Automated layout optimization for hybrid additively manufactured hydraulic manifolds

Hydraulic systems have long been an integral part of various industries, serving as a reliable source of power transmission and actuation in numerous applications (Bauer, 2016). A critical element of hydraulic systems is the hydraulic manifold, which governs and directs fluid flow within machinery (Zhang, 2018). Traditionally, these manifolds are produced through conventional manufacturing techniques such as milling (Semini et al., 2015; Zhang et al., 2020). While cost-effective, the manufacturing restrictions of milling often result in components that are suboptimal in terms of performance and weight (Ma et al., 2018; Zardin et al., 2017). With the growing demand for more energy efficiency (Blesl and Kessler, 2021), these systems must not only perform effectively but also ensure efficient energy transfer through pressurized fluids (Hofmann et al., 2023; Zardin et al., 2017), necessitating a reevaluation of these conventional manufacturing methods.

Additive manufacturing (AM) (Gibson et al., 2021) has emerged as a promising manufacturing technique for hydraulic manifolds, offering significant potential for improvements in performance, weight and size (Matthiesen et al., 2018). The ability of AM to create complex geometries enables the design of smoother channels and more compact structures, which can reduce pressure drops and enhance overall system efficiency (Barasuol et al., 2018; Diegel et al., 2020; Rolinck et al., 2021). However, the adoption of AM in the production of hydraulic manifolds is hindered by several challenges, including high production costs (Pei et al., 2023, p. 55; Ukobitz, 2020) and the need for extensive postprocessing when using laser powder bed fusion of metal (PBF-LB/M, short: LPBF). Postprocessing is required for the removal of support structures (Wohlers et al., 2022) and the machining of threads and sealing interfaces. Consequently, approaches that combine the benefits of milling and AM are required.

To address this challenge, a hybrid manufacturing approach (Jiménez et al., 2021; Pragana et al., 2021) using milling and AM via LPBF is applied in this study [Figure 1(a) and (b)]. By combining these methods, it is possible to capitalize on the advantages of each, achieving an optimal balance between performance and manufacturing cost (Trumpf, 2023). This is achieved by assigning each functional feature of the system to the manufacturing process that best suits it. The interfaces to the hydraulic components are integrated into a milled preform where tight tolerances are required. This preform is used as a base in the AM process, and the complex channel geometries are built on top. The use of the milled preform minimizes postprocessing efforts and reduces the build height and volume of the additively manufactured part. Meanwhile, flow-optimized curved channels are produced via LPBF, which benefit from its design flexibility. The combination of using LPBF on milled preforms has been presented in several applications, such as milling tools (Trumpf, 2023), valves (AM Network et al., 2019; Stoll et al., 2019; Trumpf, 2023) or medical implants (Trumpf, 2023), highlighting the benefit of using the strengths of both processes.

Hybrid AM has been used for the manufacturing of hydraulic manifolds using different design approaches. To realize these design approaches, two main steps are required during the design phase: First, defining the layout of the hydraulic components and translating this layout into the design of the milled preform, and second, routing and designing the channels for AM. The latter step has seen successful automation in recent years by automating the routing of multiple flow channels (Biedermann et al., 2022) and the adaptation of the channel cross-section considering the overhang restrictions of the LPBF process (Biedermann et al., 2021). The former step, defining the overall layout of the manifold – comprising numerous components and connections – remains a largely manual and time-consuming task. The challenge lies in the fact that the spatial arrangement of the components and therefore the locations where channels start and end, largely influence the design of the channels and therefore the performance and the cost of the manifold. To overcome this obstacle, automation of the layout optimization for hydraulic manifolds is required. Such automation could significantly reduce design efforts and allow full exploitation of the design space (DS) for the hybrid manufacturing approach, enhancing the performance and cost-efficiency of hydraulic systems.

Existing placement algorithms used in solving geometric packing problems offer some insights into addressing these challenges. Applications range from sheet metal cutting and garment manufacturing (Bennell and Oliveira, 2006) to floor plan optimization in architecture (Bausys and Pankrasovaite, 2005) and PCB design. Other applications include payload optimization in aerospace (Li et al., 2016; Xu et al., 2007) and nesting of three-dimensional (3D) components in AM machines (Yau and Hsu, 2021). The complexity of the algorithms highly depends on the dimensionality of the geometric packing problem and the shape of the objects to be nested (Dyckhoff, 1990; Wäscher et al., 2007). To reduce complexity, many algorithms rely on simplifications such as reducing the design problem to two-dimensional (2D) or simplified representations of nesting objects (Bennell and Oliveira, 2006; Jarvis, 1972).

