Evaluation of TPMS Lattice Parameters on the Mechanical Properties of Lightweight Gears Produced by Additive Manufacturing

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This study investigates the influence of TPMS lattice parameters, such as cell radius, cell height and thickness ratio between inner and outer side of the lattice, on the mechanical performance of spur gears. A series of 56 gears with unique gyroid lattices has been designed using nTop® and analysed via finite element simulation in Ansys Workbench. Results suggest that with a mass reduction of 50% in the body of the gear, the gear failure will still occur at the tooth, indicating potential for further mass reduction. Moreover, correlations between lattice parameters and stiffness and stress distribution have been identified. Study compares additionally stress distribution within the gear between various designs. Stress state is visualized as a fnction of a distance from axis of the gear. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction Developments in the additive manufacturing (AM) field shifted the approach to design and fabrication. Many constraints associated with traditional manufacturing are irrelevant for AM. New possibilities enabled by AM include the extension of functionality (intricate internal structures), multi-material design, and lightweighting, among others [ 1 , 2 ]. Similarly, it enables incorporating into the design structures that were unfeasible in the past, like TPMS structures. Those were firstly described in the 19th century [ 3 , 4 , 5 ] however, due to the limited capabilities of manufacturing and FEA at that time, they have recently become a subject of great scientific interest, and they find more and more applications [ 6 , 7 , 8 , 9 ]. It is caused by their characteristics like strength-to-weight ratio, energy absorption, heat exchange, and developing AM technologies [ 10 , 11 , 12 , 13 , 14 , 15 , 16 ]. This study is focused on investigating the first of those features on the example of an essential part in machines, like gears. Previous studies have shown significant potential for lightweighting of 3D printed gears [ 17 , 18 ], also of gears lightweighted by TPMS structures. Moreover, by adjusting the parameters of the lattice, the resulting mechanical properties can be altered [ 19 , 20 , 21 ] and further tailored for certain applications or loading conditions. Notable articles are described below. Nguyen et al [ 19 ] investigated the influence of lattice cell parameters on the mechanical performance, particularly stiffness and strength of gears manufactured from PEEK. The parameters that they had analyzed include volume fraction, cell radius, cell height, structure type, arc count of the cylindrical cell map, and thickness. To analyze the impact of the aforementioned parameters, the authors employed the Taguchi method and Face-Centered Central Composite Design (FCCCD). The results suggest that, among the investigated cases, the gyroid structure is the most efficient for preserving the mechanical properties of the gear. Similar research, concerning gears fabricated from stainless steel (316L), was performed by Felix-Martinex et al [ 23 ] In their study, the research emphasis was put on the influence of volume fraction on maximal displacement and von Mises strength. According to their results, TPMS lattices, particularly gyroid, Schwarz-P, and diamond, consistently outperform strut-based lattices in terms of stress and displacement minimization. Additionally, manufacturing feasibility considerations are addressed in this paper. The authors highlight the importance of avoiding enclosed cavities and maintaining feature sizes that are printable for specific AM techniques and machines. Nestorowski et al [ 20 ] analyzed gyroid lattices inside gears with variable volume fraction. The FEM analysis was performed on a model consisting of 2 gears in contact with a mesh densified there. Thus, the influence on contact pressure and root stress could be analyzed alongside body stress. Particularly, reduction of material leads to a significant increase in stress within the body, a slight increase in root stress, and a slight decrease in contact pressure. Notably, for the case with 48.31% of mass reduction, the concentration of the highest stress shifted to the gear body, suggesting a potential failure zone. Çalışkan et al [ 21 , 22 ] tested the additively manufactured gears with various lattice structures to evaluate their failure mode and behaviour under compression load. The tested structures included both strut-based and TPMS lattices. The experiment demonstrated that loading of gears with TPMS structures leads to tooth fracture, in contrast to tested gears with strut-based lattice, which showed failure within the lattice. This result shows the feasibility of TPMS lattices for weight reduction of gears, since even with reduced weight, the load-bearing capacity is defined by the strength of the tooth. However, until now, there is no research paper that tackles the lightweighting of gears with TPMS lattices, which focuses on investigating the various mass distributions along the radius of the gear. This article aims to fill this gap. Many studies have shown [ 21 , 22 ] superiority of TPMS lattices over strut-based lattices for the lightweighting of gears. Also, the investigations that did not focus on a particular application, like gear, but rather on unit cells or cubes, find that the gyroid’s mechanical properties are suitable for lightweighting [ 24 , 25 ]. Additionally, Fu et al [ 26 ] found that gyroids exhibit near-isotropic stiffness properties. After further investigation, the gyroid lattice results in lower stresses and deformations compared to other TPMS [ 11 , 27 , 28 , 29 ]. Thus, all of the designs prepared for this study will be based on this structure, which is moreover self-supportive in the AM process. Besides the parameters that have been investigated in the past, this paper contains considerations on the influence of mass distribution on stresses and stiffness of gears. 