaluates the heat transfer performance of a range of NCCC profiles using numerical and experimental means. Initially, numerical analyses are conducted to compare cooling effectiveness in non-circular channels (Sections 2.1 and 3.1). Experimental validation is performed using a cooling channel benchmark tool manufactured with L-PBF (referred to as the Tool 1) (Sections 2.2 and 3.3).

A high-performance NCCC profile is numerically identified, and the heat transfer performance is evaluated in a second benchmarking tool manufactured using L-PBF (referred to as tool 2). A third benchmark tool with the selected non-circular channel profile is manufactured with hybrid LP-DED process (tool 3) in order to evaluate the heat transfer and manufacturability performance against a L-PBF counterpart (see Section 2.2 for methodology and parameters). Manufacturing strategies of such series channel distributions in complex tools is also discussed, although integration of this manufacturing strategy with existing CAM software is left for future research.

To simplify the design effort associated with using non-circular channels instead of conventional circular channels, a method is developed to identify equivalently performing circular and non-circular channels allowing for direct design substitution. This allows for the design of an equivalent system to an existing CCCC and take advantage of tried and tested design strategies of CCCCs.

As analytical expressions for the heat extracted in an IM cycle are not available in literature for various channel profiles, and as one cannot utilise the general hydraulic diameter as the comparator [32]. To address this limitation, a numerical study is conducted to develop a shape correcting factor which can be applied to non-circular channel profiles to obtain equivalent performance in a circular channel profile. This is developed by applying a response surface method (RSM) to a numerical design of experiments (DoE) study which evaluates the influence on the thermal performance of various channel parameters (such as diameter, pitch and offset distances) and boundary conditions (coolant temperature, flow rate) [33, 34].

2 Methodology

This work presents a methodology for the design of conformal cooling channels (CCCs) which are reliably manufacturable with a hybrid LP-DED AM process. This is achieved by: (i) numerically evaluating the cooling performance of CCCs with different self-supporting cross-sectional profiles; (ii) experimentally evaluating the LP-DED manufacturability and thermal performance of the best-performing profiles relative to a circular conformal cooling channel (CCCC) benchmark tool and (iii) developing a response surface map using regression analysis to relate the characteristic length of channel profile (both circular and non-circular) to the associated heat transfer out of the tool. Subsequently, a preferred channel profile is identified for manufacture.

A more detailed outline of the methodology is structured as per the steps below:

• 1. Develop a numerical model of a benchmark mould tool with conformal cooling channels (Section 2.1). Validate results by additively manufacturing (using L-PBF), and experimentally testing the benchmark tool (tool 1) (Section 2.2)

• 2. Numerically evaluate and compare various NCCC benchmark tools to identify a profile with the highest thermal performance, which also satisfies Hybrid LP-DED manufacturing constraints (Section 2.1)

• 3. Manufacture benchmark tools with the identified highest performing NCCC profile using L-PBF (tool 2) and LP-DED (tool 3) (Section 2.2). LP-DED manufacturing is executed through the second approach, involving printing of NCCCs by articulating the geometry to maintain perpendicularity of the build on a 5-axis hybrid 3D printer. Experimentally evaluate the thermal performance of the benchmark tools and compare against numerical predictions (Section 2.2).

• 4. Perform a regression analysis on a numerical 3-D cooling cell. Use a sensitivity analysis to study the effects of various CCC and fluid parameters such as geometric dimensions of the cooling cell, surface roughness, mass flow rate, etc. on heat transfer into the coolant. Use the analytical expression obtained to develop a CCCC-equivalent NCCC thermal system (Section 2.3)

The numerical and experimental benchmark tools and corresponding cooling channel profiles evaluated in this work are summarised in Table 1.

Table 1 (1–5) Numerical and experimental models of benchmark tools with different channel profiles for thermal performance comparisons. Variants 6–7 are numerical model for channel thermal equivalence studies. Design variants were all evaluated numerically with some evaluated experimentally as indicated

2.1 Numerical evaluation of circular and non-circular channel thermal performance

Numerical models are constructed of simplified IM benchmark tools comprising of cooling channels with varying profiles placed parallel to a heated boundary. The models are used to compare the cooling performance of varying channel profiles. Several studies in the literature have examined the 1-dimensional heat transfer in IM tools [35,36,37]. Some have discussed the influence of cooling channel profile in heat exchangers [38]; however, it is important to note that the heat source has traditionally been treated as a uniform boundary condition applied across the entire surface of the cooling channel. This approach limits modelling accuracy when applied to non-isothermal boundary conditions in injection moulding cooling channels. To estimate the true heat flux from the IM tool into the coolant, numerical studies can be applied, where analytical solutions are limited.

In the study, predominantly steady-state conditions are assumed, as transient IM phenomena are expected to have a negligible impact on the relative thermal performance of varying channel profiles. This is also numerically validated as a final exercise in Section 2.3. Serial channels (where one channel connects an inlet and outlet pair) are employed for enhanced control over fluid flow parameters along the entire channel length, such as mass flow rate and operating pressure [39]. In contrast, parallel channels (where multiple channels connect to a single inlet and outlet pair) suffer from preferential flow according to the flow resistance within each parallel channel [40] and are only used in IM tools instead of serial channels if pressure losses exceed the pump capacity, or if the cooling efficiency of the serial channel drops severely due to localised high temperature zones [39].

ANSYS Fluent 2023 R1 (Ansys, Inc., Canonsburg, USA) was used to run the numerical simulations of a benchmark test model being subjected to thermal boundary conditions with a cooling fluid running internally. Figure 3 shows the benchmark tool model of dimensions 161.5 mm × 100 mm × 28 mm with a circular profile.