While there is a wide range of literature on placement algorithms covering many different levels of complexity in various applications, each application has its unique requirements. For the design of hybrid AM hydraulic manifolds, this unique requirement lies in the fact that not only is a compact layout of the hydraulic components required, but the channels connecting the hydraulic components must also be as short as possible to optimize the pressure drop within the system. This necessitates a tailored approach and specialized layout optimization algorithms that can accommodate the intricate requirements of these systems. However, state-of-the-art methods are valuable for transferring methods such as simplifications and placement approaches to the given application.

This publication (1) presents layout optimization algorithms tailored to three chosen design approaches for hybrid AM manifolds and (2) compares these approaches based on a case study. The goal is to enhance the efficiency and effectiveness of the design process for these complex systems and to highlight the potential and limitations of the design approaches.

The publication is structured as follows: The methods section outlines the hybrid manufacturing approach and three specific design approaches for hydraulic manifolds, focusing on the application- and manufacturing process-specific requirements, and describes the overall design workflow. In the results section, the layout optimization algorithms developed for the three design approaches are presented. Furthermore, the algorithms are applied in a case study, and the resulting parts are manufactured and compared. Thereafter, a discussion of the layout optimization methods and the specific design approaches is provided, highlighting the strengths and limitations of each. Finally, the publication concludes with a summary of key findings, proposed improvements and suggestions for future research directions.

The hybrid manufacturing approach, which is applied to the production of hydraulic manifolds, involves the combination of a milled preform with LPBF-manufactured hydraulic channels. The LPBF process requires a flat surface to build on. The hydraulic components can be positioned on the remaining sides of the preform. In the present study, rectangular cuboids are used as the preform geometry, as these can be produced efficiently by milling. Two distinct types of hydraulic components are identified for the remaining five sides of the preform. The differentiation of the two types of hydraulic components and their respective 2D representation is shown in Figure 2. The 2D layout representation facilitates visualization and is used to simplify the design problem during the layout optimization, which will be explained in Section 3.1. First, there are components for which the normal vector (depicted by the yellow arrow) of the mounting surface is parallel to the build direction. These components can be freely placed on the bottom surface of the preform and are called bottom components. Second, there are hydraulic components with a normal vector of the mounting surface perpendicular to the build direction. These components can be placed on all four sides along the border of the preform (marked in red) and are referred to as side components.

The following sections first outline the approaches that can be used to ensure functionality within the realm of the application-specific requirements, and subsequently, which requirements must be met to ensure manufacturability when using this approach.

The primary objective during the design phase is to ensure that the specified functionality is fulfilled. In the case of hydraulic systems, the functionality is defined by the hydraulic scheme, which states the hydraulic components involved and their respective connectivity. Moreover, the assembly and accessibility of the components must be considered during the layout process. Ultimately, to guarantee a leak-tight system, it is essential to ensure precise threads and sealing surfaces, which require tight tolerances and low surface roughness at the interfaces.

The differentiation between bottom and side components leads to three potential design approaches, which are illustrated in Figure 3: (a) the bottom, (b) side and (c) combination approach. Each approach considers different application-specific requirements and exhibits distinct advantages and disadvantages.

The bottom approach comprises solely bottom components, which can be positioned freely on the bottom of the preform. The primary benefit is the convenient accessibility, as all hydraulic components can be accessed from one side. A disadvantage of this approach is that when including hydraulic components with long interfaces, it may result in a preform that is thick and therefore heavy. Alternatively, if a thin preform is chosen and interfaces are partially additively manufactured, their subsequent postprocessing may be necessary. The side approach is characterized by the exclusive use of side components positioned along the border of the preform. One advantage of this approach is that the manifolds can be mounted on the bottom face. Moreover, in the event of restricted accessibility, only specific border sides can be used for the placement of the hydraulic components. Finally, the combination approach comprises both bottom and side components. The combination of both types of components enables the largest placement freedom. One potential disadvantage of this approach is the mounting of the hydraulic system, which may be challenging depending on the selected configuration and boundary conditions. However, individual faces along the border can optionally be left empty.