2. Methodology 2.1. Design The research was focused on investigating the influence of various mass distributions within the region between the gear rim and the connection to the shaft; thus, only this region was subjected to latticing, and the rest of the gear is assumed to be solid. The basic parameters of the spur gear were the same for all numerical simulations, i.e., m = 3, z = 18, h = 10 mm, pressure angle = 20°, and diameter on connection to the shaft = 9 mm. Dimensions and nomenclature of design regions are presented in Fig. 1 : For the generation of the TPMS lattice inside the design space, the cylindrical cell map was used. The defining parameters of TPMS lattice cells for this type of arrangement are arc count, cell radius, and cell height, which define the cell in a cylindrical coordinate system. All of the lattices share the same characteristics, such as type of TPMS lattice – gyroid, arc count, which is the same as the number of teeth – 18, and volume fraction, which is always 50% of solid material in the design space. Keeping the arc count equal to the number of teeth ensures the uniformity of design for each tooth. During the research, all of the combinations of parameters listed in Table 1 were simulated (56 unique geometries). The gears with lattices were generated using nTop® software. Table 1 Lattice parameters Lattice parameter Values Radius (mm) 3, 4, 6, 12 Height (mm) 5, 10 Thickness ratio between inner and outer end of lattice 1:1, 1:1.5, 1:2, 1:2.5, 1:3, 1:3.5, 1:4 Relative density in design space 50% for all The thickness ratio means the proportion of the cell’s wall thickness at the inner diameter (further referred to as Inner Thickness – IT) of the design space to the thickness in the outer diameter (Outer Thickness – OT), i.e., a ratio 1:4 means that the wall of the cell is 4 times thicker close to the teeth than close to the hub. The exact values were determined by a Python script that was iteratively progressing towards more exact values for given input parameters (radius, height, ratio, and volume reduction). Parameters for all of the geometries used for the research are juxtaposed in the Table 2 . Table 2 Thicknesses of the gyroid structure near the hub (IT - Inner Thickness) and near the rim (OT - Outer Thickness) for all 56 unique geometries Height and radius R = 3 H = 5 R = 3 H = 10 R = 4 H = 5 R = 4 H = 10 R = 6 H = 5 R = 6 H = 10 R = 12 H = 5 R = 12 H = 10 Thickness ratio 1:1 IT = 1.08 OT = 1.08 IT = 1.35 OT = 1.35 IT = 1.19 OT = 1.19 IT = 1.49 OT = 1.49 IT = 1.36 OT = 1.36 IT = 1.71 OT = 1.71 IT = 1.7 OT = 1.7 IT = 2.14 OT = 2.14 1:1.5 IT = 0.847 OT = 1.27 IT = 1.06 OT = 1.59 IT = 0.927 OT = 1.39 IT = 1.167 OT = 1.75 IT = 1.067 OT = 1.6 IT = 1.34 OT = 2.01 IT = 1.333 OT = 2 IT = 1.687 OT = 2.53 1:2 IT = 0.645 OT = 1.39 IT = 0.875 OT = 1.75 IT = 0.765 OT = 1.53 IT = 0.96 OT = 1.92 IT = 0.875 OT = 1.75 IT = 1.1 OT = 2.2 IT = 1.1 OT = 2.2 IT = 1.385 OT = 2.77 1:2.5 IT = 0.588 OT = 1.470 IT = 0.74 OT = 1.85 IT = 0.648 OT = 1.62 IT = 0.816 OT = 2.04 IT = 0.74 OT = 1.85 IT = 0.932 OT = 2.33 IT = 0.936 OT = 2.34 IT = 1.18 OT = 2.95 1:3 IT = 0.513 OT = 1.54 IT = 0.647 OT = 1.94 IT = 0.563 OT = 1.69 IT = 0.71 OT = 2.13 IT = 0.643 OT = 1.93 IT = 0.81 OT = 2.43 IT = 0.813 OT = 2.44 IT = 1.023 OT = 3.07 1:3.5 IT = 0.454 OT = 1.59 IT = 0.571 OT = 2 IT = 0.497 OT = 1.74 IT = 0.626 OT = 2.19 IT = 0.569 OT = 1.99 IT = 0.717 OT = 2.51 IT = 0.72 OT = 2.52 IT = 0.906 OT = 3.17 1:4 IT = 0.405 OT = 1.62 IT = 0.51 OT = 2.04 IT = 0.445 OT = 1.78 IT = 0.562 OT = 2.25 IT = 0.51 OT = 2.04 IT = 0.642 OT = 2.57 IT = 0.645 OT = 2.58 IT = 0.812 OT = 3.25 Moreover, for the assessment of the results in the context, the results will be compared to a spur gear with design space filled with solid (Fig. 3 ), the rest of the parameters, like module, pressure angle, etc., are the same. It is worth noting that the gear designed in this way has more material than the rest of the gears subjected to analysis. 2.2. Finite element analysis In order to set the element size for the numerical simulation, a mesh analysis was performed. Additionally, the minimal thickness at the inner end of the lattice for the worst-case scenario was taken into consideration. After analysis of various mesh generation possibilities and various element sizes, it was decided to use the Robust Tetrahedral Mesh (RTM) function available in nTop with 0.3 mm edge length. Plot of maximal stress over radius (see section 3 ) for meshes with element sizes of 0.2, 0.3, 0.6, and 0.9 mm generated by means of RTM is presented in Fig. 4 . In order to minimize the influence of mesh parameters on the results, the same parameters for mesh generation were used for all gears. The static analysis was performed in Ansys Workbench 2024 R2, using the Static Structural solver. The boundary conditions were defined as fixation on the tooth face and a moment of 5000 N · mm, which was applied to the hub. Material of simulated gear was PEEK with Poisson’s ratio: 0.4, density 1.31 g/cm3, and stress-strain relation as depicted in Fig. 5 . The boundary conditions are presented in the Fig. 6 . The same method was used by Nguyen et al [ 19 ]. 3. Results and discussion During the assessment of the results, not only the displacement and maximal stress in the design region were taken into consideration, but also the chart of maximal stress for each distance from the axis of the gear was created. This plot helps to better visualize the distribution of stress and facilitate comparison of various geometries. Moreover, it was divided into design regions as depicted in the Fig. 7 for better clarity. For further analysis, the most important will be the change in stress distribution in the design domain, since this region was subjected to latticing. 3.1. Effect of cell radius The analysis of data showed that radius has a significant influence on mechanical properties. Considering the maximal displacement, the correlation is clearly visible in the Fig. 8 – the bigger the radius, the stiffer the gear becomes. This correlation is visible for all thickness ratios and for both analyzed heights. The figure below presents the influence of radius on displacement for a gear with a cell height equal to 5 mm. Considering the von Mises stress results, one can see in the Fig. 9 that in the dedendum and addendum, they follow almost an identical pattern, the differences are in the design space. In the outer region of the design domain, the lowest von Mises stress is observed for the R12 gear. Generally, it can be observed that a greater radius yields a lower stress here. The opposite is true on the inner side of the design space. 3.2 Effect of cell height The next analyzed factor was cell height, which can also be referred to as the number of cells in the axial direction. For H = 10 mm the lattice has only one axially, whereas for H = 5 mm – 2 cells. The dependency between displacement and the cell’s height can be seen in the Fig. 10 . The lattices with heights of 5 and 10 mm are presented with shades of blue and green, respectively. Clearly, the lattices with two cells placed axially are stiffer for bending loads than the lattices with only one cell. For stress distribution, there is no direct correlation. For the radii 3, 4, 6 mm, the plot of von Mises stress over radius for H = 5 mm lies below the corresponding lattices with H = 10 mm. However, for the R = 12 mm, the situation is opposite, height influence is depicted on stress over radius plots in Fig. 11 for R = 4 mm and in Fig. 12 for R = 12 mm. 3.3 Effect of thickness ratio For all of the analyzed heights and radii, the increase in thickness ratio causes a decrease in displacement – as depicted in the Fig. 13 . This correlation is stronger for smaller radii, however, those gears also show generally higher deformation for a ratio of 1:1. The results suggest that it is beneficial for a gear’s stiffness to have more mass distributed near the rim. In the design space, near the fixed hub, the stress is higher with a rising thickness ratio, which is the effect of thinning of the inner thickness (Fig. 14 ). On the contrary, the stress is slightly decreasing