Fig. 3

Benchmark block with CCC with a circular profile, running at a constant distance of 10 mm from the base. The three probe locations are displayed at 10, 15 and 20 mm from the bottom surface (the MTPI)

To maintain the uniform heat source, a block design was selected for benchmarking different tools. The setup aimed to compare average cooling performance among different channel profiles by measuring overall heat power transfer from a constant source, ensuring channels with equal coolant volumes and flow rates. The example tool design is expected to be comparable to similar serial cooling channel layouts commonly used in injection mould tooling. The dimensions of the cooling block were determined from the maximum build dimensions (240 mm × 240 mm × 300 mm) of the L-PBF machine used (GE Additive Concept Laser M2; GE, Boston, USA) along with a few considerations to post-machining. Three serially linked parallel cooling channels were determined to be sufficiently high for obtaining a uniform heat source at the base, yet small enough to eliminate redundancy. The channel length of 500 mm proved to be sufficiently long to determine pressure drops in different CCCC and NCCC arrangements.

The model includes three temperature probe locations at 10, 15 and 20 mm from the bottom surface (MTPI), which are used for experimental validation of the numerical results. They were positioned at the centreline of two consecutive channels to mitigate the interference effects of one channel over the other. The probe height of 10 mm was selected for being at the same height as the lowest point on the cooling channels, being a key point of comparison as explained in Section 3.1. Subsequent probe locations were maintained above the initial point due to reduced gradients in temperature (less sensitive), and hence reduced error. Tables 2 and 3 show the parameters used in numerical modelling and Fig. 4 the associated boundary conditions.

Table 2 Benchmark tool numerical and experimental model parameters

Table 3 Benchmark tool numerical-only model parameters

Fig. 4

Boundary conditions as seen in the front view of the benchmark tool. The blue arrow represents the natural convection boundaries, the red represents the constant temperature heat source, and the green represents the solid–fluid interface and the inlet temperature

After validation, simulations on CCCC serve as baselines for comparing various NCCC profiles, given that CCCC is the predominant channel geometry. NCCC profiles are limited to LP-DED-manufacturable cross-sectional profiles as defined by the process MMOA for reproducibility, which has been set as 35° from the literature [11]. As a result, feasible profiles for the current study are limited to those listed in Table 1.

For comparison purposes, a common shape-defining parameter (SDP) was defined for all 4 NCCC profiles. This is the maximum diameter circle inscribable within each non-circular profile such that each has the same cross-sectional area as the CCCC, i.e. channel cross-sectional area is the basis for comparison for all 5 channel profiles. The resulting SDPs and profile shapes are highlighted in Fig. 5, and the profile dimensions and fluid and solid domains are shown in Table 1 and Fig. 3, respectively. Finally, the NCCCs are arranged within the block so as to keep constant the distance (10 mm) between the heat source and the base vertex or edge nearest to the heat source (constant offset) (Fig. 6).

Fig. 5

Profiles being studied for feasibility to replace CCCC in LP-DED printing, (a) teardrop, (b) equilateral triangle, (c) diamond and (d) prismatic pentagon. Also highlighted are the shape defining parameters (SDPs) for each profile (indicated by D), with an equal cross-sectional area to a circle of diameter 10 mm

Fig. 6

a Deposition strategy for teardrop channel segment, reproduced with permission from [41]. A similar strategy has been adopted for the triangular channel. b A derived HM strategy for manufacturing complex IM tools is shown

Note that as explained in Section 1, the use of the term ‘hydraulic diameter’ has been avoided for the purposes of the current study in favour of SDP (with the exception of the equilateral triangular channel for which they are identical) to avoid direct comparison with analytical expressions used for pipe flow and heat exchanger performance characterisation. To compare heat transfer performance of NCCCs vs. the single CCCC in the current study, as explained earlier in this section, a constant cross-sectional area, channel length and thus constant coolant volume, flow rate and mean velocity were used for all 5 profile shapes, which were compared via thermofluid heat transfer simulations of the channels using ANSYS Fluent 2023. The boundary conditions for the benchmark tool are shown in Table 2 and 3.

The heat balance for the system is governed by the conservation of energy and represented by Eq. (2.1). Equation (2.2) represents the analytical estimate for the energy transferred by the coolant and is used to compare the power drawn by the coolant in future validations.

$${\dot{Q}}_{{\text{base}}}+{\dot{Q}}_{{\text{atmosphere}}}+{\dot{Q}}_{{\text{coolant}}}=0$$

(2.1)

${\dot{Q}}_{base}$:

Heat input at heated boundary

${\dot{Q}}_{atmosphere}$:

Energy transferred to the atmosphere by natural convection

${\dot{Q}}_{coolant}$:

Energy extracted by the coolant

$${\dot{Q}}_{{\text{coolant}}}=\dot{m}{C}_{p}\times ({T}_{{\text{outlet}}}-{T}_{{\text{inlet}}})$$

(2.2)

m:

Mass flow rate

Cp:

Coolant specific heat capacity

T_outlet:

Coolant outlet temperature

T_inlet:

Coolant inlet temperature

${\dot{Q}}_{atmosphere}$ is assumed to be constant for all the benchmark tools due to the same external dimensions and negligible compared to ${\dot{Q}}_{coolant}$ (as it is typically two orders of magnitude lower). The energy extracted by the coolant between its inlet and outlet is reported in Section 3.1.

2.2 Experimental setup

The numerical results of the benchmark tools models are validated with a corresponding experimental setup, as shown in Fig. 7. The corresponding experimental benchmark tools are manufactured using L-PBF (CCCC (Tool 1) and NCCC (Tool 2)) and LP-DED (NCCC, (Tool 3)) and used to validate the numerically predicted temperature and pressure measurements (see Table 1). The experimental boundary conditions are described in Section 2.1 and summarised in Table 2 and Fig. 7. Tools 1 and 2 are used to compared cooling channel performance differences between CCCC and NCCC profiles for a common L-PBF manufacturing method. Tools 2 and 3 are used to compare cooling performance differences for a common NCCC profile but with varying manufacturing methods (tool 2 L-PBF, tool 3 HM LP-DED). To align with the steady-state results of the CCCC benchmark tool obtained from simulations, recordings were made by logging temperatures and pressures after 10-min stabilisation intervals since the start of the installation every system. This allowed the values to stabilise enough to be considered steady state. Mean values were then calculated from these logged data to ensure consistency and correspondence with the simulated steady-state conditions. Temperature data from the thermocouples placed as per Fig. 7 were recorded, time-averaged and compared with their simulation counterparts at positions shown in Fig. 3.

