Yield Strength [MPa]

Modulus [MPa]

#### *4.1. Design of the Rails*

**Table 1.** Material properties: comparison

Young's

A simplified model of the original system was initially implemented in InspireTM 2018 SolidThinking®, version 2018, build 9508, to analyze its mechanical behavior. The probe, and the vision and the lighting systems were modelled as concentrated masses. The magnetic forces from the linear motor were simulated as vertical loads. A finite element (FE) method was used to solve the model. As expected, the system showed an almost uniform stress distribution and high equivalent stress of around 20 MPa, which is far below the limit of the material (Table 1). As already mentioned, the low stresses are due to the high stiffness design criterion. Thanks to the low stress (see supplementary file), the part can be redesigned freely considering only the peculiarity of the L-PBF process. The components of the system were therefore redesigned to achieve an efficient new material distribution and weight reduction while only coupling areas were constrained.

As far as the X-rail is concerned, the design starts with a redesigning of the vertical walls (Figure 3a,b). Each vertical wall was replaced by two thin honeycomb-structure walls. These structures were demonstrated to be self-supported, and allow better stress distribution and light. The walls were also placed out of sync in order to distribute the stresses more evenly during the production of the components and during operation. A new material distribution was considered for the bottom wall using the Voronoi algorithm (Figure 3c). The cover was then welded to the rail (Figure 3d) to improve the stiffness of the rail and it was shaped like a cross. A similar approach was followed to redesign the Y-Rail (Figure 3e).

After the redesign of every single part, the parts were assembled and unnecessary features were removed. The whole system was therefore redesigned to be produced as a single monolithic part as follows. The two rails were then welded together. However, the component had to be split into three parts to fit most commercial and industrial L-PBF systems. Owing to the dimensions of the new parts, with the aim to produced them in a single job, an EOS M400 machine (400 × 400 × 400 mm3) has been considered for the production. Figure 4a shows the results of the optimization phase (Section 2 and Figure 1) in which the support structures and the surface finishing are minimized. In this way, only the top surfaces of the X-rail, and the bottom surfaces of the X and Y rails have to be finished. The bottom surfaces are finished directly by EDM when the parts are removed from the building platform. The top surfaces of the X-rail are machined by milling after the assembly of the parts to

ensure a good geometrical tolerance so that they can be joined to the linear motor guides. Figure 4 shows a simulation of the fastening systems during a milling step.

**Figure 3.** Details of the redesigned features for (**<sup>a</sup>**–**d**) the X-rail and (**e**) the Y-rail.

**Figure 4.** (**a**) manufacturing orientation for L-PBF production by EOS M400 and (**b**) machining using a three-axis machine.

According to the support optimization indications (Section 2 and Figure 1), all surfaces were modified to avoid the need of support structures (e.g., Figure 5a) and where the geometrical features were not accessible for manual or mechanical support removal (e.g., Figure 5c, an internal section of the y-rail). A grid (Figure 5d) that also works as a support during the L-PBF process was designed to increase the stiffness of the systems. A shaft-hub interference fit was designed (Figure 5e) to assemble the three parts (details provided in the supplementary file). The connection only included features that are self-supported. The connection between the two parts was also ensured by two bolts (Figure 5b). The component parts were all numbered to make the assembly easier (e.g., Figure 5a red square). After the geometry modification, Figure 6 shows the result of the support optimization according to Section 2 and Figure 1.

**Figure 5.** Modifications of the part features according to the support optimization procedure presented in Section 2. (**a**) modification of the bottom part of the rail to reduce the number of support structures; (**b**) removing material and modification of the surfaces to avoid inaccessible area for the support removal (a section is showed in (**c**)) and adding a link to improve the assembly strength; (**d**) features that support the overhang both during the construction of the part and the working conditions; (**e**) particulars of the shaft–hub interference fit (details are provided in the supplementary file).

**Figure 6.** The layout of the parts with the support structure (in blue). All supports can be removed manually, except the ones on the bottom surfaces which are removed during the detachment of the parts from the building platform by EDM.