near the rim for a higher thickness ratio. It is also worth noting that for a ratio of 1:1 for all gears, the global trend of stress within the design domain is increasing, besides fluctuation caused by geometry transitions within the gyroid cell. For higher thickness ratios, the von Mises stress in the design space is quite large in the region near the hub, then it drops in the middle and rises in the region near the rim. 4. Conclusions The main findings of the conducted research can be summarized in the following points: For all lattice parameters, the von Mises stress distribution (as depicted in the von Mises stress over radius plot) in the tooth and rim (ignoring the region near the design space) is almost identical. Thus, the influence of the analyzed values of parameters on the stress state in the tooth is negligible. For all analyzed cases, the highest von Mises stress is observed in the tooth, in other words the failure of the gear is likely to occur at the tooth, not the lattice. Hence, further increasing the volume fraction within the design space is feasible. Furthermore, extending the region subjected to latticing may also be considered. A greater radius of the gyroid unit cell has a positive impact on the stiffness of the gear. Moreover, the stress distribution within the design space is more uniform for the greatest investigated radius (R = 12 mm), compared to corresponding gears with smaller radii. For uniform thickness (ratio 1:1), the stress values increase with radius, and the highest stress values are observed at the outer edge of the design domain. With an increased thickness ratio, in other words, a thicker lattice near the outer diameter, the stress in this area decreases at the expense of a stress spike at the connection of the hub to the design space. This effect can be minimized by ensuring a smoother transition. In general, from a lightweighting and stress distribution standpoint, higher thickness ratios are preferable. Having more cells in the axial direction has a positive influence on stiffness. Comparison of all H10 lattices with corresponding H5 lattices showed that for each case, the displacement is lower for H5. The effect on stress is not straightforward and depends on the relative elongation of the cell. For further research, a more gradual geometry transition between solid elements and latticed design space shall be used to minimize excessive stress peaks. Another potential is further diversification of thickness values by increasing them in the regions with stress peaks. Declarations Conflicts of interest: The authors declare no conflict of interest. Funding: This research received no external funding. Authors’ contribution: Norbert Banaś and Jacek Sawicki are contributed equally to this work. References Schumacher C, Bickel B, Rys J, Marschner S, Daraio C, Gross M (2015) Microstructures to control elasticity in 3D printing. ACM Trans Graphics 34(4):1–13. https://doi.org/10.1145/2766926 Rosen DW (2014) Research supporting principles for design for additive manufacturing. Virtual Phys Prototyp 9(4):225–232. https://doi.org/10.1080/17452759.2014.951530 Neovius ER (1883) Bestimmung Zweier Spezieller Periodischer Minimalflächen. Akad. Abhandlungen H. A. Schwarz. Gesammelte Mathematische Abhandlungen. Berlin: Springer; (1933) Schoen A (1970) Infinite periodic minimal surfaces without self-intersections Gupta A, Babu LS (2023) Triply Periodic Minimal Surfaces: An Overview of Their Features, Failure Mechanisms, and Applications. J Mines Metals Fuels 211–221. https://doi.org/10.18311/jmmf/2022/31230 Nazir A, Abate KM, Kumar A, Jeng JY (2019) A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures. Int J Adv Manuf Technol 104(9–12):3489–3510. https://doi.org/10.1007/s00170-019-04085-3 Wawryniuk Z, Brancewicz-Steinmetz E, Sawicki J (2024) Revolutionizing transportation: an overview of 3D printing in aviation, automotive, and space industries. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-024-14226-y Günther F, Pilz S, Hirsch F, Wagner M, Kästner M, Gebert A et al (2023) Shape optimization of additively manufactured lattices based on triply periodic minimal surfaces. Additive Manuf 73:103659. https://doi.org/10.1016/j.addma.2023.103659 Nagesha BK, Dhinakaran V, Varsha Shree M, Manoj Kumar KP, Chalawadi D, Sathish T (2020) Review on characterization and impacts of the lattice structure in additive manufacturing. Materials Today: Proceedings. ;21:916–9. https://doi.org/10.1016/j.matpr.2019.08.158 Qiu N, Wan Y, Shen Y, Fang J (2024) Experimental and numerical studies on mechanical properties of TPMS structures. Int J Mech Sci 261:108657. https://doi.org/10.1016/j.ijmecsci.2023.108657 Jin M, Feng Q, Fan X, Luo Z, Tang Q, Song J et al (2022) Investigation on the mechanical properties of TPMS porous structures fabricated by laser powder bed fusion. J Manuf Process 76:559–574. https://doi.org/10.1016/j.jmapro.2022.02.035 Liu J, Cheng D, Oo K, McCrimmon TL, Bai S (2024) Design and Additive Manufacturing of TPMS Heat Exchangers. Appl Sci 14(10):3970. https://doi.org/10.1016/j.jmapro.2022.02.035 Tang W, Zhou H, Zeng Y, Yan M, Jiang C, Yang P et al (2023) Analysis on the convective heat transfer process and performance evaluation of Triply Periodic Minimal Surface (TPMS) based on Diamond, Gyroid and Iwp. Int J Heat Mass Transf 201:123642. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123642 Challis VJ, Xu X, Zhang LC, Roberts AP, Grotowski JF, Sercombe TB (2014) High specific strength and stiffness structures produced using selective laser melting. Mater Design 63:783–788. https://doi.org/10.1016/j.matdes.2014.05.064 Yan K, Wang J, Li L, Deng H (2023) Numerical investigation into thermo-hydraulic characteristics and mixing performance of triply periodic minimal surface-structured heat exchangers. Appl Therm Eng 230:120748. https://doi.org/10.1016/B978-0-12-824438-8.00002-9 Brummer M, Raddatz KJ, Schmitt MM, Schlick G, Tobie T, Daub R et al (2023) Static load-carrying behavior and material properties of additively manufactured gears (PBF-LB/M, 16MnCr5). Rapid Prototyp J 29(11):117–130. https://doi.org/10.1108/RPJ-02-2023-0035 Mura A, Curà F, Pasculli L (2018) Optimisation methodology for lightweight gears to be produced by additive manufacturing techniques. