Cost-Efficient Injection Mold Design: A Holistic Approach to Leveraging Additive Manufacturing’s Design Freedom Through Topology Optimization

Abstract

Additive manufacturing offers significant design freedom for injection mold tooling, particularly in optimizing cooling performance and reducing mass. This study presents a holistic framework for the topology optimization of mold inserts considering design for additive manufacturing principles, integrating essential boundary conditions from the mold making, injection molding process, and post-processing operations. A slider component with conformal cooling channels serves as the case study. Using simulation-driven design and finite element analysis, two design variants, based on conventional and modified design spaces, were evaluated. Mechanical loads from clamping and the injection process were considered, with safety factors applied to reflect industrial misuse scenarios. The topology optimization process was implemented using Altair OptiStruct and validated through displacement and stress analyses. The results show savings in both mass and costs of up to 60% while maintaining structural integrity under operational and misuse conditions. The maximum displacements—only a 4 µm increase compared to the reference—remained within DIN ISO 20457 tolerances, and stresses did not exceed 170 MPa under operational conditions, confirming industrial applicability. This study concludes with a proposed framework for integrating topology optimization into mold design workflows.

1. Introduction

The cost-effectiveness of the injection molding (IM) process is primarily determined by mold temperature control. Mold temperature control determines, amongst others, cycle time and plastic part quality [1,2]. For this reason, additive manufacturing (AM) has become widely used in tooling applications due to its design freedom, which enables improved cooling channel designs [3,4,5,6]. In addition to this, the development of new tool steel powder materials, with improved material properties such as higher hardness and toughness as well as corrosion resistance, enables its use in highly demanding industrial applications [7,8,9,10,11]. Recent advances in material-specific process parameters and heat treatment routes guarantee almost pore-free additively manufactured parts with material properties like bar stock materials, even regarding polishability [12,13].

As costs for AM parts or inserts are mainly determined by engineering design effort and the production process, they can be reduced through both semi-automated design methods and mass reduction [14]. Since cost sensitivity is particularly high in the AM of mold inserts, both aspects are required. On the one hand, standardized workflows and simulation-driven design approaches are employed to utilize the potential of conformal cooling and to leverage benefits such as reduced cycle time and warpage, thereby lowering IM process costs [15,16,17,18,19,20]. On the other hand, design tools have been developed to minimize the build volume, mass, and production time of AM inserts including topology optimization (TO) [21,22,23] or (graded) lattice structure methods [24,25].

1.1. Literature Review

The literature review analyzes the use of TO methods in mold insert design for both conformal cooling channel design and mass reduction.

1.1.1. TO Methods for Generating Conformal Cooling Channel Designs

The optimization of mold temperature control, utilizing AM’s design freedom for conformal cooling channel designs to improve cooling efficiency, is widely used in industrial applications to lower costs by reducing cycle costs or scrap rates [18,19,21]. In academic research, there are different approaches to optimizing cooling efficiency, using, for example, simple or more complex nature-inspired channel designs such as vascular networks [26], origami-inspired structures [27], or twisted geometries [28]. In addition to channel designs, AM also enables the use of lattice structures, e.g., triply periodic minimal surfaces (TPMSs), for optimizing the thermal management of flat surfaces or heat sinks, for example, in electrical applications [24,29]. Based on a comprehensive review of current developments in conformal cooling channel design generation, Masoudi et al. [26] highlight the importance of automation and optimization algorithms based on part or mold geometry and cooling requirements.

For an automated design of optimal three-dimensional cooling networks, Wu and Tovar [30] and Jahan et al. [31] developed a method that uses a specific thermal fluid TO method. Their approach is mainly limited by the poor balancing of the generated parallel channels. And due to the differences in the individual flow rates, the cooling performance is not sufficient for IM. Liang Wang et al. [27] proposed a more general method for topology-optimized cooling channels with highly parallel-connected channels using origami-inspired geometries. They showed that the computational effort of the three-dimensional TO process for thermal fluid problems can be significantly reduced. The practical use of this method is yet limited by assuming a steady-state process instead of a transient one. In comparison to this, Navah et al. [32] used the porous modeling of conjugate heat transfer to create conformal cooling channel designs. However, the manufacturing constraints of the AM process are not considered in design generation, and high effort is needed for surface reconstruction.

1.1.2. TO Methods for Mass Reduction in Injection Mold Designs

Compared to optimizing the cooling performance of injection molds, approaches to minimizing the mass of parts focus on saving production costs by reducing both production time and the amount of metal powder used. In the field of design for AM (DfAM), there are two different approaches to reducing mass that is not needed for the performance of the mold or insert. On the one hand, there is the classic TO approach [21]; and on the other hand, AM enables the manufacture of lightweight designs using self-supporting, uniform, or graded lattice structures [33,34]. Thus, multifunctional optimized mold designs that account for both structural and thermal loads can be realized by fully exploiting the design freedom offered by AM [25]. In fact, lightweight and cooling-efficient mold designs minimize material and manufacturing costs, as well as energy consumption during the injection process, while maintaining the structural integrity of the mold tool [35].

Several approaches have been proposed to reduce the weight of injection molds and inserts. Sinico et al. [21] developed a TO method for a conformal cooled injection mold (fixed and moving side) that considers thermal constraints and overhang limitations of the AM process. By setting a maximum allowable displacement of 130 µm for the optimized mold under the applied clamping force, they achieved a mass reduction of nearly 50% and a processing time reduction of approximately 43%. The tolerated mold displacement, however, is relatively high compared to the typical manufacturing accuracy in mold making. Moreover, since the displacement in the cavity, and thus the deviation in part dimensions, was not specifically analyzed, compliance with the tolerances defined in DIN ISO 20457 [36] cannot be evaluated. To address uncertainties in the input variables for the TO of injection molds, Hasan et al. [37] proposed a robustness- and reliability-based design optimization method using a multi-cavity mold as a case study. In their approach, in addition to the operating conditions, design variables regarding manufacturing tolerances are also considered in the TO.