The required components and the design approach are specified at the beginning of the design process. Before the initial utilization of a component, its interface must be defined and stored within the component library. This encompasses the 3D geometry of the interface and the 2D representation of the component for layout optimization, as both a bottom and a side component. Furthermore, the port locations must be specified for both component types. Ports are the inlets/outlets of the components. Figure 4 illustrates this process for a cartridge valve with three ports. Cartridge valves regulate fluid flow, pressure or direction of flow between the ports, often by moving a spool inside the cartridge. Bottom components with interfaces fully integrated into the preform may only have axial ports due to manufacturing restrictions. The interfaces of components with radial channel connections used as bottom components must extend beyond the preform [Figure 4(a)] to enable radial access to the ports. In the 2D representation, bottom components are defined as a circle, with an additional accessory and actuator space. The component space defines the effective space required for the milled interface in the preform. The accessory space defines the minimum space required to assemble the components and, therefore, the minimum distance from other components. Finally, the actuator space includes the space required to mount external actuators. Because these usually only extend in one direction, it is optional to include this space in the optimization. Including this space limits the compactness that can be achieved during layout optimization. If not included, the actuator assembly must be manually checked for the selected layout. If the component is used as a side component [Figure 4(b)], it is represented by a rectangle in 2D. Again, the accessory space defines the additional distance required along the border until the next component can be placed. Once all the necessary components are available in the component library, the components for the given case can be selected.

Both manufacturing processes possess inherent requirements. Milling is used for the preform, which incorporates all interfaces with the hydraulic components. These require tight tolerances and low surface roughness to ensure precise threads and leak-tight seals. Furthermore, all inlets at the interfaces are guided to the intersection plane via straight channels in the milled preform. This intersection plane serves as the interface to the additive part. Regarding the AM process, the channel design must adhere to the LPBF design guidelines to guarantee the production of a defect-free part. Such constraints include the maximum overhang angle and minimum feature sizes. These constraints are automatically considered by the algorithms used for designing the channel geometries. During the preparation of the LPBF process, the preforms are mounted in the AM machine. They must be precisely placed to ensure a good fit between the milled channels in the preform and the additively manufactured channels. To guarantee this exact positioning, the preforms are fastened to the adapter plate in the AM machine in a defined position. To eliminate the need for adapter plate adaptations for each part, the spacing between the screws was defined as a multiple of 10 mm. Accordingly, the adapter plate of the AM machine incorporates a grid of threads with a grid length of 10 mm. Figure 5 illustrates the assembly of a milled preform on the adapter plate. The described mounting procedure enables the precise and efficient mounting of preforms, as well as the cost-effective manufacturing of custom manifolds.

In alignment with the proposed manufacturing concepts, a design workflow has been developed that translates the user input into the manufacturing files in two design steps [Figure 6(a)–(d)]. The user input includes selecting the required hydraulic components and specifying their connectivity. Subsequently, the design approach is selected from among the bottom, side and combination approaches. If the combination approach is selected, users must specify each component as a bottom or side component. Moreover, users specify the diameters of the channels associated with each connection. Once all user inputs have been defined, step 1 can be initiated, where the layout is optimized and the preform is generated. The optimization process entails the calculation of two fitness values: the area of the bounding box and the total channel length of all connections along the shortest 2D path. The optimization process yields a Pareto front, which allows the user to select designs that balance spatial efficiency with minimized connection lengths. Step 2 involves the routing and design of the 3D channels, which are automatically routed, avoiding collisions. During this step, the system prioritizes the shortest feasible channels, progressing toward optimal solutions until the particle simulation converges. Users also have the option to manually adjust the channel positions, allowing them to modify the channel arrangement and specify layering preferences, such as which channels should be positioned above others. Based on the converged routing solution, the 3D channels are generated. The routing and channel design workflow builds on prior work by Biedermann et al. (Biedermann et al., 2021, 2022). Finally, the 3D files of the preform (.step) and the channels (.stl) can be exported in the file format required for the respective manufacturing process.

The workflow has been implemented in the CAD software Rhinoceros and its graphical programming interface, Grasshopper. The developed placement rules were implemented in custom C# components, and the Wallacei plugin was used for the optimization based on a genetic algorithm.

The following section on results is divided into two parts, corresponding to the two main contributions of this publication. First, the layout optimization algorithms tailored to the three design approaches are presented. Second, these algorithms are applied in a case study, and the resulting designs serve as the basis for a comparison of the three approaches.

The goal of the optimization is to determine the optimal position of each component within the milled preform, effectively generating the layout of the hydraulic manifold. The current optimization problem is defined by minimizing the two objectives of the channel length and the total area occupied by the components. Given that the optimization is performed in a 2D plane, the channel length is approximated by the minimal distance between the ports on this plane. In addition, it is crucial to ensure that no overlap occurs between the components and that minimal distances are maintained.