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. ;232(19):3512–23. https://doi.org/10.1177/0954406217737107 Nguyen L, Nguyen K (2022) Lightweight Plastic Gear Body using Gyroid Structure for Additive Manufacturing. J Mach Eng. https://doi.org/10.36897/jme/157077 Nestorovski B, Angeleska E, Avramov N (2023) Load carrying capacities of gears with a lattice structure body. MATEC Web of Conferences. ;387:02001. https://doi.org/10.1051/matecconf/202338702001 Çalışkan Cİ, Khan HM, Özer G, Bulduk ME, Coşkun M (2025) Evaluation of Lattice Material Suitability for Additive Manufactured Gears under Compression Loads. Trans Indian Inst Met 78(2):36. https://doi.org/10.1007/s12666-024-03529-z Bulduk ME, Çalışkan Cİ, Coşkun M, Özer G, Koç E (2022) Comparison of the effect of different topological designs and process parameters on mechanical strength in gears. Int J Adv Manuf Technol 119(9–10):6707–6716 Félix-Martínez C, Piedra S, Perez-Barrera J, González-Carmona JM, Franco Urquiza EA, Gómez-Ortega A (2025) Lightweighting and performance analysis of a spur gear by implementing cellular structures and additive manufacturing. Int J Adv Manuf Technol 136(5–6):2291–2303. https://doi.org/10.1007/s00170-024-14977-8 Wallat L, Altschuh P, Reder M, Nestler B, Poehler F (2022) Computational Design and Characterisation of Gyroid Structures with Different Gradient Functions for Porosity Adjustment. Materials 15(10):3730. https://doi.org/10.3390/ma15103730 Maskery I, Aboulkhair NT, Aremu AO, Tuck CJ, Ashcroft IA (2017) Compressive failure modes and energy absorption in additively manufactured double gyroid lattices. Additive Manuf 16:24–29. https://doi.org/10.1016/j.addma.2017.04.003 Fu J, Ding J, Qu S, Zhang L, Wang MY, Fu MW et al (2022) Improved light-weighting potential of SS316L triply periodic minimal surface shell lattices by micro laser powder bed fusion. Mater Design 222:111018. https://doi.org/10.1016/j.matdes.2022.111018 Maskery I, Ashcroft IA (2020) The deformation and elastic anisotropy of a new gyroid-based honeycomb made by laser sintering. Additive Manuf 36:101548. https://doi.org/10.1016/j.addma.2020.101548 Teng F, Sun Y, Guo S, Gao B, Yu G (2022) Topological and Mechanical Properties of Different Lattice Structures Based on Additive Manufacturing. Micromachines 13(7):1017. https://doi.org/10.3390/mi13071017 Szatkiewicz T, Laskowska D, Bałasz B, Mitura K (2022) The Influence of the Structure Parameters on the Mechanical Properties of Cylindrically Mapped Gyroid TPMS Fabricated by Selective Laser Melting with 316L Stainless Steel Powder. Materials 15(12):4352. https://doi.org/10.3390/ma15124352 Cite Share Download PDF Status: Published Journal Publication published 06 Mar, 2026 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Major Revisions Needed 29 Nov, 2025 Reviewers agreed at journal 26 Oct, 2025 Reviewers invited by journal 24 Oct, 2025 Editor assigned by journal 08 Oct, 2025 First submitted to journal 06 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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08:39:20","extension":"xml","order_by":89,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":92840,"visible":true,"origin":"","legend":"","description":"","filename":"JAMTD25057030structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/0283b924179dc4e5bccabd04.xml"},{"id":95183149,"identity":"611278f8-fde7-4fef-bda1-c3aff647136b","added_by":"auto","created_at":"2025-11-05 08:39:21","extension":"html","order_by":90,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":106825,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/2b2a5cbc770fc6a7fac4ebd8.html"},{"id":95183108,"identity":"a1f281cc-8191-4f25-ac11-163682f908fb","added_by":"auto","created_at":"2025-11-05 08:39:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":77116,"visible":true,"origin":"","legend":"\u003cp\u003eDimesions and nomenclature of design regions of the gear\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/5d246e299235d81b4575c749.png"},{"id":95228153,"identity":"76f7410c-a8cd-42af-813e-7fcd4b4f692b","added_by":"auto","created_at":"2025-11-05 16:33:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":687858,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of R6H10 gears with thickness ratio of 1:1 (left) and 1:4 (right)\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/559aa1e6294d5d70f6ddc54f.png"},{"id":95183080,"identity":"753db705-4c59-45d4-a70a-0d1f1cba36a9","added_by":"auto","created_at":"2025-11-05 08:39:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":95476,"visible":true,"origin":"","legend":"\u003cp\u003eBenchmark gear used for results comparison\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/a66054a91125550998adfcc4.png"},{"id":95227405,"identity":"67f0a9f8-b203-4f73-a880-b59614a01014","added_by":"auto","created_at":"2025-11-05 16:32:27","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":424406,"visible":true,"origin":"","legend":"\u003cp\u003ePlot of maximal stress over radius (see section 3) for gears with various mesh elements sizes\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/2a3d204265268c7e53824813.png"},{"id":95183084,"identity":"db6de546-e79e-4754-a240-ed55f181f6a0","added_by":"auto","created_at":"2025-11-05 08:39:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":81598,"visible":true,"origin":"","legend":"\u003cp\u003eStress-strain relation for PEEK material used in simulation\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/01509e4c5c698a1336842118.png"},{"id":95183081,"identity":"5547845c-16fb-4146-98ab-4671414902ae","added_by":"auto","created_at":"2025-11-05 08:39:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":474948,"visible":true,"origin":"","legend":"\u003cp\u003eBoundary conditions used in simulation\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/054bc02ac2cc689f0e1a5a23.png"},{"id":95183094,"identity":"5f665e65-cad8-4a75-8a7b-72ec09685c26","added_by":"auto","created_at":"2025-11-05 08:39:19","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":317583,"visible":true,"origin":"","legend":"\u003cp\u003ePlot used for analyzing of influence of latticing on stress distribution in the gear\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/dbf3646d36d67fc6b8c2722c.png"},{"id":95183131,"identity":"82bbebef-609c-4a13-a95e-0383387f638f","added_by":"auto","created_at":"2025-11-05 08:39:20","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":332799,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of radius on max displacement (H=5 mm for all gears in this figure)\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/899b287dee185f9ed993d457.png"},{"id":95228165,"identity":"1abc7f85-c8ed-4686-a990-da3c43625d70","added_by":"auto","created_at":"2025-11-05 16:33:27","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":406547,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of cell's radius on stress distribution\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/70198eb60931b7388fa92c05.png"},{"id":95226998,"identity":"1c820613-4553-42bc-a5da-e323d890377a","added_by":"auto","created_at":"2025-11-05 16:31:59","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":132057,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of maximal displacements, points in shades of green correspond to lattices with 10mm cell's height, while those in shades of blue to 5mm height\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/36fb7d1f31fca09df05cced4.png"},{"id":95183075,"identity":"d1d0b3a9-d5cc-404d-9ec4-939c3d17031f","added_by":"auto","created_at":"2025-11-05 08:39:17","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":1363842,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution for small cell radius. In that case smaller height leads to lower stress in the design domain.