The benefits of lightweight mold design using TO methods have also been demonstrated in industrial applications [22,23]. Hartmann-H’Lawatschek [22] developed a mass-reduced injection mold for a fixture application in the optical industry. By implementing a seamless digital process chain, the weight of the mold was reduced by 50% (~30 kg). The high mass savings were achieved through a reduction in the number of parts to one on each mold half, namely the fixed and moving sides. However, because of this, the approach is limited to simple molds without moving parts such as sliders. PROTIQ GmbH [23] demonstrated the potential of AM injection molds by combining conformal cooling and TO-enabled mass reduction. As a result, the weight of the mold was reduced by 75%, and 25% of the production costs were saved.

In addition to TO methods, the utilization of lattice structures is continuously increasing in additively manufactured lightweight designs. In the field of mold design, Šakalys et al. [35] presented a design methodology for inserts that utilizes gradient body-centered cubic lattice structures. They employed a field-driven design approach based on a static finite element analysis (FEA) within the defined non-design space. By applying their method for generating density gradient lattice structures to an injection mold, they achieved mass reductions of approximately 22% and 24% for the moving and fixed sides, respectively (~0.91 kg on the moving side and 0.89 kg on the fixed side). In addition to mass savings, the design also affects the thermal performance of the mold. The optimization results of Šakalys et al. indicate that the mass-optimized mold exhibits a less homogeneous cavity wall temperature distribution compared to the solid mold design when using a cooling medium temperature of 90 °C. The non-design space around the cooling channels was set to only 5 mm. The higher ΔT on the cavity wall results in a greater deviation of the nominal plastic part geometry. However, the reliability of the mold was validated, since after 1500 IM cycles, the mass-reduced mold showed no defects.

Park et al. [38] investigated the potential of mass reduction in injection molds using the LPBF and Ti-6Al-4V powder material. Based on an analysis of the mechanical performance of the lattice structures under compressive load, they developed a lightweight mold design for producing a simple PVC part. The developed lattice design enabled a mass reduction of approximately 79% compared to the solid mold design. In IM tests, 400 parts were produced without any damage. However, no investigations were conducted regarding the impact on the thermal mold behavior, cycle time, or part quality.

A methodology for the design optimization of plastic injection molds considering both thermal and mechanical performance to achieve better cooling performance and lower AM production costs, was proposed [16,39,40]. The approach is based on a combination of a thermomechanical FE model and a multiscale thermomechanical TO using lattice structures. However, since the manufacturing constraints of the LPBF process were not considered in the optimization, extensive manual work was required to reconstruct the 3D models for the AM process. Wu and Tovar [41] further developed this multiscale thermomechanical TO approach. They designed a conformally cooled, weight-optimized insert design using graded lattice structures based on experimental studies analyzing both the mechanical and thermal properties of the AM-processed structures. Consequently, the mass of the insert could be reduced by approximately 25%.

1.1.3. TO for Additive Manufacturing

TO has been extended towards manufacturability considerations in conventional manufacturing processes, utilizing density-based, level-set or binary/discrete formulations [42,43,44]. In contrast, AM fundamentally alters the design freedom by enabling layer-wise fabrication and thereby alleviating many of the geometric constraints traditionally imposed on TO. Nevertheless, AM is subject to its own set of process-specific constraints, which need to be explicitly integrated into the optimization framework to ensure designs that are not only structurally efficient but also readily manufacturable without extensive manual post-processing.

Liu and Ma [42] performed a survey on manufacturing-oriented TO methods. The study highlights key challenges, such as ensuring part buildability, restricted minimum component or feature sizes, and non-manufacturable interior voids related to TO in AM. They pointed out that the control of minimum and maximum feature sizes, such as wall thicknesses, has already been widely addressed in TO for conventional manufacturing.

The necessity of integrating manufacturability constraints into TO for AM is also emphasized in the survey by Liu et al. [45]. They specifically stress part buildability aspects through overhang restrictions and connectivity requirements aimed at preventing non-manufacturable interior voids. The authors further identify one main gap for an efficient use of TO, namely the lack of standards for describing individual constraints and for testing the threshold values or parameters for specific materials and machines.

Regarding part buildability, two main approaches can be distinguished [46]. One is to apply overhang angle constraints to obtain self-supporting designs. According to Liu et al. [47] and Zhu et al. [48], overhang limitations can be incorporated through density-projection schemes in the context of density-based TO [49,50], or by explicitly formulating them as constraints within the optimization problem (e.g., [51]). Density-based filter approaches have also been adopted in commercial software, such as Altair OptiStruct [50,52], underlining their practical relevance for the design of self-supporting structures.

Alternatively, overhanging areas can be stabilized by adding support structures. However, the associated drawbacks in terms of the post-processing effort and material consumption have motivated strategies such as optimized build orientation [53,54] and the integration of the support volume as either a constraint or an objective to limit or minimize its extent [55,56], and also accounting for thermal deformations (e.g., [57]).

An integrated topology and build orientation optimization method was proposed by Crispo and Kim [58], incorporating overhanging areas and build height to better reflect manufacturing costs. Thereby, a novel build height calculation and overhang area formulation were used. The approach demonstrates a trade-off between overhang area and build height. Validations on academic models and slicer verification showed print time reductions of 27% compared to optimization of the overhang area alone.