The optimization is based on the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) (Deb et al., 2002). The NSGA-II is a multiobjective genetic algorithm chosen for its balance of speed and performance compared to other multiobjective genetic algorithms. Compared to the original NSGA, it requires less computational effort. The NSGA-III, however, is designed for problems with more than three objectives. To apply this approach to the design problem, an appropriate genetic representation is essential. This representation includes four key components: genes, gene decoding, genotype-to-phenotype mapping and fitness functions. Genes are the variables that define an individual solution within the population and are subject to modification during the optimization process through operations such as selection, crossover and mutation. Gene decoding and genotype-to-phenotype mapping are required to generate a population from the genes. Gene decoding enables the translation of the genes into the form required during genotype-to-phenotype mapping. Genotype-to-phenotype mapping determines how an individual’s phenotype, or physical manifestation, is expressed based on their underlying genetic makeup. The fitness functions are used to evaluate the fitness values of each phenotype. The genetic algorithm (Figure 7) begins by randomly setting an initial set of genes and generating an initial population. Subsequent populations are derived from this initial population through a process of selection, crossover and mutation, which iteratively refines the population toward an optimized solution.

For this design problem, the genetic representation is structured as follows:

1. Genes: The genome of each individual consists of one or two genes, depending on the design approach. The first gene defines the order in which the components are placed, referred to as the permutation, and is required for all design approaches. If side components are present, a second gene defines their side allocation. This gene is a vector that measures the length of the number of side components and determines the manifold’s sides on which the side components are placed. The side allocation gene is dominant and can adapt the order in which the components are placed.

2. Gene decoding: To decode the genes for the genotype-to-phenotype mapping, two steps are necessary. The permutation must be translated into a placement order, which may be adapted based on the dominant side allocation gene. These two steps are explained in Section 3.1.2.

3. Genotype-to-phenotype mapping: The genotype is mapped to the phenotype using placement rules, which will be described in detail in Section 3.1.3. These rules define how the components are arranged based on the placement order.

4. Fitness values: The fitness of each individual is evaluated based on two fitness values: the area of the bounding box that encompasses all components and the total channel length of all connections between components.

The permutation gene defines the placement order of the components. The advantage of encoding the order in a permutation lies in the fact that one gene is sufficient to define a unique placement order. Based on combinatorics, the number of ways to arrange n components is given by n!, called the factorial of n. The permutation gene p_g can take any value from 0 to n!-1, which can then be translated into a unique placement order. To derive the specific placement order from p_g, a factorial decomposition is used. This procedure is based on equations (1) and (2):

Figure 8 describes how the factorial coefficients C_n can be calculated from the permutation gene p_g. Based on these coefficients, the placement order v_po of the components can be determined starting from the initial component order v_i. An example that illustrates this process for four components is shown in  Appendix 1 (Figure A1).

When side components are present, the genes of an individual also include a side allocation for all side components, ranging from 1 to 4. This information is defined in the side allocation vector, v_sa, that measures the length of the number of side components. The side allocation gene is the dominant gene, and it can adapt the placement order defined by the permutation gene to place all components on one side before continuing to the next side. Figure 9(a) shows the method of the placement order adaptation based on the side allocation vector v_sa. It is based on a bubble sorting algorithm. Figure 9(b) illustrates this methods’ functionality using an example.

Translating the placement order of an individual into the phenotype is achieved based on placement rules. The rules differ depending on the chosen design approach and the corresponding boundary conditions of the components.

The bottom approach exhibits only bottom components, which are approximated by circles for the bottom approach. The locations are controlled via the control points, which lie in the center of the circles [Figure 10(a)]. The general procedure for placing bottom components is split up into two steps: identifying potential placement locations, and selecting a location and placing the component. The following example in Figure 10 illustrates the placement process for a scenario with four components. The connectivity between the components is abstracted and visualized through the curved red lines in Figure 10(a) and later through straight lines, representing the shortest possible channel between two components. The permutation is set to b, d, c and a. The first component (b) is placed at the origin of the coordinate system. A circle with radius r_b + r_d around the control point of component (b) represents all the potential placement locations of the control point of the second component (d) [Figure 10(b)]. Because all the locations are equal in terms of the resulting channel length, component d is placed on the positive x-axis. For the third component (c), the potential placement locations are determined by the intersections of a circle with radius r_b + r_c around the control point of component (b), and a circle with radius r_d + r_c around the control point of component (d) [Figure 10(c)]. As before, the identified placement locations are equal in terms of the resulting channel length, and component (c) is placed on the positive y-axis [Figure 10(d)]. The potential placement locations for the last component (a) are determined using three circles around the control points of the already placed components. There are six intersection points, but only three are feasible [Figure 10(e)] because the others are located within previously placed components. The identified placement positions differ in terms of the resulting channel length. Because component (a) is connected to components (b) and (c), position 1 leads to the shortest channel length and is selected as the position for component (a) [Figure 10(f)]. These rules guarantee that the layout is as compact as possible while ensuring that there is no overlap between components. After placing all components, the screw interfaces are added [Figure 10(g)] to enable precise mounting of the preform in the AM machine. The detailed steps to achieve a screw layout with distances of a multiple of 10 mm while minimizing the increase in area are described in  Appendix 2 [Figure A2(a)–(d)].