\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/b1b53645a305896bb5739fc5.png"},{"id":95183106,"identity":"f98d2791-34f5-43b7-87ae-86522f819d78","added_by":"auto","created_at":"2025-11-05 08:39:19","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":1577559,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution for larger cells radius. For elongated cell bigger height leads to smaller stresses\u003c/p\u003e","description":"","filename":"image12.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/3ba79ba4a5aec8be5ea6f8bb.png"},{"id":95183079,"identity":"dee93e24-943b-4075-86c1-72b19c89046b","added_by":"auto","created_at":"2025-11-05 08:39:18","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":144508,"visible":true,"origin":"","legend":"\u003cp\u003eDependency between displacement and thickness ratio. Having more material at OT increases stiffness of the gear.\u003c/p\u003e","description":"","filename":"image13.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/1869331a18649b92a3885e9e.png"},{"id":95228466,"identity":"8b96182c-c97a-4a86-9213-da811226adfd","added_by":"auto","created_at":"2025-11-05 16:33:47","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":435785,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of thickness ratio on stress distribution.\u003c/p\u003e","description":"","filename":"image14.png","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/84de6b1fbebd3220bdafb4bf.png"},{"id":104251371,"identity":"3005824e-c163-4513-8480-94b14d9c8380","added_by":"auto","created_at":"2026-03-09 16:12:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6688357,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7772615/v1/420c32c6-5ea5-4ad2-8dca-674198fdb9b5.pdf"}],"financialInterests":"","formattedTitle":"Evaluation of TPMS Lattice Parameters on the Mechanical Properties of Lightweight Gears Produced by Additive Manufacturing","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eDevelopments in the additive manufacturing (AM) field shifted the approach to design and fabrication. Many constraints associated with traditional manufacturing are irrelevant for AM. New possibilities enabled by AM include the extension of functionality (intricate internal structures), multi-material design, and lightweighting, among others [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Similarly, it enables incorporating into the design structures that were unfeasible in the past, like TPMS structures. Those were firstly described in the 19th century [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] however, due to the limited capabilities of manufacturing and FEA at that time, they have recently become a subject of great scientific interest, and they find more and more applications [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. It is caused by their characteristics like strength-to-weight ratio, energy absorption, heat exchange, and developing AM technologies [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. This study is focused on investigating the first of those features on the example of an essential part in machines, like gears.\u003c/p\u003e\u003cp\u003ePrevious studies have shown significant potential for lightweighting of 3D printed gears [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], also of gears lightweighted by TPMS structures. Moreover, by adjusting the parameters of the lattice, the resulting mechanical properties can be altered [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and further tailored for certain applications or loading conditions. Notable articles are described below.\u003c/p\u003e\u003cp\u003eNguyen et al [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] investigated the influence of lattice cell parameters on the mechanical performance, particularly stiffness and strength of gears manufactured from PEEK. The parameters that they had analyzed include volume fraction, cell radius, cell height, structure type, arc count of the cylindrical cell map, and thickness. To analyze the impact of the aforementioned parameters, the authors employed the Taguchi method and Face-Centered Central Composite Design (FCCCD). The results suggest that, among the investigated cases, the gyroid structure is the most efficient for preserving the mechanical properties of the gear.\u003c/p\u003e\u003cp\u003eSimilar research, concerning gears fabricated from stainless steel (316L), was performed by Felix-Martinex et al [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] In their study, the research emphasis was put on the influence of volume fraction on maximal displacement and von Mises strength. According to their results, TPMS lattices, particularly gyroid, Schwarz-P, and diamond, consistently outperform strut-based lattices in terms of stress and displacement minimization. Additionally, manufacturing feasibility considerations are addressed in this paper. The authors highlight the importance of avoiding enclosed cavities and maintaining feature sizes that are printable for specific AM techniques and machines.\u003c/p\u003e\u003cp\u003eNestorowski et al [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] analyzed gyroid lattices inside gears with variable volume fraction. The FEM analysis was performed on a model consisting of 2 gears in contact with a mesh densified there. Thus, the influence on contact pressure and root stress could be analyzed alongside body stress. Particularly, reduction of material leads to a significant increase in stress within the body, a slight increase in root stress, and a slight decrease in contact pressure. Notably, for the case with 48.31% of mass reduction, the concentration of the highest stress shifted to the gear body, suggesting a potential failure zone.\u003c/p\u003e\u003cp\u003e\u0026Ccedil;alışkan et al [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] tested the additively manufactured gears with various lattice structures to evaluate their failure mode and behaviour under compression load. The tested structures included both strut-based and TPMS lattices. The experiment demonstrated that loading of gears with TPMS structures leads to tooth fracture, in contrast to tested gears with strut-based lattice, which showed failure within the lattice. This result shows the feasibility of TPMS lattices for weight reduction of gears, since even with reduced weight, the load-bearing capacity is defined by the strength of the tooth.\u003c/p\u003e\u003cp\u003eHowever, until now, there is no research paper that tackles the lightweighting of gears with TPMS lattices, which focuses on investigating the various mass distributions along the radius of the gear. This article aims to fill this gap.\u003c/p\u003e\u003cp\u003eMany studies have shown [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] superiority of TPMS lattices over strut-based lattices for the lightweighting of gears. Also, the investigations that did not focus on a particular application, like gear, but rather on unit cells or cubes, find that the gyroid\u0026rsquo;s mechanical properties are suitable for lightweighting [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Additionally, Fu et al [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] found that gyroids exhibit near-isotropic stiffness properties.