Figure 7 shows the differences between the original and the new design. The displacements showed the same distribution. The new material distribution that led a reduction in weight of about 32% was achieved as a result of the implementation of the new design, without any significant changes in terms of stiffness. A technical prototype for the experimental tests was produced according to the designed working cycle. The total production time, including the heat treatment, the support removal, the EDM, and the finishing operations, was about three days. The final component is shown in Figure 8. The total material swarf was about 200 g. The material cost (powder cost equal to 65€/kg) of producing the component was around €197, which is comparable with the material cost of the original component (€196 [35]). However, considering that the initial components were machined from an ingot [35], the material saving, with respect to the original component, was around 99%. The assembly operation flow was simplified because all the operations to join the rails and the covers were removed.

**Figure 7.** Comparison of the maximum displacements between the original and the new design. The maximum displacement is registered as the extremity of the probe. The slight difference in the displacements values between the two designs demonstrates that the stiffness of the system has been preserved while the material efficiency has been improved.

**Figure 8.** Technical prototype with details of the walls of the X-rail (**A**) and the shaft-hub interference fit (**B**).

### *4.2. Bracket Design*

As already mentioned, the redesigning process had the aim of designing a bracket that would satisfy the original requirement, in terms of displacement, while maintaining its original weight. In order to maintain the original rail assembly operational flow, the coupling areas were constrained with other systems to avoid modifications as a result of the redesign. Some other surfaces were also included as constrained areas so that the same fastening tools used for the original geometry could be used during the finishing operations.

Di fferently from the previous case, an increase of the sti ffness is required here. Practically, this means a search of a new material distribution which considers a larger design domain of the original component. The design domain needs to be large enough to include the anticipated optimal material distribution, but also had to be as small as possible to avoid unfeasible structures and increases in the computational costs due to an abundance of unnecessary elements [36]. The potential design domain has been considered as the design space that does not compromise the fastening operations with the other systems. The design domain was therefore increased and optimized iteratively according to the following procedure:

	- • Identifying the areas with high deformation energy from the computer-aided engineering (CAE) analysis of the original design;
	- • Adding material to the areas that showed high deformation energy, after controlling that the total volume did not increase excessively. It noticed that, for small components, the total volume should not have exceeded twice the updated volume in order to avoid an excessive increase in the computational time. This rule was therefore followed in the subsequent steps.

The as-defined design space results in being the smallest that would allow a solution to be found for the global displacement. In short, the proposed design space optimization procedure solves a displacement control problem by means of a series of structural TO problems in which the minimum compliance and volume constraint are considered. The maximum displacement is considered as the ideal design optimization criterion for the design space. Therefore, the design space is redefined several times, and the optimized geometry is obtained after iterations. These iterations work as a design space optimization as they allow the domain to be expanded, where necessary, regardless of the shape of the initial design domain. In other words, the displacement control problem is solved by means of iterative lightening procedures, in which the optimized goal is to find the structures with the maximum sti ffness. That obtained design space design space was used in a free constraint TO using an improved mesh quality to provide a more precise solution [7] and allow a better representation of the structure.

The design optimization of both initial design domain and final geometry have been obtained by the TO method. The TO and validation of the optimized geometry were implemented and solved using Abaqus Standard and a TOSCA algorithm. Thanks to the design freedom, which is guaranteed by the design for the L-PBF process, TO was run with free constraints [38] and using the SIMP method [37]. A tetrahedral mesh was used for the design space optimization and for the final TO in order to decrease the computational time. Hexahedral elements were used for the analysis and validation of the geometry because the accuracy of the results was considered of utmost importance.