To demonstrate the placement rules for the side approach, the example in Figure 11 is used. The placement starts on the side where the components take up the most space. To calculate this length for each side, the respective components are arranged as close together as possible, such that there is no overlap between the accessory spaces. The measurement is taken from the beginning of the component space of the first component to the end of the component space of the last component. After defining the side where the components take up the most space, the placement starts by placing a screw interface [Figure 11(a)]. Next, the components are placed according to the placement order and as close together as possible. The side is concluded by placing a screw interface and moving it in the positive x-direction until the distance of the center points of both interfaces is equal to a multiple of 10 mm before the placement rules continue on the next side [Figure 11(b)]. The first component always lies next to the screw interface, and the x-value of the control points is calculated such that there is no overlap of any components on side 2 with the last component on side 1, thereby defining the total length of side 1. This procedure continues for sides 3 [Figure 11(c) and 4 [Figure 11(d)]. To avoid overlap with components on opposite sides, all components on sides 3 and 4 may be moved outward if the prior adjacent side did not create enough space.

The combination approach consists of bottom and side components. For the combination case, the bottom components are represented by squares with the diameter as the side length. To promote compact layouts, the side components of the side which take up the most space are placed first. This is done according to the rules for the first side in the side approach [Figure 11(a)], however, leaving the second screw interface away. As the second side, the components of the adjacent side to the left of the first side (side 4, side naming counterclockwise as for the side case) are placed in the positive y-direction [Figure 12(a)]. Next, the bottom components are placed. For each bottom component, the placement rules first identify the available space between the previously placed side components before selecting a placement position. To identify the DS, the outline of the previously placed components is extracted, expanded in positive x- and y-directions to ensure sufficient space, and closed [Figure 12(a)]. Next, the placement rectangle (PR) origins are identified, which are comprised of two types [Figure 12(b)]. First, the corner points of the DS with available space in the positive x- and y-directions (blue circles). Second, points derived from corner points that can be shifted closer to the origin within the DS (blue dot). The identification is based on the value of the scalar product of the x- and y-unit vectors and the vectors from the testing point to the previous or next vertex. To conclude this step, the PRs are generated [Figure 12(c)]. Each point identified in the previous step serves as the origin of a PR expanding in positive x- and y-directions to the border of the DS. Figure 12(c) shows these rectangles for three points. Based on the identified PRs, the first bottom component is placed [Figure 12(d)]. The PR, which leads to the shortest channel length and is big enough to accommodate the first bottom component, is selected, and the bottom left corner of the component is placed in the PR’s origin. This process of identification of the DS and corner points, generation of PRs, choice of the best PR and placement of the component is repeated for all further bottom components based on the placement order [Figure 12(e) and (f), ]. After placing all bottom components, the two screw interfaces are placed in the bottom right and top left corners [Figure 12(g)]. Here, again, the distance between both must be a multiple of 10 mm. The placement rules continue with the side components on side 3. The component space of the first component lies next to the screw interface, and the y-value of the control points is calculated such that there is no overlap with any previously placed component [Figure 12(g)]. Following this step, the final screw interface is placed. The y-value of both screw interfaces and all components on side 3 is increased, ensuring that the distance of the interfaces is a multiple of 10 mm [Figure 12(h)]. To complete the layout, the side components of side 2 are placed. If there is not enough space available to place the components, the DS is expanded in the positive y-direction. This means that the side components and screw interfaces on side 3 are also moved in a positive y-direction. In the example, this is not necessary, and the final layout is shown in Figure 12(i).

To demonstrate the methods presented in the previous section, they were applied to the case study, which is outlined in [36]. The manifold described in the case study is part of a test equipment system for aircraft landing gear, requiring a compact and portable design. It integrates three distinct cartridge valves and three identical connectors for the outlet, pressure and tank return. For comparative analysis, three designs were generated and manufactured, each based on one of the proposed design approaches: bottom, side and combination. For the layout optimization of the cartridge valves as bottom components, the actuator space was not considered because the actuators only extend in one direction. If space in all directions were considered in the layout optimization, the compactness of the resulting layouts would be severely limited. For this number of components, the assembly of the actuators can be easily judged based on the resulting layouts. Therefore, the diameter of the approximating circles of the cartridge valves was defined based on the accessory space.