\u003c/p\u003e\u003cp\u003eAfter further investigation, the gyroid lattice results in lower stresses and deformations compared to other TPMS [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Thus, all of the designs prepared for this study will be based on this structure, which is moreover self-supportive in the AM process. Besides the parameters that have been investigated in the past, this paper contains considerations on the influence of mass distribution on stresses and stiffness of gears.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Design\u003c/h2\u003e\u003cp\u003eThe research was focused on investigating the influence of various mass distributions within the region between the gear rim and the connection to the shaft; thus, only this region was subjected to latticing, and the rest of the gear is assumed to be solid. The basic parameters of the spur gear were the same for all numerical simulations, i.e., m\u0026thinsp;=\u0026thinsp;3, z\u0026thinsp;=\u0026thinsp;18, h\u0026thinsp;=\u0026thinsp;10 mm, pressure angle\u0026thinsp;=\u0026thinsp;20\u0026deg;, and diameter on connection to the shaft\u0026thinsp;=\u0026thinsp;9 mm. Dimensions and nomenclature of design regions are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e:\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFor the generation of the TPMS lattice inside the design space, the cylindrical cell map was used. The defining parameters of TPMS lattice cells for this type of arrangement are arc count, cell radius, and cell height, which define the cell in a cylindrical coordinate system. All of the lattices share the same characteristics, such as type of TPMS lattice \u0026ndash; gyroid, arc count, which is the same as the number of teeth \u0026ndash; 18, and volume fraction, which is always 50% of solid material in the design space. Keeping the arc count equal to the number of teeth ensures the uniformity of design for each tooth. During the research, all of the combinations of parameters listed in Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e were simulated (56 unique geometries). The gears with lattices were generated using nTop\u0026reg; software.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eLattice parameters\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLattice parameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eValues\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRadius (mm)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3, 4, 6, 12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHeight (mm)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5, 10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThickness ratio between inner and outer end of lattice\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1:1, 1:1.5, 1:2, 1:2.5, 1:3, 1:3.5, 1:4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRelative density in design space\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50% for all\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe thickness ratio means the proportion of the cell\u0026rsquo;s wall thickness at the inner diameter (further referred to as Inner Thickness \u0026ndash; IT) of the design space to the thickness in the outer diameter (Outer Thickness \u0026ndash; OT), i.e., a ratio 1:4 means that the wall of the cell is 4 times thicker close to the teeth than close to the hub. The exact values were determined by a Python script that was iteratively progressing towards more exact values for given input parameters (radius, height, ratio, and volume reduction).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eParameters for all of the geometries used for the research are juxtaposed in the Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThicknesses of the gyroid structure near the hub (IT - Inner Thickness) and near the rim (OT - Outer Thickness) for all 56 unique geometries\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHeight and radius\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;3\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;10\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;10\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;6\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;6\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;10\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;12\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;5\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eR\u0026thinsp;=\u0026thinsp;12\u003c/p\u003e\u003cp\u003eH\u0026thinsp;=\u0026thinsp;10\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThickness ratio\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.08\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.35\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.19\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.49\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.36\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.71\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.7\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;2.14\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.14\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.847\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.06\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.927\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.167\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.067\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.34\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.333\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.687\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.53\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.645\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.875\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.765\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.96\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.875\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.1\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.1\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.385\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.77\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:2.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.588\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.470\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.74\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.648\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.816\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.74\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.932\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.936\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.18\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.513\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.647\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.563\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.71\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.643\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.81\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.813\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;1.023\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;3.07\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:3.