#### 4.2.1. Redesigning and Prototyping

A preliminary static analysis of the original design of the bracket was performed to validate the FE model for the sti ffness optimization. The analysis involved the implementation of an FE model of the original bracket, in which the mechanical stress and displacement behaviors were included. The probe and the vision system weights and the probing force during the measurement are the main causes of the bending of the bracket. The bending of the bracket was thus simulated for two di fferent load cases. Load case 1 represents the situation in which the bracket is subjected to its own weight and to that of the other systems (vision and lighting systems and probe), while load case 2 represents the phase in which the probe tests a MEMS relay, and a probing force is therefore added. The maximum equivalent stress on the component was around 15 MPa which was still below the limit of the material so as not to decrease the sti ffness of the component. However, the maximum equivalent displacement was around 35 μm, in agreemen<sup>t</sup> with the specifications provided by the manufacturer. According to the procedure mentioned above, the design space was subjected to several iterations. An expansion of the original design is possible if the geometry modifications do not lead to a change in the finishing and assembly operations. The starting point was the original design for which the stresses and the displacements were known (Figure 9).

**Figure 9.** Iterations of the design space optimization. At each iteration, the material has been removed from the area at low energy deformation and has been added in the ones at high energy deformation. The iterations ended when the maximum displacement of the bracket under the load was less than the prescribed requirement (20 μm).

Design space 0 was obtained by adding material to the areas with high deformation energy (Figure 9) while controlling that the total volume did not exceed twice the original volume. TO was then run by constraining the weight to be equal to the original design and maximizing the sti ffness. The stresses and displacements were then analyzed. Design spaces 1 and 2 (Figure 9) were obtained from the previous design space in order to consider the optimized geometry by adding material to the areas with high deformation energy while controlling that the total volume did not exceed twice the original volume. Finally, when TO was run using design space 2, the displacement values did not exceed the prescribed condition, that is, 20 μm and the space design was therefore considered

optimal. Each design space was using Abaqus CAE and re-meshed considering the same element size. Design space 2 was then used to perform a more detailed optimization. The element was decreased in size to improve the approximation of the geometry.

The optimized geometry was redesigned, according to Section 2. Figure 10 shows a comparison of the original and the redesigned geometry displacements, which are reduced to the prescribed constraint in each direction. The maximum displacement was along axis 2 and was equal to 18 μm. Furthermore, the final design weighed 184 g, which is about 10% less than the original bracket. This reduction in weight, in AM material, cannot be ascribed to the slightly lower density (Table 1) because the difference between the material density values is about 5%.

**Figure 10.** Comparison of the original and new designs for load case 1 (the bracket is subjected to its own weight and to that of vision and lighting systems and a probe) and load case 2 (the probe tests a MEMS). The lower displacements in the case of the new design demonstrated an overall increasing of the stiffness of the bracket.

The feasibility of the bracket in terms of part and process (choice of supports and orientation) designs has been verified by producing a single part. With this scope, the production has been performed by an EOSINT M270 Dual Mode machine that has a small production volume (250 × 250 × 215 mm3) which is suitable for the preliminary prototyping tests. An Ytterbium fiber laser system is used to melt powders with a continuous power of up to 200 W, a spot of 100 μm, and scanning rate up to 7000 mm/s in an argon atmosphere. The used process parameters are shown in Table 2. The produced component was heat-treated in a furnace (2 h at 300 ◦C) to prevent inaccuracies due to stresses induced thermally during removal of the parts. Figure 11 shows the as-built technical prototype in AlSi10Mg manufactured by the EOSINT M270 machine.


**Table 2.** Process parameter values employed for the bracket production.

**Figure 11.** The technical prototype produced by EOSINT M270.

#### 4.2.2. Cost of the Bracket

A production series of the bracket with the new design has been considered to compare the feasibility of the product and the actual cost with those of the original design. A production quantity of 400 parts per year was considered [35].

The time to produce the original design, using a milling machine, is about 1.40 h, and the total cost is around €116 [35].