Interior voids, for instance, can lead to material entrapment in powder-based processes or to support structures that cannot be removed. Consequently, various constraints have been investigated in the context of TO. Liu et al. [59] proposed a method that incorporates a dedicated powder removal passageway to prevent powder entrapment within internal voids. The passageway is generated by sequentially connecting the inlet, the voids, and the outlet, with each void restricted to a single pair of inlet and outlet to ensure a continuous flow path. Its trajectory is optimized to minimize the impact on stiffness.

Complementarily, Zhou and Zhang [60] introduced a constraint scheme that employs void features as design primitives. By bounding the design variables associated with the void centers outside of the design domain, structural connectivity is maintained without the need for additional constraints, effectively eliminating enclosed voids.

In the context of self-supporting voids, Wang et al. [61] presented an approach in which both the part and its support structures are optimized simultaneously. The method ensures that the overhangs are either self-supporting or stabilized by supports placed in accessible regions, while enclosed voids remain self-supporting.

1.2. Analysis of Research Gaps and Aim of This Work

The literature review reveals that several studies have addressed TO in the context of injection molds, focusing both on the generation of conformal cooling channel layouts and on mass reduction. Although practically and industrially validated lightweight molds have already been introduced [22,23], these approaches are limited to simple mold geometries and, thus, also to simplified boundary conditions and loads. Furthermore, maximum displacements or misuse cases have not been reported in these studies. Moreover, compared to the optimization of cooling channel designs, the topic of mass reduction, particularly under consideration of specific manufacturing constraints associated with AM processes remains insufficiently investigated in the context of mold design.

This study therefore aims to present a holistic methodology for the TO of injection molds and mold inserts, outlining a standardized workflow that incorporates the essential boundary conditions and loads derived from the IM process and post-processing operations such as machining. Furthermore, this work demonstrates the benefits of tool optimization in terms of mass reduction and cost savings by using a slider component with complex boundary and load conditions as a case study, applying DfAM principles regarding the minimum required design space. The technical feasibility of the optimized design, including potential misuse scenarios relevant to industrial applications, is validated through FE analysis. Finally, based on the findings, recommendations and a conceptual framework are proposed to systematically integrate the potential for TO-based mass reduction into the design process of injection molds.

2. Materials and Methods

The following section outlines the key data and process steps required to implement the TO of the injection mold component or insert. This study takes a systematic approach to the weight optimization of an additively manufactured slider with integrated conformal cooling channels. Figure 1 summarizes the input data used for the TO. This methodology considers the mechanical loads resulting from both the operational conditions during the IM process and post-processing operations such as machining and heat treatment. In this work, two design variants are investigated: one based on the conventionally manufactured slider design space, and another with a modified design space developed in accordance with DfAM principles.

2.1. Materials

The following sections provide the background information necessary to understand this work. They include details on the injection mold and the IM process, the AM process, and the powder material used. Additionally, the boundary conditions, loads, and manufacturing constraints considered in the TO are described.

2.1.1. Injection Mold

The injection mold used in this study is shown in Figure 2a. It was designed to produce a cup with a shot weight of approximately 78 g (see Figure 2b). The plastic parts are produced using an Arburg 470 S (ARBURG GmbH + Co KG, Loßburg, Germany) injection molding machine with a maximum clamping force of 1000 kN. The cup is molded using Moplen EP448T, a nucleated polypropylene resin supplied by LyondellBasell, with a density of 0.9 g/cm³ and a melt flow index of 48 g/10 min (measured at 230 °C under a load of 2.16 kg) [62].

The cup has a slightly conical outer surface featuring diamond-shaped elements and a functional microstructure that has been incorporated using Femto-laser technology to provide a soft-touch feel. These elements enhance the product’s esthetic appeal and its functional grip. The wall thickness is uniformly 3 mm, except in the areas of the diamond pattern and in the snap groove below the inner lip, where it is reduced to 2.5 mm.

Due to the intricate surface geometry and functional texture, a slider-based mold design was required for demolding. The cavity is formed by the gate bushing on the fixed mold half, while the moving half comprises the slider, the core and the stripper plate. To accurately replicate the surface texture on the slider surfaces, it is essential to maintain a homogeneous cavity wall temperature of 40 °C and a sufficiently high packing pressure of approximately 400 bar. To minimize the cycle time, particularly given the relatively high wall thickness, and to reduce part warpage, conformal cooling is implemented in all cavity inserts.

Figure 2c shows the conformal cooling layout within the two slider components, which was designed using a semi-automated approach that ensures a uniform distance between the cooling channels and the cavity wall. The channels have a diameter of 5 mm and are positioned 3 mm from the cavity surface. An inner and an outer channel are connected in parallel to reduce the overall channel length and to ensure sufficient coolant flow at a reduced pressure of 3.5 bar from the temperature control unit.

Compared to conventional cooling channel layouts, the use of conformal cooling significantly reduces the installation space required, which would otherwise constitute non-design space. The sliders have a relatively large overall volume compared to the gate bushing and the core. Therefore, the weight of these components was selected for optimization in this study.

2.1.2. Additive Manufacturing

For the AM laser powder bed fusion (LPBF) process, the powder material Uddeholm Tyrax^® for AM (Uddeholms AB, Hagfors, Sweden) was used on an EOS M290 (EOS GmbH, Krailling, Germany) printer. The LBPF process parameters for Tyrax for AM, listed in

Table 1. LBPF basic process parameters for Uddeholm Tyrax^® for AM [13].

Machine	Protective Gas	Layer Thickness	Laser Power	Scan Speed	Hatch Distance	Hatch Mode	Build Plate Temp.
EOS M290	Argon	60 µm	338 W	1008 m/s	0.094 mm	Stripes 9.75 mm	200 °C

, were internally optimized to achieve mechanical properties comparable to those of bar stock material.