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.454\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.571\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.497\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.74\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.626\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.569\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.717\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.72\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.906\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;3.17\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1:4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.405\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.51\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.445\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;1.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.562\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.51\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.642\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.645\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;2.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eIT\u0026thinsp;=\u0026thinsp;0.812\u003c/p\u003e\u003cp\u003eOT\u0026thinsp;=\u0026thinsp;3.25\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eMoreover, for the assessment of the results in the context, the results will be compared to a spur gear with design space filled with solid (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), the rest of the parameters, like module, pressure angle, etc., are the same. It is worth noting that the gear designed in this way has more material than the rest of the gears subjected to analysis.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Finite element analysis\u003c/h2\u003e\u003cp\u003eIn order to set the element size for the numerical simulation, a mesh analysis was performed. Additionally, the minimal thickness at the inner end of the lattice for the worst-case scenario was taken into consideration. After analysis of various mesh generation possibilities and various element sizes, it was decided to use the Robust Tetrahedral Mesh (RTM) function available in nTop with 0.3 mm edge length. Plot of maximal stress over radius (see section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3\u003c/span\u003e) for meshes with element sizes of 0.2, 0.3, 0.6, and 0.9 mm generated by means of RTM is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. In order to minimize the influence of mesh parameters on the results, the same parameters for mesh generation were used for all gears.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe static analysis was performed in Ansys Workbench 2024 R2, using the Static Structural solver. The boundary conditions were defined as fixation on the tooth face and a moment of 5000 N \u0026middot; mm, which was applied to the hub. Material of simulated gear was PEEK with Poisson\u0026rsquo;s ratio: 0.4, density 1.31 g/cm3, and stress-strain relation as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe boundary conditions are presented in the Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The same method was used by Nguyen et al [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003eDuring the assessment of the results, not only the displacement and maximal stress in the design region were taken into consideration, but also the chart of maximal stress for each distance from the axis of the gear was created. This plot helps to better visualize the distribution of stress and facilitate comparison of various geometries. Moreover, it was divided into design regions as depicted in the Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e for better clarity. For further analysis, the most important will be the change in stress distribution in the design domain, since this region was subjected to latticing.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Effect of cell radius\u003c/h2\u003e\u003cp\u003eThe analysis of data showed that radius has a significant influence on mechanical properties. Considering the maximal displacement, the correlation is clearly visible in the Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e \u0026ndash; the bigger the radius, the stiffer the gear becomes. This correlation is visible for all thickness ratios and for both analyzed heights. The figure below presents the influence of radius on displacement for a gear with a cell height equal to 5 mm.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eConsidering the von Mises stress results, one can see in the Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e that in the dedendum and addendum, they follow almost an identical pattern, the differences are in the design space. In the outer region of the design domain, the lowest von Mises stress is observed for the R12 gear. Generally, it can be observed that a greater radius yields a lower stress here. The opposite is true on the inner side of the design space.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Effect of cell height\u003c/h2\u003e\u003cp\u003eThe next analyzed factor was cell height, which can also be referred to as the number of cells in the axial direction. For H\u0026thinsp;=\u0026thinsp;10 mm the lattice has only one axially, whereas for H\u0026thinsp;=\u0026thinsp;5 mm \u0026ndash; 2 cells. The dependency between displacement and the cell\u0026rsquo;s height can be seen in the Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The lattices with heights of 5 and 10 mm are presented with shades of blue and green, respectively. Clearly, the lattices with two cells placed axially are stiffer for bending loads than the lattices with only one cell.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFor stress distribution, there is no direct correlation. For the radii 3, 4, 6 mm, the plot of von Mises stress over radius for H\u0026thinsp;=\u0026thinsp;5 mm lies below the corresponding lattices with H\u0026thinsp;=\u0026thinsp;10 mm. However, for the R\u0026thinsp;=\u0026thinsp;12 mm, the situation is opposite, height influence is depicted on stress over radius plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e for R\u0026thinsp;=\u0026thinsp;4 mm and in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e for R\u0026thinsp;=\u0026thinsp;12 mm.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Effect of thickness ratio\u003c/h2\u003e\u003cp\u003eFor all of the analyzed heights and radii, the increase in thickness ratio causes a decrease in displacement \u0026ndash; as depicted in the Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e. This correlation is stronger for smaller radii, however, those gears also show generally higher deformation for a ratio of 1:1. The results suggest that it is beneficial for a gear\u0026rsquo;s stiffness to have more mass distributed near the rim.