A SLM500 machine, made by SLM Solution, was considered for the simulation because, among the industrialized L-PBF systems, its building volume fits in a single job a higher number of brackets. The build volume is 500 × 280 × 365mm3, where 500 × 280 mm<sup>2</sup> are the dimensions of the build platform (WxH). The price of the machine is around €1,200,000. The powder necessary to fill the tank (Matfilldisp) is about 50 kg in which a maximum height of the job and a dose factor equal to 27.3 mm and 4, respectively, have been considered. The manufacturing costs were simulated by considering the build platform to have been filled according to the procedure reported in Section 2. Nine parts can be produced for each job. An aliquot of 0.240 kg of material is necessary to build the part and supports (Wm). An additional 5% is considered as powder lost during the cleaning of the part. After the production, the loose powder is removed from the parts and the as-built parts (attached to the building platform) are heat-treated to release the residual stresses. The supports are then removed manually. The pinholes and the holes for the bolts that join the probe to the bracket are the only surfaces that must be finished. It was assumed that all the manufacturing operations were performed in the same workshop.

The above-mentioned data are summarized in Table 3. The coefficient k1 is calculated by the ratio between the VO+A+<sup>S</sup> and the total job volume Vjob, k2, and k3 are calculated according to Equations (4) and (5), while k4 is equal to zero because no cooling time is required after the production. The times included in Table 3 that are necessary to complete any manual operation or task was measured in real production. With this scope, a single part was produced using an SLM500 (Figure 12).


**Table 3.** General information about the cost of the model.

**Figure 12.** Part manufactured by SLM500. The idle times (Table 3) have been measured during the production.

Table 4 shows the calculation of each costs. The cost for a single part is obtained by dividing the cost for the number of brackets that are fabricated in a single job. The machining times were numerically calculated performing a 3-axis milling using computer-aided manufacturing (CAM) software, Visi 19. The same clamps used for the original designed were used. The costs of designing the part and the job were neglected because a large production was considered.


**Table 4.** Calculation of the total manufacturing costs according to the model presented in Section 4.1. \* The volume of Argon necessary to fill the chamber, VAr, is the product of tfillAr and Arp.

The manufacturing cost for the new design (€300.37) results in being more than twice those of the original bracket. Figure 13 compares the distribution of each cost item over the total manufacturing costs for the new design and the original one. It may be observed that the largest contributions to the AM processes are those of the depreciation of machinery and the indirect costs. This is because these costs are computed on the basis of the build time. In fact, the production time of L-PBF machines is longer than that of the traditional manufacturing process. The depreciation of machinery and the production costs for a 3-axis CNC (computer numerical control) process are distributed equally over the total costs. In fact, the total hourly production cost for a traditional machine considers the maintenance of the machine, the tools, the equipment, the lubrication, the cooling system and energy consumption, the operator, movement of the pallet, and so on. As a result, the total hourly production cost for a traditional process is higher than that of an AM process. A large part of the cost of the new design is due to the post-processing and finishing operations. As the currently used L-PBF processes can only produce near-net shaped parts, the total production cost of obtaining a functional part, by means of L-PBF, should be considered as the sum of the production cost, the post-processing and the finishing cost. Accordingly, it is evident that the distribution of the costs of traditional and AM processes is similar. Although it is generally believed that the price of powders influences the final cost of the part to a grea<sup>t</sup> extent, the here presented analysis instead shows that the main influence on L-PBF is the production rate, in other words, the time necessary to produce a part and to finish it. The cost of the material to produce the original design, by means of milling, is comparable with the cost of the material necessary to produce the newly designed part produced by L-PBF. However, the cost of the material for 3-axis CNC has a significant e ffect on the total cost because a large quantity of material is wasted during machining. In fact, a 2.2 kg ingot of material is needed to produce a bracket that weighs 203 g.

**Figure 13.** Distribution of the manufacturing costs.

Besides the increased cost, the benefit that was achieved by adopting the new geometry, and thus the AM process adopted to produce the part, should be considered from an overall point of view. The new design for L-PBF has shown the possibility of achieving the required sti ffness, which in turn improves the actual machine accuracy and dynamics because the load on the electric motor is decreased. Therefore, the higher cost, with respect to the 3-axis CNC, could be justified by the increase in the performance of the component and in turn of the whole machine. The same conclusion cannot be reached when the new design and the 3-axis CNC process are adopted because the complexity of the geometry would lead to an exponential increase in manufacturing costs.