The printed inserts are characterized by high hardness and toughness, as well as good corrosion resistance and excellent polishability, resulting from a high part density of 99.997%. The material properties listed in

Table 2. Mechanical properties in vertical direction and thermal properties of Uddeholm Tyrax^® for AM [13].

Elastic Modulus E	Yield Strength Rp0.2	Tensile Strength Rm	Elongation A5%	Thermal Conductivity κ
209 GPa	1600 MPa	1830 MPa	13%	22.3 W/(m·K) at 20 °C

are measured after direct tempering heat treatment at 560 °C for 2 × 2 h, resulting in a hardness of 55 ± 1 HRC.

2.2. Methods

The following sections outline the load and boundary conditions and the methodological framework employed to implement the TO process.

2.2.1. Injection Molding Process

For the TO, the forces acting on the mold during the IM process must be known. For this purpose, the filling and holding pressure phases are relevant and were simulated using the IM simulation software CADMOULD V17.1 (SIMCON kunststofftechnische Software GmbH, Würselen, Germany). The parameters listed in

Table 3. Injection molding parameters used for injection molding simulation analysis.

Filling	Packing	Cooling	Demolding	Melt Temp.	Medium Temp.
1.6 s	19 s 400 bar	25 s	4 s	230 °C	Gate Bushing: 20 °C Core: 20 °C Sliders: 40 °C Mold Base: 40 °C

were obtained from a sensitivity analysis and subsequent optimization aimed at minimizing warpage in the critical part dimensions, using the AI-based tool VARIMOS integrated within CADMOULD [63]. Minimum warpage is achieved with different medium temperatures applied in the different conformally cooled, additively manufactured cavity inserts.

Due to the high wall thickness (3 mm) of the analyzed plastic part, the relatively long injection time, and the high melt flow index of the polymer used [62], the maximum filling pressure is only 36 bar. The maximum pressure on the cavity wall builds up during the packing phase, reaching a maximum of 370 bar at around 4 s at the end of the fill phase (see Figure 3, right). The high wall thickness of the plastic part enables effective pressure transmission, resulting in a uniform pressure distribution within the cavity at the beginning of the packing phase (Figure 3, left).

As the plastic part continues to solidify, the pressure increases to a maximum of 396 bar at the gate point at the end of the packing phase. The high wall thickness indicates that the part is ejected with a residual cavity pressure of approximately 200 bar. The simulated cavity pressure corresponds to a minimum required clamping force of 314 kN.

2.2.2. Formulation of TO Problem

To analyze the potential for weight reduction through TO, the slider and its base body were examined. In the original mold design, the slider consists of a conventionally manufactured base body and an additively manufactured insert with conformal cooling channels (see Figure 4, left). The two bodies are joined by four screws and a mating surface. In the following, two TO problems are formulated to compare the results in terms of the potential for weight reduction as well as production time or cost.

Figure 4 illustrates the two design variants selected for TO. The central image shows the configuration based on the original design space, whereas the right-hand image depicts the reduced design space, which was derived from the conformal cooling requirements and mold boundary conditions. By consolidating the slider and the base body into a single component, the overall design space can be significantly reduced, as additional allowances for assembly and mating surfaces are no longer required. This integration results in a 48.6% reduction in the required design volume.

To structure the present optimization problem with the objective of mass reduction while ensuring efficient AM, the “Three-Columns-Concept” proposed by Eschenauer [64] was applied. According to this concept, structural optimization problems can be classified into three columns: the structural model (Column 1), the optimization model (Column 2), and the optimization algorithm (Column 3). The structural model allows the prediction of the physical behavior of a design, for example, with respect to stresses or displacements. The optimization model comprises the design variables to be varied, the objective function, and the constraints, which may be structural–mechanical (e.g., maximum stresses or displacements) or manufacturing-related. A suitable optimization algorithm is then combined with both the structural and the optimization model to form an optimization procedure, ultimately yielding an optimal design.

The structural FE model used for the TO was preprocessed in Altair HyperMesh (release 2022.1) and ANSA (BETA CAE Systems, release v 24.1.0). The geometry was discretized using tetrahedral elements with an average edge length of 1 mm. The considered loads include the clamping force, the IM process pressures, and the machining forces. These forces and pressures were applied to the corresponding surfaces using PLOAD4 definitions. Figure 5 shows the applied boundary conditions and loads related to the structural model (Column 1).

During the design process, subsequent process data can be derived from simulations and used for the optimization. Additionally, potential misuse cases are either directly considered or covered by applying appropriate safety factors. To ensure that movement-relevant surfaces are connected to the main slider body structure, dummy loads are defined.

Although the required clamping force derived from the IM simulation is 314 kN, most IM machines are operated at their maximum clamping force to avoid burr [65]. Since the mold is designed for a 1000 kN machine, the maximum clamping force, instead of the simulated force of 314 kN, is considered to account for potential operator misuse, where the mold might be subjected to the full clamping load. Applying an additional safety factor of 1.5×, the resulting clamping force F_c is set to 1500 kN.