Fig. 7

Setup for experimental validation of numerical simulations on the circular channel trial design. Hot plate maintained at 100 °C at the model-plate interface

Tools 1 and 2 were manufactured from Stainless Steel 316L using a GE Additive Concept Laser M2 L-PBF system, with the AM parameters listed in Table 4.

Table 4 LP-DED AM parameters for the NCCC HM method

Tool 3 was manufactured from Stainless Steel 316L with a 5-axis (3 linear and 2 rotating degrees of freedom) hybrid additive-subtractive laser and powder-based directed energy deposition system (LP-DED) with integrated subtractive machining capabilities (Lasertec 65, DMG Mori Co. Ltd, Pfronten, Germany). The AM deposition parameters used are listed in Table 5. Most of the parameter values were customised settings obtained from the machine and powder suppliers. The stepover values were chosen to be near the half-bead diameter mark in order to maintain a lower surface roughness. A lower stepover value than the radius is not preferred due to the detrimental effect on the deposition height within the same layer. Higher values increase the build surface roughness. A finish stepover of 0 mm (implying a complete overlap of contour and infill passes) was selected to maintain a flat surface edge and prevent a convex shape.

Table 5 LP-DED AM parameters for the NCCC HM method

As mentioned in Section 1, NCCCs selected can be manufactured using both 3-axis and 5-axis machines. In a 3-axis LP-DED printer, each layer remains horizontal which limits the manufacturability of self-supporting surface to those defined by the minimum manufacturable overhang angle (MMOA). A 5-axis hybrid LP-DED system HM can extend the manufacturable self-supporting geometry limits by articulating the deposition head with a fixed nozzle of 3-mm diameter to avoid the issues surrounding overhang angles and reduce material wastage. This has been demonstrated in Fig. 6. This ensured that the nozzle always remained perpendicular to the build plane, and thus, no overhang was necessary. This strategy was applied in this work. Machine control was achieved with CELOS® control system operating on Siemens SINUMERIK 840D (SIEMENS, Munich, Germany), with the CAM software being Siemens NX v1872.

The benchmark tools used in the experimental setup (Fig. 7) were clamped, and a thin layer of thermal paste was applied at the heater-tool interface to ensure conductive heat transfer. The temperature was measured at benchmark tool at the locations shown in Fig. 3 and at the tool-heater block interface. The coolant mass flow rate and pressure correspond to values in Table 2. Coolant pressure, mass flow rate and temperature were measured external to the benchmark tool and were used to assess the cooling performance of the channel profile. Temperatures were measured with insulated K-type ungrounded thermocouples (TC) with an accuracy of ± 4.0 °C manufactured by Hales (Hales Australia Pty Ltd, Braeside, Australia). A 629HLP Dwyer Instruments differential pressure transducer (Dwyer Instruments Inc., California, USA) was used to measure pressure across the channel inlet and outlet. The operating range was 0–1 bar, with a ± 1% accuracy. Temperature and pressure measurements were taken once the system reached steady state.

2.3 Response surface model for circular and non-circular channel performance matching

The manufacture of circular cooling channels with a LP-DED process is challenging as the top of the channel requires the deposition of unsupported horizontal layers. By using non-circular channel profiles with a similar thermal performance (equal heat flux and MTPI temperature response), LP-DED manufacturability can be improved while maintaining thermal performance.

To identify corresponding circular and non-circular channel parameters, a design study is conducted to map the design space of channels for a range of parameter values (Table 6), and their corresponding predicted heat transfer performance. The design study is conducted using a sensitivity and regression analysis approach.

Table 6 Channel parameters for shape factor parameterisation

For a synthesised or existing IM tool with CCCCs, some changes must be made to the channel parameters for it to be substituted directly by an NCCC system and maintain the same thermal performance. Equation (2.3) and Eq. (2.4) are 1-dimensional analytical estimates for a circular profile cooling cell [35] (Fig. 8), that provides control over the tool’s performance. Currently, no 2- or 3-dimensional analytical estimates exist for conformal cooling of IM tools in the literature to the author’s knowledge which can provide similar control over channel performance, that can be used during the CCCC-to-NCCC substitution.

$${{\text{T}}}_{{\text{mold}}}={{\text{T}}}_{{\text{coolant}}}+\frac{{\uprho }_{{\text{p}}}{{\text{c}}}_{{\text{p}}}{{\text{t}}}_{{\text{part}}}\times \left(2{{\text{K}}}_{{\text{m}}}{\text{W}}+\mathrm{h\pi D}{{\text{l}}}_{{\text{m}}}\right)\times \left({{\text{T}}}_{{\text{melt}}}-{{\text{T}}}_{{\text{eject}}}\right)}{\mathrm{h\pi D}{{\text{K}}}_{{\text{m}}}{{\text{t}}}_{{\text{cycle}}}}$$

(2.3)

where:

Fig. 8

Simulation Models of parametrically defined conformal channel geometries for (a) Circular CS and (b) non-circular CS. The symbols are explained in Table 6

T_mold:

Mean MTPI temperature

T_coolant:

Coolant temperature

ρ_p:

Polymer density

c_p:

Polymer specific heat at constant pressure

t_part:

Half part thickness

K_m:

Mould conductivity

$${{\text{t}}}_{{\text{cycle}}}=\frac{{{\text{t}}}_{{\text{part}}}^{2}}{{\mathrm{\alpha }}_{{\text{p}}}{\uppi }^{2}}{\text{ln}}\frac{4\times \left({{\text{T}}}_{{\text{melt}}}-{{\text{T}}}_{{\text{mold}}}\right)}{{\uppi }^{2}\times \left({{\text{T}}}_{{\text{eject}}}- {{\text{T}}}_{{\text{mold}}}\right)}$$

(2.4)

W:

Channel pitch length

h:

Convection heat transfer coefficient

D:

Channel (hydraulic) diameter

l_m:

Channel offset distance from MTPI

T_melt:

Polymer injection temperature

T_eject:

Polymer ejection temperature

t_cycle:

IM cycle time

α_p:

Polymer diffusivity

To provide a low computational cost analytical model with the ability to capture 3D phenomena, a regression model is developed from a design of experiments (DOE) study of a parametric, high-fidelity 3D cooling channel numerical model (Fig. 8). The boundary conditions for the numerical simulations are shown in Table 7.

Table 7 Boundary conditions for the 3-D cell used for the RSM simulations

The numerical experiments were conducted in ANSYS Design Explorer 2023 using the default settings for Central Composite Design with 27 design points. The boundary conditions for the numerical simulations are shown in Table 7.

The DOE parameter combinations are defined using the central composite design (CCD) fractional factorial design incorporating three or more odd-numbered levels for each parameter [34]. CCD was selected as it allows for multi-level factorials irrespective of the arrangement of factors [42]. The model parameters considered in the DOE are shown in Table 6 and were selected based on their influence on channel heat transfer as indicated in Eq. (2.3) and Eq. (2.4). Overall, 27 design points were evaluated.

Following the DOE, a response surface methodology (RSM) regression model was developed based on the DOE results. RSM is a statistical technique to model the relationship between input parameters and the response variable [34] (see Eq. (2.5). The input variables ${\upxi }_{{\text{k}}}$ are normalised to between ${-1\le {\text{x}}}_{{\text{k}}}\le 1$.

$${\text{y}}=\mathrm{ f }\left({\upxi }_{1}, {\upxi }_{2}, . . . ,{\upxi }_{{\text{k}}}\right)+\upepsilon$$

(2.5)

f:

True response function

k:

Number of input variables

ξ_i:

Natural i'th independent input variable

$\upepsilon$:

Variability unaccounted for in ${\text{f}}$

For the current study, the second order polynomial approximation was employed to model the response ${\text{y}}$, represented in Eq. (2.6) from the literature [34].

$${\text{y}}={\upbeta }_{0}+ \sum_{{\text{i}}=1}^{{\text{k}}}{\upbeta }_{{\text{i}}}{{\text{x}}}_{{\text{i}}}+\sum_{{\text{i}}=1}^{{\text{k}}}{\upbeta }_{{\text{ii}}}{{\text{x}}}_{{\text{i}}}^{2}+\sum \sum_{{\text{i}}<{\text{j}}=2}^{{\text{k}}}{\upbeta }_{{\text{ij}}}{{\text{x}}}_{{\text{i}}}{{\text{x}}}_{{\text{j}}}+\upepsilon$$

(2.6)

β₀:

Constant

β_i:

Coefficient for the first-order dependency of ${\text{y}}$ on ${{\text{x}}}_{{\text{i}}}$

β_ii:

Coefficient for the second-order dependency of ${\text{y}}$ on ${{\text{x}}}_{{\text{i}}}$

β_ij:

Coefficient for the first-order interactive dependency of ${\text{y}}$ on ${{\text{x}}}_{{\text{i}}}{{\text{x}}}_{{\text{j}}}$, ${\text{i}}\ne {\text{j}}$

Equation (2.6) can be rewritten in matrix form and solved numerically with known parameters and resultant heat fluxes as:

$$\begin{array}{l}\left[\begin{array}{c}{{\text{y}}}_{1}\\ \vdots \\ {{\text{y}}}_{{\text{n}}}\end{array}\right]=\left[\begin{array}{cccccccccccc}1& {{\text{x}}}_{11}& \cdots & {{\text{x}}}_{1{\text{k}}}& {{\text{x}}}_{11}^{2}& \cdots & {{\text{x}}}_{1{\text{k}}}^{2}& {{\text{x}}}_{11}\bullet {{\text{x}}}_{12}& \cdots & {{\text{x}}}_{11}\bullet {{\text{x}}}_{1{\text{k}}}& \cdots & {{\text{x}}}_{1\left({\text{k}}-1\right)}\bullet {{\text{x}}}_{1{\text{k}}}\\ \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots & \ddots & \vdots \\ 1& {{\text{x}}}_{{\text{n}}1}& \cdots & {{\text{x}}}_{{\text{nk}}}& {{\text{x}}}_{{\text{n}}1}^{2}& \cdots & {{\text{x}}}_{{\text{nk}}}^{2}& {{\text{x}}}_{{\text{n}}1}\bullet {{\text{x}}}_{{\text{n}}2}& \cdots & {{\text{x}}}_{{\text{n}}1}\bullet {{\text{x}}}_{{\text{nk}}}& \cdots & {{\text{x}}}_{{\text{n}}\left({\text{k}}-1\right)}\bullet {{\text{x}}}_{{\text{nk}}}\end{array}\right]\left[\begin{array}{c}{\upbeta }_{1}\\ \vdots \\ {\upbeta }_{{\text{m}}}\end{array}\right]\\ {\text{n}}={\text{no}}.\mathrm{of trials};\\ {\text{m}}={\text{no}}.\mathrm{ of coefficients}=1+2{\text{k}}+{\text{k}}({\text{k}}-1)/2\end{array}$$