The design workflow illustrated in Figure 6 starts with the user inputs. First, the functional requirements are defined by selecting the required components from the component library and defining their connectivity. As described above, this case includes three cartridge valves (FMBD, PRDL and FPCH) and three connectors for the outlet, pressure and tank return. The connectivity is illustrated in Figure 13. In this case study, a design is generated for each design approach, making the choice of an approach unnecessary. For the combination case, the cartridge valves were designated to be side components, and the connectors were bottom components. All channel diameters were chosen to be 9 mm. Finally, LPBF process constraints must be defined. For this study, conservative constraints such as a maximum overhang angle of 45° were chosen to ensure manufacturability on any LPBF machine.

After establishing the design problem, layout optimization is performed for each of the three design approaches. The layout optimization minimizes two fitness values: the area and the channel length in 2D. Therefore, the multiobjective optimization does not lead to a single optimal solution, but rather to a Pareto front with solutions that may be dominated by another solution with respect to one fitness value but not the other. These solutions represent the smallest area, shortest channel length or a trade-off between the two fitness values. The layout optimization was completed in a matter of seconds. In some cases, two different layouts may have identical fitness values. Figure 14(a) shows the optimization results of the bottom approach for 30 generations with a population size of 30. It highlights the improvement of the fitness values from generation 0 in blue to generation 29 in red and the propagation of the Pareto front. Figure 14(b)–(d) show the Pareto optimal solutions after 30 generations and the selected layouts for manufacturing. For the bottom and side approach, there are three Pareto optimal solutions each. The optimization of the combination approach converged to one Pareto optimal solution, which was consequently selected for manufacturing. Which of the Pareto optimal solutions is chosen when more than one Pareto optimal solution exists depends on the specific requirements of the application and can be decided by the designer. For the bottom approach, the solution with the shortest and simplest channels was chosen, as more efficient channels were prioritized over the slightly smaller areas of the other two solutions. For the side approach, the most compact solution was selected, because here the difference in size was much more significant than the difference in 2D channel length. Based on the selected layout, the 3D geometries of the milled preforms were generated.

Based on the chosen layout and milled preform geometry, the routing of the channels is initiated [Figure 15(a)]. After convergence of the iterative particle simulation [Figure 15(b)], the 3D channels are generated [Figure 15(c)]. Next, the required support structures are added and the geometry of the milled preform is subtracted from the resulting geometry. Figure 15(d) shows the 3D geometries of the milled preform and the additively manufactured part. Finally, the 3D files of both geometries can be exported for manufacturing.

The manufacturing process of the hybrid hydraulic manifolds is illustrated in Figure 16, which is based on the digital design of the parts [Figure 16(a)]. First, the preforms are machined from stainless steel (316 L/1.4404) bulk material using a 5-axis Computer Numerical Control (CNC) milling machine [Figure 16(b)]. In this phase, the required interfaces to the hydraulic components are machined, ensuring the necessary surface finish and dimensional accuracy. Subsequently, the preforms are mounted onto the adapter plate of the LPBF machine via threaded connections [Figure 16(c)]. It should be noted that the complete grid of threads in the adapter plate was not manufactured for this study; rather, it was included in Section 2.1.2 to demonstrate the vision and feasibility of the mounting procedure for custom manifolds. In preparation for AM, the cavities of the preforms are filled with metal powder, creating a level surface for the initial layer of the AM process. This step is crucial to ensure a defect-free powder surface and guarantee the proper fusion of the additively manufactured channels with the milled preform. Next, the channels are manufactured using the LPBF process [Figure 16(d)] on an Aconity MIDI+ machine (Aconity 3D, 2019). The material used was stainless steel (316 L/1.4404) powder, with a layer thickness of 30 µm. To ensure a strong metallurgical bond between the two regions, it is important to use the same material for the LPBF process as for the milled preform. To further strengthen this bond, the first layer of the LPBF process is exposed three times before the next layer of metal powder is applied to improve bonding with the milled preform. The process parameters included a laser power of 180 W and a simple scan strategy, wherein the scan direction was rotated by 67° layer-by-layer. The build chamber was flooded with nitrogen. Upon completion of the LPBF process, the excess powder is removed by brushing until the screws holding the preform to the adapter plate are accessible. The hybrid manifolds can be directly demounted from the adapter plate [Figure 16(e)], eliminating the necessity for support removal. For the side and combination approaches, no further postprocessing is required [Figure 16(f)]. The parts are prepared for immediate utilization following their removal from the LPBF machine, demonstrating the benefits of the hybrid manufacturing approach. For the bottom approach, the manifold is transferred back to the CNC machine, where the interfaces are finished.