In slider molds, the clamping force acts on two perpendicular parting planes. The main parting line is aligned perpendicular to the direction in which the mold closes. The second parting plane is formed by the jaws (see Figure 6). According to Hopmann et al. [66], the clamping force acting on this second parting line can be calculated as follows:

$${\mathrm{F}}_{\mathrm{sy}}= {\displaystyle \frac{{\mathrm{F}}_{\mathrm{c}}}{\tan \mathsf{\alpha }}}$$

(1)

When the friction between the flat guide and the slider body is also taken into account, the friction coefficient μ [67] must be considered:

$${\mathrm{F}}_{\mathrm{sy}}= -{\displaystyle \frac{{\mathrm{F}}_{\mathrm{c}}·(\mathsf{\mu }·\sin \mathsf{\alpha }-\cos \mathsf{\alpha })}{\mathsf{\mu }·\cos \mathsf{\alpha }+\sin \mathsf{\alpha }}}$$

(2)

The lubricated steel-on-steel contact between the flat guide and the slider body was characterized by a static friction coefficient of µ_1–6 = 0.15. The total clamping force is divided by the number of sliders. With a wedge angle of 70°, the resulting clamping force in the slider parting plane is F_sy = 446 kN. Based on this, the clamping force F_C can be decomposed into a normal component (F_N) and a tangential component (F_T) using the principle of a force parallelogram, in order to model the load transfer on the respective load surfaces (see Figure 6). Due to the mold design, the slider is supported in both the x- and the y-directions. The movement of the slider generates a reaction force at the sliding interface between the angle pin and the slider body (A₄, µ₄), which is represented by a gravitational force in the model. This approach ensures that the non-design space associated with the internal guiding mechanism remains structurally connected to the slider body during mass reduction in the TO process.

In the IM simulation, a maximum cavity pressure of 396 bar was observed near the gate. Rather than applying the localized pressure distribution across the cavity surface, this peak pressure value was uniformly applied to the entire surface area. Given the complex geometry and microstructural features of the final plastic component, a higher packing pressure reserve was required to ensure adequate moldability. Consequently, the pressure input for the TO was conservatively increased by a factor of two, and an additional safety margin was incorporated. The resulting cavity pressure considered for the TO was therefore set to p_cav = 960 bar.

To enable precise milling operations, the slider must be securely clamped in a precision machinist’s vise. The slider base, which moves within the guide rails of the mold, was defined as the clamping surface for all milling steps. Such vises typically provide clamping forces in the range of 10–30 kN. In this study, a clamping force of F_m = 20 kN was selected to ensure reliable fixation of the slider while avoiding deformations that could compromise machining accuracy.

The water pressure in the conformal cooling channels was not considered, as it is two orders of magnitude lower than the other applied loads (3.5 bar vs. several hundred bar). To ensure the structural connection of the moving planes during optimization, dummy loads of F_con1 = 5 kN were applied to the lateral moving connections of the slider, as well as to the guiding pin (F_con2).

Table 4. Overview of loads from IM process simulation and considered loads in the TO with corresponding safety factors.

	IM Machine Clamping Force (Fc)	Cavity Packing Pressure (pcav)	Cooling Medium Pressure	Machinist Vise Clamping Force (Fm)	Moving Connections (Fcon1/Fcon2)
IM process simulation	1000 kN	max. 400 bar	3.5 bar
Machining				20 kN
Considered Loads in TO (Safety Factor)	1500 kN (×1.5)	960 bar (×2.4)	-	20 kN	5 kN/8.55 N

summarizes the loads considered for the structural model.

Based on this, two load steps were defined for the analysis model. Load case 1 represents the combined effects of the IM machine clamping force, the cavity packing pressure, and the dummy loads, whereas load case 2 corresponds to the clamping force applied during milling as part of the post-processing of the additively manufactured component.

The TO was performed in Altair OptiStruct (release 2022.1), which employs a density-based formulation, namely the SIMP method. In this approach, each finite element (FE) represents a continuous design variable that can vary between zero and one, where the value of one corresponds to solid material and zero corresponds to void. In this context, the following optimization model (Column 2) was established. Figure 7 illustrates the design space, in which the design variables are allowed to vary, as well as the defined non-design space. The non-design space includes, on the one hand, the surfaces on which the different loads, such as clamping forces, are applied, and on the other hand, those that are connected to other components, such as the guiding surfaces at the bottom. For all these surfaces, a wall thickness of 4 mm was used. Conversely, the volumes required for the conformal cooling channels were defined as a non-design space. The conformal cooling channels, each with a diameter of 5 mm, are positioned equidistant from the cavity surface at 3 mm. To ensure a robust connection of the topology-optimized structure and to reduce heat transfer to the environment by convection, a wall thickness of 8 mm was chosen behind the cooling channels.

The objective was to minimize weighted compliance considering the two load cases. Since load case 1 represents the dominant loading condition, load case 2 was weighted by a factor of ten to ensure structural connectivity of non-design regions that are not directly aligned with the main load path.

A volume fraction constraint of 0.55 was imposed on the original design space and 0.75 on the modified design space. To avoid non-manufacturable fine geometric features, a minimum length scale control of 6 mm was defined. Furthermore, to prevent the need for support structures, an overhang angle constraint of 30° relative to the build direction (z-axis) was applied, using the constrained approach (cf. [52]) with large step length control and the RAMP penalization scheme. To exploit geometric symmetries and reduce computational cost, pattern grouping with a single plane of symmetry in the x–z plane was introduced to the TO formulation.

To solve the optimization problem, the gradient-based algorithm DUAL2 (enhanced dual optimizer based on separable convex approximation) implemented in Altair OptiStruct (release 2022.1) was utilized (Column 3).

For the interpretation of the optimization results, the element densities were converted into a geometric representation using the OSSmooth tool in Altair HyperMesh (release 2022.1). A density threshold of 0.5 was applied, such that elements with higher densities were considered solid, whereas those below this value were treated as void, resulting in smooth iso-surfaces for design evaluation.

3. Results

The results obtained by following the methodology described above are presented in the following sections. Section 3.1 highlights the savings achieved by applying the proposed TO method, while Section 3.2 presents the design validation performed via FEA.