Once the coefficients for the regression model have been determined, we can compute ${\text{y}}$, in our case being the heat flux, by substituting ${{\text{x}}}_{{\text{i}}}$ within (− 1,1). Similarly, for a given heat flux, we can ascertain ${{\text{x}}}_{{\text{i}}}$ through back-calculation from ${\text{y}}$. The analytical expression for the unknown offset distance is presented in Eq. (2.7). In this equation, the heat flux of the NCCC is solely dependent on the offset value, while the remaining coefficients are obtained from Eq. (2.6) by substituting the relevant values from the existing CCCC.

$$\begin{array}{cc}\dot{{\text{q}}}={\mathrm{\alpha }}_{0}+{\mathrm{\alpha }}_{1}{\text{O}}+{\mathrm{\alpha }}_{2}{{\text{O}}}^{2}& {\mathrm{\alpha }}_{{\text{i}}}=\mathrm{ f}({\text{P}}, {{\text{D}}}_{{\text{H}}}, {{\text{T}}}_{{\text{c}}},{\text{MFR}});\mathrm{ i}=\mathrm{1,2},3\end{array}$$

(2.7)

O:

Offset distance from part cavity

$\dot{{\text{q}}}$:

Heat Flux

In response surfaces, the magnitude of the partial derivative of the response surface equation with respect to a factor indicates its corresponding sensitivity, implying that small changes in the input factors result in significant changes in the response [43]. ANSYS internally calculates the sensitivity factor from the norm of the partial derivative of the regression equation for the chosen objective function (Eq. (2.6)) concerning its independent variables, which, in this context, are the channel parameters listed in Table 6.

The subset of parameters in Table 6 which were considered in the RSM model are presented in Table 8. Other parameters in the sensitivity study were not found to be as influential and were not included in the RSM model. Furthermore, these parameters cannot be changed without significantly affecting the tool design. For example, overhead distance, channel length and surface roughness depend on the specific part-mould-coolant combination and vary with each tool design.

Table 8 Parameter value ranges for response surface mapping. These operating ranges were defined based on design history for PP, which can be manufactured using LP-DED or L-PBF

The parameter operating ranges in Table 8 were based on historic data collected on the tooling requirements for various parts, as well as conformal cooling strategies adopted in literature [44,45,46].

Throughout the IM cycle, the cavity wall temperature undergoes changes while the part cools. In designing an NCCC system to achieve equivalent performance to a pre-existing CCCC, it is crucial to ensure their comparable performance during the entire cycle and across the temperature range. Consequently, numerical validation of the NCCC’s performance against the CCCC's, with input temperature aligned to the IM cycle, becomes imperative.

Post-analysis, a sample test was conducted for a CCCC with parameters listed in Table 9, and a corresponding NCCC is generated with the same heat flux by adjusting the offset distance to verify the resulting coefficient matrix. The variation of the offset distance is made using a linear search algorithm (golden section search method) over the range used for the RSM study (5–15 mm from Table 6). This search algorithm provides a reliable solution to a unimodal problem with the fewest functional solution through reuse from previous calculations. While pertinent to this problem, any heuristic or deterministic search methods can be used in place of golden section search and the choice is trivial to the problem statement being discussed in this study. While the polynomial degree may be greater than one, the response surface behaviour remains unimodal. The search algorithm is not further elaborated in the study and is left for the readers to assume their own formulations to derive the required offset for a given solution. Different methods would yield similar results varying in accuracy.

Table 9 Sample input parameters for the CCCC RSM equivalent NCCC

A validation numerical experiment is run using an average MTPI temperature against time plot as a temperature input for the CCCC 3-D cooling cell heat source. The average MTPI temperature input is taken from an IM cycle found in literature, as seen in Fig. 9 [47]. A transient area-averaged heat flux profile is extracted from the MTPI, and then supplied as an input for the NCCC 3-D cooling cell heat source. The resulting average MTPI temperature profile is compared against the one in literature for variations. The process is visualised in Fig. 10.

Fig. 9

Injection moulding average MTPI temperature profile found in literature, used for validation of RSM. The current study utilises the average MTPI temperature profile with a maximum temperature of 180 °C [47]

Fig. 10

NCCC cooling cell validation process

3 Results and discussion

3.1 CCCC and NCCC benchmark numerical analysis results

Figure 11 shows the local temperature contours for a transverse cross section at the midplane of the benchmark tool (see Fig. 12) of the benchmark tools (1 × CCCC and 4 × NCCCs) at the XZ plane. The results from Fig. 11 show that the triangular profile has a higher temperature uniformity and increased heat transfer from the MTPI compared to other channels. This is indicated by the triangular channel exhibiting lower temperature isotherms as well as closer isotherm band spacing (evident in the narrow 45–50 °C bands).

Fig. 11

Transversal temperature contours for (a) CCCC; and NCCCs with the following profiles: (b) teardrop, (c) equilateral triangle, (d) diamond and (e) prismatic pentagon. Simulation condition specified in Table 2 and 3

Fig. 12

a Probe placed at the channel wall (red) and at the bulk of the triangular NCCC benchmark tool at the same height between the channels (blue), b temperature at the channel wall and the variation between the two temperatures probes

The magnitude of the temperature gradient increases as one approaches the MTPI. Furthermore, observable fluctuations in temperature occur when observing the channel either directly from below or when comparing temperatures between two adjacent channels situated in the same plane. This observation at the vicinity of the channels allows for the analysis of potential temperature homogeneity at the MTPI. This is possible with the assumption that the heat source surface belongs to a polymer melt starting to cool from a constant injection temperature. The use of polymer melt heat source was avoided to reduce problem complexity due to an extra material undergoing change of state as well as a change in thermal conductivity, thereby also increasing reliability.

One can therefore infer: equidistant parallel section planes (assumed to be the MTPI) to the heat source surface (assumed to be polymer melt at half-thickness) must have an even temperature band to be truly homogenous. If a temperature gradient across that section plane is lower, the MTPI temperature and its heat transfer to the channels are more homogenous. As the largest temperature gradient between tool bulk and channel wall is observed just underneath the channels, the section plane of the channel wall has been used for comparison.