One design was manufactured for each of the design approaches based on the chosen layout. Figure 17(a)–(c) show images of the fabricated manifolds. To compare the different design approaches, various properties that are indicators for the performance and cost of the parts were identified and evaluated, categorized into performance- and cost-related criteria. These are summarized in Table 1.

In the context of performance evaluation, critical indicators encompass channel length, mass and volume, which collectively determine the design’s overall value for a specific system. Channel length is particularly important, as it correlates with pressure drop; longer channels result in greater pressure loss. Both 2D and 3D channel lengths are provided to reflect the values of the layout optimization and after the channel routing. The results show that the bottom approach exhibits the shortest channel length, followed by the combination approach and the side approach. Next, the weight of the manifolds is evaluated, as lightweight systems can be beneficial in some applications. The bottom approach has the lowest total weight (1.19 kg), followed by the combination approach (2.46 kg) and the side approach (3.06 kg). The analysis indicates that for both the side and combination approaches, the milled preform contributes most significantly to the overall weight, with the preform accounting for roughly 90% of the total weight. The compactness of the manifold is a further desirable quality for some applications. Therefore, the bounding box dimensions and corresponding volumes are evaluated, with the combination approach proving the most compact (635.60 cm³). The bottom and sides approaches have similar volumes (877.14 and 861.66 cm³). While the compactness of the manifold itself is generally desirable, the overall size after assembling all components and the accessibility of the components must also be considered when determining the optimal design approach for a specific application.

Regarding cost-related factors, the LPBF costs exceed those of milling, due to the substantial expenses associated with the LPBF process. Consequently, the build height, build volume and area are identified as the primary indicators of manufacturing costs. The build volume is greatest for the bottom approach (67.25 cm³), followed by the sides (40.86 cm³) and combination approach (27.05 cm³). Alongside build volume, the build height significantly impacts the LPBF costs. The build height is largest for the bottom approach (71.44 mm), while the side and combination approaches have shorter build heights of 32.9 and 24.61 mm, respectively. Furthermore, machine utilization, influenced by the number of parts that can be arranged on the adapter plate, significantly affects the LPBF costs. In a series production scenario, a smaller area allows for more parts to be produced simultaneously. The milled preform area analysis shows that the bottom approach requires the least amount of space (110.42 cm²), followed by the combination (116.39 cm²) and side (136.99 cm²) approaches. Finally, it is important to note that the bottom approach requires postprocess milling of interfaces after LPBF, as most interfaces are printed and cannot be prefinished during the milling of the preform. With the other two approaches, the parts are ready for immediate use, as all interfaces, including the threads and sealing surfaces, were completed during the preparation of the preform.

In conclusion, the bottom approach demonstrates the greatest potential for performance-related factors, with the shortest channel length (292.18 mm) and lowest total mass (1.19 kg). While its bounding box volume (877.14 cm³) is larger than that of the combination approach (635.60 cm³), the overall space requirements often depend on the specific application, and the assembled volume should also be considered. The combination approach stands out due to its compactness. In terms of cost, the bottom approach is likely the most expensive, due to its larger build height (71.44 mm) and additional milling requirements, while the combination approach offers a promising balance of compactness and cost-efficiency. Although the side approach appears to lag in terms of these performance- and cost-related criteria, its advantage lies in making the bottom face available for mounting, which could be a critical factor depending on the application.

This section discusses the two key contributions of this publication: the automated layout optimization as the addressed step in the design process, and the comparison of the three hybrid design approaches for hydraulic manifolds.

To efficiently generate design variants for each design approach, rule-based placement algorithms based on a permutation were developed, considering the unique requirements of each approach. The rule-based approach consistently produces compact and feasible solutions, eliminating the need for further manual adjustments. Despite these strengths, some limitations were identified. One issue arises from the simplified 2D representations of components: circles are used in the bottom approach, and rectangles in the side and combination approaches. In some cases, these simplified shapes result in larger layouts than are necessary for assembly. Modifying the algorithms to work with more complex shapes, such as concave boundaries, could yield more compact layouts. However, this would significantly increase the complexity of the algorithms, while the overall impact on the solutions is expected to be small.