3.1. Results of the Topology Optimization

Figure 8 illustrates the smoothed surface reconstruction resulting from the topology-optimized sliders. The structural integrity and functionality of the slider were maintained. The functional surfaces within the non-design space are structurally connected through the modified design space.

Material distribution is primarily concentrated in the upper cavity section, driven by the clamping force and the cavity pressure acting in this region. In contrast, the sliding connections are subjected to lower loads, resulting in significant material reduction, especially within the previously defined design space. On the side of the slider facing away from the cavity, the material savings in the original design space are comparable to those in the modified design space, as no loads are acting in this area.

After surface reconstruction, the cooling channels in the non-design space were manually routed in the CAD model through the design space to the original water connections, maintaining a wall thickness of 5 mm around each channel. This approach provided greater flexibility for the TO process.

Table 5. Comparison of TO results with savings in mass, costs, and production time compared to their non-TO reference designs.

	TO Design with Original Design Space	TO Design with Modified Design Space
Mass non-TO start design	21.50 kg	10.13 kg
Mass of design space	17.45 kg	7.30 kg
Mass of TO design Total mass reduction	14.50 kg 32.6%	8.44 kg 16.7%
Production time reduction	30.3%	16.0%
Production cost reduction	30.9%	16.2%

provides an overview of the savings achieved through TO for the two variants. As expected, the topology-optimized design based on the original design space shows higher mass savings (32.9%) compared to the TO design with the modified design space (16.7%) due to the larger volume of the design space. Nevertheless, the reduction in production time is significant in both cases, amounting to 30.3% and 16.0%, respectively. The production time refers solely to the estimated duration of the AM build process, as calculated by the build preparation software. The production costs include machine hours and material consumption.

Table 6. Overview of the savings achieved by the TO design variants compared to both the original hybrid slider variant and the non-optimized design with the original design space.

	Comparison to Original Hybrid Slider Design		Comparison to non-TO-Design with Original Design Space
	Production time	Production costs	Production time	Production costs
TO design with original design space	-	+24.0%	−30.3%	−30.9%
TO design with modified design space	-	−26.8%	−58.8%	−59.2%

compares the two topology-optimized designs to the original hybrid slider design and the non-TO design with the larger original design space, with respect to production time and costs. The results demonstrate that TO significantly reduces mass and, consequently, the production time by 30.3% and approximately 58.8%, respectively, compared to the non-To design with the original design space. When comparing production costs, it becomes evident that the TO design based on the original design space is 24.0% more expensive than the hybrid slider design with a conventionally manufactured slider body (see Figure 4, left). This increase is attributed to the large build volume, which is determined by the boundary conditions of the mold design. However, when the potential of TO is considered holistically and integrated at the early stages of the mold design, the cost of the insert can be significantly reduced. The topology-optimized design with the minimum required (optimized) design space shows a notable decrease in production costs of 26.8%.

3.2. Finite Element Analysis and Design Validation

To ensure the reliability of the topology-optimized designs and to assess their suitability for practical application in injection molds, a FEA was performed. Two load cases were considered for this purpose, using the loads summarized in

Table 7. Overview of loads considered in the FEA for TO design validation regarding maximum displacement and maximum stress.

	IM Machine Clam-ping Force (Fc)	Cavity Packing Pressure (pcav)	Machinist Vise Clamping Force (Fm)	Moving Connections (Fcon1/Fcon2)
Maximum displacement	600 kN (µ = 0.15)	400 bar	20 kN	5 kN/8.55 N
Misuse case, maximum stress (considered safety factor)	1500 kN (×1.5)

.

First, the maximum displacement of the mold insert was evaluated under realistic operating conditions, including clamping forces and pressures applied to the cavity surface. The maximum allowable displacements are derived from the tool-specific tolerances defined in DIN ISO 20457 [36].

In the second step, a misuse scenario was analyzed, representing a situation in which the operator applies the machine’s maximum clamping force instead of the process-specific required force. This case was included to ensure that the maximum stress in the topology-optimized slider does not exceed the material’s yield strength, even under unintended overload conditions.

3.2.1. Analysis of Maximum Displacement Under Operational Conditions

For the analysis of the maximum displacement of the optimized slider design, the loads from the IM process using Moplen EP448T [62] with the non-optimized slider design were used (see Table 7). Compared to the IM process simulation, the clamping force was set to 600 kN compared to 314 kN. Additionally, the clamping force from the machinist vise was applied to verify whether the allowable stresses in this area were exceeded. Based on preliminary analyses, it was concluded that the frictional contact between the stripper plate and the slider, as well as between the gate bushing and the slider, could be neglected in the maximum displacement FEA, as the resulting deviation was less than 10%. This aspect is further discussed in Section 3.2.2. To reduce computation time, these contact surfaces were fixed in the subsequent FE simulations.

To ensure proper mold functionality, the stiffness of the topology-optimized design variants must be sufficiently high to keep deformations within the specified tolerance limits. In this context, the displacement in the x-direction within the parting plane primarily determines the formation of burrs, whereas the radial displacement relatively to the radius defines the dimensional deviation on the outer diameter of the molded part, specifically on the top surface of the cup, and thus affects the fit of the lid.

For this reason, it is necessary to ensure that no burrs form along the parting line. According to Hopmann et al. [66], the maximum permissible gap before burr formation in low-viscosity polymers, such as thermoplastic elastomers, is less than 3 µm. This implies that the displacement in the x-direction per side—or slider—must not exceed 1.5 µm.