Figure 12a shows temperature probe location in the tool; Loc #1 corresponds to the centre of the channel wall, and Loc #2 corresponds to the midpoint in the bulk tool between parallel channels, with both located 10 mm above the MTPI. Figure 12b shows the channel wall (Loc #1) and tool (Loc #2) temperatures for various CCCs, as well as the temperature difference, i.e. $\Delta {\text{T}}= {{\text{T}}}_{{\text{loc}}\#2}-{{\text{T}}}_{{\text{loc}}\#1}$. The ∆T is an indicator of temperature homogeneity; a smaller ∆T indicates a more uniform temperature distribution.

The lowest channel wall and $\Delta {\text{T}}$ temperatures were predicted for the triangular profile as shown in Fig. 12b. Figure 13a shows the total channel surface area for channel of equal length with varying profiles. The channel surface area is calculated from the product of the channel perimeter and length. The channel surface area values vary as the channel profiles have varying perimeters, such that a constant cross-sectional area for all profiles is maintained (equivalent to that of a 10-mm diameter circle). The equilateral triangle profile has the highest perimeter, while the circle profile has the lowest. The prismatic pentagon also offers this advantage. However, it has a lower fraction of surface area parallel to the MTPI (20% compared to 33% for the triangle). Figure 13b shows the heat transfer coefficient (HTC) at the channel wall for the CCCs. The triangular NCCC exhibits the lowest HTC, while the circular channel exhibits the highest HTC, and it is apparent that a lower overall area-averaged heat transfer coefficient of the triangle can be attributed to its higher surface area exposed to the coolant compared to the other channels. For any given pitch distance between parallel CCCs, the effective channel-channel distance is lower for triangular channels due to higher aspect ratios compared to the other polygonal NCCCs for a given profile area, as seen in Fig. 11. In Fig. 14c, the net power supplied by the heat source to sustain an MTPI temperature of 100 °C is depicted. The chart reveals a significant energy extraction advantage exhibited by the triangular NCCC. The diamond NCCC is the poorest performer in this instance, showing a lower energy supplied value than the CCCC.

Fig. 13

Simulation results for different cross-sectional benchmark tools; (a) net surface area, (b) Heat transfer coefficient at the channel wall, c total surface heat transfer and (d) differential pressure across the inlet and outlet of the benchmark tool. Net surface area is the net wetted surface area of the serpentine channel shown in Fig. 3

Fig. 14

Manufacturing stage of the serpentine benchmark tool with triangular profile channel. The initial stages of LP-DED construction are shown in (1–4), (5) shows the part completed and (6) shows the subtractive machining

However, the acute angle corners in a channel can increase pressure losses, as seen in Fig. 13d and reduce endurance of the tool due to stress concentrations at the profile corners. Both can be reduced by introducing rounded corners (fillets).

Due to the improved heat transfer rates in the triangular NCCC, and compatibility with LP-DED manufacture, the triangular profile has been selected for manufacture and response surface generation as detailed in Section 2.3.

3.2 Manufacture of benchmark tools

L-PBF has been used to AM CCCC and NCCC benchmark tools 1 and 2 as per Table 1. While the HM process for the triangular NCCC benchmark tool (Tool 3) was performed using articulation of the benchmark tool, the triangular profile is also manufacturable without part articulation as the MMOA for equilateral triangles is 60° from the horizontal, which are considered self-supporting in LP-DED (Section 1). Similarly, all other NCCC profiles listed in Fig. 5 are LP-DED manufacturable with or without part articulation. However, hybrid machining of the various NCCC may impose different requirements, for example the teardrop channels would require a ball-nosed milling tool, the diamond profile a conical tool and the prismatic pentagon a flat end mill.

The benchmark tool was also able to be machined and checked for tolerances while on the same build plate. This reduces setup efforts and increases the turnaround time compared to a purely AM build using L-PBF.

Figure 14 shows the different stages of HM for the triangular NCCC benchmark tool. Stages (1–4) show the triangular channel being built, taken at different layers. Stage (6) shows the subtractive side of HM wherein the tool is machined to build specifications while it is on the same build plane. The benchmark tool has been prepared using part articulation for building the triangular overhanging edges. The same edge can also be manufactured in a 3-axis machine while building them out as overhangs with the nozzle perpendicular to the build plane.

Finally, differences in the internal channel profiles at the tool inlet for the triangular NCCC builds using LP-DED and L-PBF can be seen in Fig. 15a and b respectively. The inlets were drilled and tapped into the tool at a depth of 10 mm from the side wall. While the LP-DED profile in Fig. 15a is not wholly indicative of the true internal profile, due to melt pool runoff during closing off of the transverse wall, it still provides a clearer idea of the difference in internal dimensional tolerances involved in the two prints. The difference observed between the two channel profiles can be explained by the difference in resolutions of the AM methods. L-PBF has a spot size of 180 μm, whereas the nozzle diameter in LP-DED is 3 mm. This order of magnitude difference in resolution can be seen visibly in the form of unevenness in the profile boundary. Due to the lack of bed support, the LP-DED build is also susceptible to edge defects and runoffs, all of which manifest at the edge of the cooling channel as shown in the figure.

Fig. 15

Visual comparison for the internal channel profile at the tool inlet for the triangular NCCC builds using (a) LP-DED and (b) L-PBF

3.3 Validation and thermofluidic performance comparison of L-PBF and LP-DED manufactured CCC benchmark tools

Figure 16 shows the numerically predicted and experimentally measured temperatures for the CCCC benchmark tools. As also seen in the case of the contour plots in Fig. 11a, the temperature gradient is more closely packed nearer to the MTPI.