The optimization uses a genetic algorithm, which has the advantage of efficiently exploring a large DS with relatively low computational effort, compared to many other optimization techniques. The optimization of the layouts of the case study converged in seconds. While efficient, this approach also presents a drawback. The genetic algorithm is not a global optimization technique, meaning that the best possible solution may not always be found. For the case study presented, not every optimization run resulted in the same Pareto front. However, comparing solutions from multiple optimization cycles revealed only minor variations, with fitness value deviations remaining below 2%.

Another trade-off arises from evaluating the layouts in 2D rather than 3D. While optimizing in 2D reduces computational time and effort, it can affect the accuracy of channel length predictions. In some cases, designs with shorter channel lengths in 2D may result in longer channels in 3D due to intersections of channels in 2D, which are then resolved by the routing algorithm. Nevertheless, generating 3D designs for each layout would be significantly more computationally expensive. This trade-off can be mitigated by reviewing layouts from the Pareto front and considering this while choosing the layout, or by generating 3D designs of the Pareto front layouts, to make the final decision based on the effective 3D channel length.

During the design of a component and the selection of a manufacturing process, it is often necessary to consider the trade-offs between various factors. In the case of hydraulic manifolds, the choice often lies between milling and AM. Milled manifolds are generally bulkier and heavier, while AM enables the creation of lightweight, fluid-optimized parts with many functional advantages. However, from a cost perspective, milling remains significantly more economical than AM, and the choice therefore often results in milling.

The hybrid manufacturing approach used in this study aims to combine the strengths of both milling and AM, offering a balanced solution that leverages the cost-effectiveness of milling and the design flexibility of additive techniques. The case study demonstrates how the three chosen design approaches can be applied to a hydraulic manifold that forms part of a test system for aircraft landing gear. All manufactured manifolds met the system’s functional requirements, but each approach showed distinct trade-offs in terms of channel length, mass and accessibility. It is not possible to definitively determine the best design approach for all applications; this depends heavily on specific project requirements, boundary conditions and budget considerations, along with alternative options like fully milled or additively manufactured designs.

This study presents layout optimization algorithms for three design approaches of hydraulic manifolds produced by a hybrid AM process. The algorithms facilitate the exploration of the DS while accommodating application-specific requirements. Feasible layouts without overlaps are generated along a Pareto front within seconds, offering a trade-off between the shortest channel length and the smallest bounding box area. Based on the selected layout, the required manufacturing files can be automatically generated and exported.

To validate the proposed layout optimization algorithms and compare the design approaches, the fully automated design process was applied in a case study. The developed layout optimization algorithms were used, and one part was manufactured for each design approach. The results demonstrate the potential of hybrid AM compared to fully milled or fully additively manufactured parts while highlighting the distinct differences between the three hybrid design approaches. They provide a range of trade-offs between performance and cost, bridging the gap between the extremes of fully additively manufactured and fully milled manifolds.

Although the hybrid design approaches and developed layout optimization algorithms yielded promising designs, further investigation is necessary to fully assess the potential and limitations. First, the performance- and cost-related assessment in this study relies on simplified metrics. Channel length was used as a proxy for performance (pressure drop), while build volume and build height served as cost indicators for the AM process. Although these metrics provide useful approximations, they lack the precision needed for definitive conclusions. Future studies could enhance these evaluations by conducting detailed performance tests, such as pressure drop measurements, and by performing comprehensive cost analyses based on actual manufacturing data. In addition, the limitations of the proposed layout optimization algorithms, as discussed in Section 4.1, should be addressed. Specifically, incorporating more complex algorithms or evaluating designs based on their 3D topology rather than 2D representations could yield more accurate results. However, the trade-off between improved performance evaluation and increased computational effort must be carefully considered. Finally, to prove the viability of the hybrid design approaches and the functionality of the developed optimization algorithms, they should be applied and validated in further, more complex cases.

In summary, this study provides algorithms for automated layout optimization in hybrid manufacturing, advancing the design and production of hydraulic manifolds. While challenges remain, the proposed methods represent a significant step toward achieving efficient, cost-effective and high-performance hydraulic systems.

The authors would like to express their gratitude to Julian Ferchow for his valuable support during the writing of the manuscript. Special thanks go to Dario Fenner for the manufacturing of the milled preforms. The authors also thank their colleagues at inspire-icams, particularly Silke Bramann and Matteo Turani, for their support during the AM process.

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

Urs Hofmann: conceptualization, investigation, methodology, software, writing – original draft, visualization; Patrick Beutler: conceptualization, investigation, methodology, writing – review and editing; Oliver Haselbach: investigation, methodology, software, writing – review and editing; Mirko Meboldt: supervision, writing – review and editing.

During the preparation of this work, the author(s) used DeepL Write and ChatGPT 4o in order to improve language and readability. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.