To evaluate this, a simulation model is used that includes the slider pair with appropriate contact conditions, allowing the transitioning from adhesion to sliding under load. Figure 9 illustrates the displacement along the parting line for one of the topology-optimized sliders with the modified design space, which is considered the most critical case in terms of deformation. The results show that the maximum displacement in the x-direction is approximately 0.1 µm when applying a clamping force of 600 kN and a packing pressure of 400 bar on the cavity surface (see Table 7), which is significantly below the allowable limit of 1.5 µm. Therefore, burr formation is not expected in the topology-optimized variants. The subsequent analysis focuses on the deformation within the cavity to assess potential shape deviations of the molded plastic part.

Based on DIN ISO 20457 [36] and considering the nominal size range corresponding to the outer diameter of the cup (80 mm), the maximum acceptable deviation is ±0.037 mm for tolerance grade 1 (TG1) and ±0.06 mm for tolerance grade 2 (TG2). Due to the requirements for a tight snap-fit connection and the need for a visually perfect fit between the cup’s outer diameter and the lid, the part is classified under TG2. Accordingly, for the slider component, the maximum allowable displacement per side, using the center axis as reference, must not exceed 30 µm.

Compliance with the maximum permissible displacement in the cavity area was verified using the results of the FEA shown in Figure 10. The displacement evaluation was carried out for the round cup geometry in cylindrical coordinates, both in the radial direction and along the z-axis at the cup center. As previously described, the sliding contact between the slider and the stripper plate, as well as the gate bushing, was suppressed to simplify the model. This results in the main deformation occurring along the cavity circumference. The deformation in the z-direction is primarily concentrated in the region where the clamping force is introduced, at the upper end of the slider. For the variants with the modified design space, the maximum displacement is −12 µm, which is slightly higher than that of the original design space variants (−9 µm). This difference can be attributed to the reduced wall thickness in this area.

Since the closing force is applied laterally to the upper half of the slider, a maximum radial deformation of 15 µm occurs in the direction parallel to the parting line both in the non-TO design and in the TO design with modified design space. This value is higher than the deformation in the direction orthogonal to the parting plane, which is approximately 10 µm, where the clamping force is introduced over the entire height on the back side of the slider. When comparing the topology-optimized variant with the non-TO design, it becomes apparent that, while the maximum displacement remains unchanged, the region exhibiting the highest displacement increases as a result of the optimization. A similar trend is observed for the variant based on the original design space, although the maximum displacements are slightly lower, at approximately 11 µm. Overall, the TO results in only a slight increase in deformation under the given load and boundary conditions. Both topology-optimized designs meet the required tolerances for TG1 according to DIN ISO 20457 [36]. Due to the higher residual wall thickness in the non-design space of the variant based on the original design space, the maximum deformation is approximately 4 µm lower. This difference is more dominant in the direction parallel to the parting line (x-direction) than in the orthogonal direction (y-direction).

The deformation pattern observed in all variants results from the superposition of the laterally acting closing force applied to the upper part of the slider via the slider supports and the packing pressure, which also acts on the entire surface in the indirectly supported regions (see Figure 11). It becomes evident that the clamping force alone compresses the upper part of the slider radially by up to −21 µm. This deformation is largely compensated by the packing pressure. In the lower region, the displacement is smaller, with a maximum of −11 µm, indicating an outward movement caused by the packing pressure. The displacement in the z-direction across the cavity surface is predominantly governed by the clamping force in both load cases considered.

Orthogonal to the parting plane (x-direction), the highest displacements occur in all variants in the region where the cooling circuits converge, representing the least supported area (Figure 10, r-direction). In this zone, a displacement of up to 11 µm is observed, which is comparable to the displacements in the outer areas. However, the stress analysis in the cooling channels shows, that despite the displacements, the maximum stresses remain below 250 MPa, confirming that the 3 mm distance between the cooling channels and the cavity surface is sufficient to ensure the mechanical stability of the cavity.

3.2.2. Analysis of Maximum Stresses in the Misuse Case

In addition to the displacements, the maximum stress is a critical factor in developing a reliable, industry-ready, mass-optimized mold insert design. The objective of this analysis is to ensure that the slider does not fail under critical loading conditions. Two cases were considered: a misuse scenario and regular operating conditions. For simplicity, only quasi-static loading was analyzed, and thermal effects were not included. To obtain a conservative yet valid assessment, the stress was limited to 50% of the material’s yield strength (R_p0.2), corresponding to 800 MPa (see Table 2).

To evaluate whether the boundary conditions in the FEA could be simplified, a comparative simulation was performed using both frictional contacts and fully constrained degrees of freedom (DOFs) at the contact surfaces (see Figure 12). The left side of the figure shows the resulting stress distribution when considering frictional contact between the slider, the gate bushing, and the stripper plate. The right side of Figure 12 displays the stress distribution obtained with locked DOF at the contact interfaces. The comparison reveals that, aside from local stress peaks, the overall stress distribution remains very similar, allowing for a justified simplification of the model. In the case with locked DOFs between the slider and the gate bushing (Figure 12, right), local stress concentrations of approximately 650 MPa occur at the lower edge due to excessive element distortion caused by a localized contact-model artifact—effects that would not realistically appear in practice. However, the defined stress limit of 800 MPa is not exceeded. Under operational conditions, the highest stress levels, ranging from approximately 250 to 280 MPa, are observed in the upper cavity region and along the outer wedge surfaces.