Fig. 16

Circular channel validation study: predicted (simulation) and measured (experiment) temperature vs. distance from the MTPI of the benchmark tool

The pressure differential across the inlet and outlet of the channel in the experimental setup for the CCCC benchmark tool was compared against its prediction in the numerical setup. The measured value was 3581 Pa, while the predicted (numerical) pressure drop was found to be 2443.5 Pa. As the CCCC benchmark tool was manufactured using L-PBF, the surface roughness of the channels, while being comparatively lower than that of those manufactured via LP-DED, vary across the channel based on the build inclination angle of segment of the circular profile [48].

The experimental temperature and pressure results coincide well with the numerical results. The disparities and errors have been discussed alongside potential reasons and mitigation strategies.

The variation in temperatures recorded and predicted in Fig. 16 may arise due to errors in the following conditions:

• Disparity in probe thermal behaviour, i.e. air/thermal paste gaps at probe points cause discontinuities in the MTPI temperature distributions.

• Differences in real interface temperatures, as the interface temperature throughout the surface is assumed to be representative of the temperature recorded by a thermocouple placed in contact with the heated bed wall.

• In the simulation, probe locations within the solid are modelled as points and are not modelled as thermocouples placed in cavities due to increased computational expense. Hence, it predicts recorded surface temperatures in the experiments as point temperatures in the bulk material.

• Relatively low resolution of thermocouple, i.e. a durable thermocouple is used due to the harsh operating environment, which was found to necessitate a compromise on both its resolution (± 4 °C) and response time.

• Conduction through thermocouple stem, i.e. stem conduction can affect both steady-state measurements of temperature and sensor response time to temperature changes.

• Simplified wall roughness representation, i.e. the surface roughness in the internal channel, while accounted for in the simulation, might not be an accurate representation of the physical roughness across the channel with uneven distributions relating to bends, angled surfaces and anomalies such as cracks and voids.

• Presence of impurities within the water supply in the form of dissolved salts, all the way up to corrosion debris, may impact the heat carrying capacity of the fluid. These factors are not accounted for in simulations as channel wall surfaces are assumed clean from any depositions, insulating layers or coolant additives.

While the temperature predictions are under or almost equal to 5% (°C/°C) for all the readings, the pressure prediction is more displaced. The variation in the numerical and experimental pressure drop is 1137.5 Pa or 31.7%. This large pressure drop differential can be attributed to the following issues:

• Differences in internal channel dimensions due to the manufacturing methods used. Due to a higher level of unpredictability in printing overhanging structures and the higher powder particle size, this issue arises more commonly for the LP-DED prints compared to the L-PBF prints.

• Wall roughness, i.e. it is higher than the emulated value in the solver due to manufacturing method, therefore pressure loss due to roughness is underestimated in the simulation. This wall roughness is also non-uniform in the printed benchmark tool depending on the local surface inclination relative to the build plate, compared to the numerical model, where the roughness is applied uniformly across the channel walls.

• Additional pressure losses, i.e. coolant supply connections and fitting introduce changes in frictional pressure losses not captured in the simulation.

• Pressure transducer resolution limits, i.e. the pressure transducer compatible with the pressure in the channel has a measurement resolution limit of ~ 1000 Pa and pressure changes below this limit are not reliable. A higher resolution pressure transducer capable of handling the fluid operating pressure in the channel was not available.

Low accuracy of readings seems to be the main reason for this displacement in the two parameters (temperature and pressure) measurements. This can likely be improved with high sensitivity sensors to improve readings and more accurately predict the baseline case to predict external pipe losses.

On confirming the HM process for the NCCC benchmark tool, an experimental comparison was made between the three benchmark tools—L-PBF CCCC, L-PBF triangular NCCC and LP-DED triangular NCCC. The temperature profiles were recorded as shown in Fig. 17. The coolant temperature was recorded to estimate the energy transferred to the benchmark tool as per Eq. (2.2).

Fig. 17

Temperature comparison at different probe points (20, 15 and 10 mm above the MTPI) in the experimental benchmark tools—L-PBF CCCC (tool 1) and equilateral triangle NCCC (tool 2), and LP-DED equilateral triangle NCCC (tool 3)

The temperature and the corresponding energy absorbed per second by the coolant is shown in Fig. 18. Calculations for the coolant power draw in Fig. 18a were made as per Eq. (2.2). The outlet temperature recorded for the triangular NCCC benchmark tool manufactured using L-PBF is higher than that for the CCCC benchmark made using the same AM method. The outlet temperature is also higher for the LP-DED HM tool compared to that of the L-PBF benchmark tool with the same profile. This reflects in the larger power drawn by the coolants in the respective tools.

Fig. 18

a Coolant outlet temperature, along with the corresponding estimated energy absorbed by the coolant per second calculated as per Eq. (2.2). b Differential pressure values between inlet and outlet for the benchmark tools manufactured using different AM methods or with different CCC profiles

Figure 18b shows the differential pressure values for the three benchmark tools. As one may expect, triangular NCCCs experience higher pressure drops across channels compared to CCCCs due to their sharp corners and low aspect ratios. Among the same profile NCCCs, the pressure drop differs for the two different AM tools, with the LP-DED hybrid manufactured benchmark tools having approximately twice the pressure drop compared to that of the L-PBF manufacture tool.

On comparing the heat transfer for the benchmark tools manufactured using different profiles and manufacturing methods, it was observed that LP-DED manufactured triangular NCCCs had the highest rate of heat transfer, and the L-PBF manufactured CCCCs had the lowest. This validates the initial assumption that the triangular channel has improved heat transfer characteristics compared to a circular profile with the same initial conditions. It also pointed towards the fact that increased surface roughness values or difference in build quality seems to affect the thermal performance of the NCCCs more predominantly compared to the profile. Due to the larger roughness values, thermal performance improves for the triangular NCCC manufactured using LP-DED due to increased agitation. Conversely, this also means they suffer from larger pressure drops compared to a smoother L-PBF build, thereby limiting the maximum flowrate available from a given pump.