The misuse scenario illustrated in Figure 13 represents a practical case in which the operator applies the machine’s maximum clamping force during setup, spotting, or surface matching of the mold components. The topology-optimized insert must withstand this load without failure. To simulate this condition, the maximum clamping force was increased by a safety factor of 1.5, resulting in a total load of 1500 kN. The boundary conditions are identical to those described in Section 3.2.1. Figure 13 presents the results of the misuse scenario, comparing both optimized designs with their respective reference models. The results indicate that the maximum stress in the cavity area remains well below the allowable limit of 800 MPa, while the stresses in the cooling channels do not exceed 250 MPa. As described above, the localized stress peaks at the lower edge of the contact between the slider and the gate bushing are excluded from the interpretation due to the chosen boundary conditions. For this reason, the analysis focuses on the cavity region. Compared to the reference models, the stress distribution in the cavity region of the optimized variants shows only a slight increase relative to the non-TO designs. As expected, the mass reduction primarily occurs in low-stress regions between the non-design area of the cavity and the rear slider support. The variants with reduced design space, the two left-hand models in Figure 13, exhibit higher maximum stresses in the clamping force application area, which is expected due to lower residual wall thicknesses. However, these stresses remain non-critical at approximately 280 MPa, well below the limit of 800 MPa.

Figure 14 shows the von Mises stress distribution under mechanical operating loads without safety factors, including a clamping force of 600 kN and packing pressure of 400 bar, which were also used to determine displacements in Section 3.2.1. Only the optimized design with modified design space is shown, as it represents the most critical case. The results indicate that a maximum stress of 170 MPa occurs in the region behind the cavity, while the maximum stresses within the cavity area remain below 100 MPa. As these values are well below the defined limit of 800 MPa, the stresses can be considered non-critical. This confirms that the topology-optimized designs possess sufficient structural strength for industrial application.

4. Discussion

Based on a universally applicable framework for tool design and incorporating comprehensive boundary conditions, the TO was performed with an unprecedented level of detail. Rather than analyzing a simple two-plate mold (e.g., [21,35]), the complexity was increased by examining a slider from a jaw-type mold, which features more intricate tool kinematics and a more complex clamping force distribution.

In addition to redesigning the original design space of an existing mold insert, a second variant was developed considering DfAM principles to minimize the required design space. This variant featured a modified design space and demonstrated significant additional potential for savings in both mass and cost. By applying TO in combination with DfAM principles, a mass reduction of up to 60.7% and a cost reduction of 59.2% were achieved while maintaining defined displacement limits.

Regarding mechanical stability, the optimized variants exhibited only marginally higher displacements, approximately 4 µm under process conditions, compared to the reference designs. Using the presented approach, a significantly stiffer design was achieved compared to previous investigations, such as [21], ensuring compliance with plastic part tolerances according to DIN ISO 20457 [36]. Even under the investigated misuse scenario, which is highly relevant for the industrial application of TO-based inserts, the resulting stresses remained below the assumed fatigue strength limit of 800 MPa. Under operational conditions, the maximum stresses reached only 170 MPa, confirming the long-term structural integrity of the designs.

It should be noted that practical validation through IM trials is still pending. However, a sectional model of the optimized design was additively manufactured using the original design space (Figure 15), and no manufacturability issues were observed.

The presented approach accounts for the boundary conditions of both the mold design and manufacturing phases. However, certain simplifications were necessary. For example, the pressure distribution during the injection and packing phases was assumed to be constant across the entire cavity surface as a worst-case scenario. To obtain more accurate load boundary conditions, the maximum cavity pressure distribution during the IM process should be applied to define the process loads. Currently, IM simulations provide the pressure distribution only at certain time stamp. To reduce the number of load cases, the maximum load acting on each surface element of the cavity throughout the entire cycle could be used. Furthermore, the resulting part quality was evaluated solely based on mold displacements, without additional validation through coupled thermal–mechanical simulation to account for potential changes in cavity wall temperature distribution (see [35]).

The results obtained, both from the overall process and from the individual steps of the methodology, can serve as input for subsequent design iterations. Figure 16 illustrates the workflow of a continuous optimization framework that considers all relevant boundary conditions. Based on the inputs from the various phases of tool development, as well as the consideration of machining and IM parameters, corresponding data are derived to define the design spaces and performing TO. The methodology also incorporates feedback loops between the individual steps, with the goal of achieving the required part quality.

As illustrated in the framework, an IM simulation incorporating the topology-optimized sliders should be carried out to ensure part quality. The objective is to identify and evaluate potential process influences resulting from the reduced mass. Particular attention should be given to the thermal design of the mold, as mass reduction could lead to local temperature inhomogeneities on the cavity surfaces, which may negatively affect part quality. However, the influence of the mass reduction on the homogeneity of the cavity wall temperature is expected to be lower than, for example, reported in [35]. This discrepancy can be attributed to the fact that, in the example utilized within this study, the coolant temperature is 40 °C, whereas it was 90 °C in [35]. Additionally, the maximum surface temperature variation observed in the reference design does not exceed 1.7 K.

The TO presented in this work is based on the manual preparation of the required input data, the execution of the optimization steps, and the subsequent transfer of the results into the mold design. To increase the efficiency of the overall process, future research should focus on investigating and implementing automated data transfer between the individual process steps, as well as on determining the minimum required design and non-design spaces. Such automation could significantly reduce the total optimization time and improve reproducibility.

Furthermore, the long-term durability of topology-optimized mold inserts under real operating conditions, both during testing and in series production, must be evaluated. In addition, a thermo-mechanical analysis of the TO design was not conducted, as the original design has already been- validated and the non-design space behind the cooling channels was set to 5 mm, which is typically not critical under the given boundary conditions. It should also be investigated whether targeted post-processing of the freeform surfaces within the design space is necessary, as these areas could act as potential crack initiation sites and thereby impair the structural integrity of the tool.

In conclusion, this study has demonstrated that TO offers great potential for reducing the mass and cost of additively manufactured mold inserts without compromising plastic part quality or mechanical integrity. Given the increasing scarcity of resources and the growing demand for sustainable production, such additively manufactured lightweight mold inserts are expected to play an increasingly important role in the future.