3.4 Sensitivity and regression analyses

Figure 19 displays the sensitivity analysis, illustrating the varying dependence of different parameters on the heat flux per unit area from the MTPI for each channel cross-section. The sensitivity analysis shows that the performance of channels depends on quite a few factors. Rather than solely depending on the channel and flow characteristics (hydraulic diameter and fluid velocities), the heat transfer depends quite heavily on other tool-specific factors such as channel pitch distance, offset distance and, in some cases, channel length. To maintain a constant heat flux through an NCCC when compared to a CCCC, the most influential parameter was found to be the offset values from the MTPI for both cooling cells. However, it is important to account for their co-dependence on the heat transfer rate with other parameters. The response surface produced to relate the limited controllable different parameters is used to produce equivalent cooling cell parameters which have the same thermal efficacy (heat flux in the present study).

Fig. 19

Heat flux sensitivity tornado chart for the (a) circular profile and (b) triangular profile. MFR is the mass flow rate of the coolant and diameter refers to the SDP in the case of the triangular channel

The channel offset distance has the greatest effect on heat flux within the operating range and is chosen as the influential unknown NCCC parameter for the RMS study. Pitch distance is significant but has limited adjustability due to potential interference with surrounding features. Coolant temperature, although not readily changed in a system along with the mass flow rate, exerts a high level of influence. Surprisingly, the diameter, despite being more easily adjustable, does not exhibit as much influence. Wall roughness, channel length and overhead height have negligible influence and are neglected for RSM regression analysis.

Multiple simulations were conducted, varying key parameters from Fig. 19 based on Section 2.3. Heat flux data was obtained for triangular NCCCs and CCCCs using different parameter settings as per the DoE. Using a matrix solver, β coefficients in Eq. (2.6) were computed. Coefficients for CCCCs and NCCCs are in Table 10.

Table 10 Coefficients of polynomials from RSM quadratic regression results for CCCC and triangular NCCC

The CCCC parametric values generating the RSM predicted heat flux, as well as the simulation predicted values for the final validation test of the regression analysis results, are shown in Table 11.

Table 11 Validation test results for the sample test in Section 2.3

As one can see from Table 11, the error in predictions using the RSM relationship is under 2% for both the CCCC and the NCCC. This points to the RSM model being a good predictor for the adjusted offset value for equivalent CCCC and NCCC systems.

The validation numerical experiment for simulating an IM cycle performance of the two profiles is shown in Fig. 20.

Fig. 20

Numerical validation results for triangular NCCC. The output MTPI temperature contour follows the supplied input MTPI temperature in the CCCC system closely

The regression analysis was successful in providing an equivalent triangular NCCC cooling cell relative to a conventionally defined CCCC with a numerical error of 2%, as shown in Table 11. The resultant NCCC temperature at the MTPI was validated against one from literature, as shown in Fig. 20. The MTPI temperature profile of the NCCC followed the input temperature to the CCCC with minimal error (~ 0.02% RMSE), which validates the RSM for variable MTPI temperatures.

4 Conclusions and future work

A study is performed to observe the manufacturability of IM tools with CCCs using the hybrid manufacturing capability of additive-subtractive hybrid laser powder-based DED with integrated NC based subtractive machining. A benchmark test model is used to observe and compare the LP-DED-manufacturable NCCC profiles and compared to an LPBF manufactured CCCC benchmark tool. The validation study shows good agreement between the numerical and experimental data. However, some factors, such as probe thermal behaviour, thermocouple resolution and surface roughness representation, can affect the accuracy of the results. The pressure drop differential is relatively large, and the displacement between the numerical and experimental data can be attributed to issues such as wall roughness, additional pressure losses and low-pressure transducer resolution limits.

Comparisons are made between different NCCCs and CCCCs through steady-state heat transfer numerical simulations for the benchmark tool. The numerical results show that triangular profiles offer a 15% improvement in the heat transfer rate from the MTPI to the coolant due to the larger surface area exposed uniformly to the heated source compared to other profiles. However, the transition to a triangular NCCC comes with challenges such as increased pressure drops and reduced mechanical strength due to stress concentrations at the profile corners.

The experimental results suggest that HM for IM tooling can be used to manufacture triangular NCCCs, as shown in the benchmark tool. The AM was performed on the inclined faces using part articulation, but the geometry is self-supported, and AM can be performed using overhangs.

In conclusion, the performance of channels in NCCC and CCCC depends on several factors, including tool-specific factors such as channel pitch distance, offset distance and channel length, along with their equivalent diameters and fluid velocities. To maintain a constant heat flux through an NCCC compared to a CCCC, the channel SDP needs to be adjusted while maintaining the same tool and flow parameters. However, a regression analysis is necessary to account for the co-dependence of these factors on net heat transfer. The response surface regression analysis is limited to controllable variables in an ideal tool-design environment, and the diametric variable is observed to have a significant influence on CCC performance, as seen in the sensitivity analysis. Overall, understanding the impact of various factors on heat transfer in CCCs can inform the design of efficient heat exchangers that can be manufactured in a hybrid manner using LP-DED.

Future work involves ensuring the manufacturability of NCCCs using 5/6-axis method is enforced during the design stage to reduce the dependence on overhang angles that would normally be present in 3-axis HM. Another aspect that needs further research is the creation and impact of variable surface roughness of the print at different spatial positions and orientations, as well as the impact of the print parameters on the thermal performance of the resulting IM tool. It also entails recording and comparing the experimental performance of the equivalent NCCCs to the respective CCCCs obtained with the help of regression analysis to further improve confidence in the models. The current study also lacks the impact of changing CCC profiles on the structural and fatigue strength of the tool in a cyclically loaded environment. However, the potential for rapid prototyping of IM tools with CCCs using HM definitely exists and can hold the key for reducing costs and lead times.