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn the design space, near the fixed hub, the stress is higher with a rising thickness ratio, which is the effect of thinning of the inner thickness (Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e). On the contrary, the stress is slightly decreasing near the rim for a higher thickness ratio. It is also worth noting that for a ratio of 1:1 for all gears, the global trend of stress within the design domain is increasing, besides fluctuation caused by geometry transitions within the gyroid cell. For higher thickness ratios, the von Mises stress in the design space is quite large in the region near the hub, then it drops in the middle and rises in the region near the rim.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThe main findings of the conducted research can be summarized in the following points:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eFor all lattice parameters, the von Mises stress distribution (as depicted in the von Mises stress over radius plot) in the tooth and rim (ignoring the region near the design space) is almost identical. Thus, the influence of the analyzed values of parameters on the stress state in the tooth is negligible.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFor all analyzed cases, the highest von Mises stress is observed in the tooth, in other words the failure of the gear is likely to occur at the tooth, not the lattice. Hence, further increasing the volume fraction within the design space is feasible. Furthermore, extending the region subjected to latticing may also be considered.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eA greater radius of the gyroid unit cell has a positive impact on the stiffness of the gear. Moreover, the stress distribution within the design space is more uniform for the greatest investigated radius (R\u0026thinsp;=\u0026thinsp;12 mm), compared to corresponding gears with smaller radii.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFor uniform thickness (ratio 1:1), the stress values increase with radius, and the highest stress values are observed at the outer edge of the design domain. With an increased thickness ratio, in other words, a thicker lattice near the outer diameter, the stress in this area decreases at the expense of a stress spike at the connection of the hub to the design space. This effect can be minimized by ensuring a smoother transition. In general, from a lightweighting and stress distribution standpoint, higher thickness ratios are preferable.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eHaving more cells in the axial direction has a positive influence on stiffness. Comparison of all H10 lattices with corresponding H5 lattices showed that for each case, the displacement is lower for H5. The effect on stress is not straightforward and depends on the relative elongation of the cell.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFor further research, a more gradual geometry transition between solid elements and latticed design space shall be used to minimize excessive stress peaks. Another potential is further diversification of thickness values by increasing them in the regions with stress peaks.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eConflicts of interest:\u003c/h2\u003e\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e\u003cp\u003eThis research received no external funding.\u003c/p\u003e\u003ch2\u003eAuthors\u0026rsquo; contribution:\u003c/h2\u003e\u003cp\u003eNorbert Banaś and Jacek Sawicki are contributed equally to this work.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSchumacher C, Bickel B, Rys J, Marschner S, Daraio C, Gross M (2015) Microstructures to control elasticity in 3D printing. ACM Trans Graphics 34(4):1\u0026ndash;13. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1145/2766926\u003c/span\u003e\u003cspan address=\"10.1145/2766926\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRosen DW (2014) Research supporting principles for design for additive manufacturing. Virtual Phys Prototyp 9(4):225\u0026ndash;232. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/17452759.2014.951530\u003c/span\u003e\u003cspan address=\"10.1080/17452759.2014.951530\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNeovius ER (1883) Bestimmung Zweier Spezieller Periodischer Minimalfl\u0026auml;chen. Akad. Abhandlungen\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eH. A. Schwarz. Gesammelte Mathematische Abhandlungen. Berlin: Springer; (1933)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSchoen A (1970) Infinite periodic minimal surfaces without self-intersections\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGupta A, Babu LS (2023) Triply Periodic Minimal Surfaces: An Overview of Their Features, Failure Mechanisms, and Applications. J Mines Metals Fuels 211\u0026ndash;221. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.18311/jmmf/2022/31230\u003c/span\u003e\u003cspan address=\"10.18311/jmmf/2022/31230\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNazir A, Abate KM, Kumar A, Jeng JY (2019) A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures. Int J Adv Manuf Technol 104(9\u0026ndash;12):3489\u0026ndash;3510. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-019-04085-3\u003c/span\u003e\u003cspan address=\"10.1007/s00170-019-04085-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWawryniuk Z, Brancewicz-Steinmetz E, Sawicki J (2024) Revolutionizing transportation: an overview of 3D printing in aviation, automotive, and space industries. Int J Adv Manuf Technol. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-024-14226-y\u003c/span\u003e\u003cspan address=\"10.1007/s00170-024-14226-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eG\u0026uuml;nther F, Pilz S, Hirsch F, Wagner M, K\u0026auml;stner M, Gebert A et al (2023) Shape optimization of additively manufactured lattices based on triply periodic minimal surfaces. Additive Manuf 73:103659. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.addma.2023.103659\u003c/span\u003e\u003cspan address=\"10.1016/j.addma.2023.103659\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNagesha BK, Dhinakaran V, Varsha Shree M, Manoj Kumar KP, Chalawadi D, Sathish T (2020) Review on characterization and impacts of the lattice structure in additive manufacturing. Materials Today: Proceedings. ;21:916\u0026ndash;9. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.matpr.2019.08.158\u003c/span\u003e\u003cspan address=\"10.1016/j.matpr.2019.08.158\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eQiu N, Wan Y, Shen Y, Fang J (2024) Experimental and numerical studies on mechanical properties of TPMS structures. Int J Mech Sci 261:108657. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijmecsci.2023.108657\u003c/span\u003e\u003cspan address=\"10.1016/j.ijmecsci.2023.108657\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJin M, Feng Q, Fan X, Luo Z, Tang Q, Song J et al (2022) Investigation on the mechanical properties of TPMS porous structures fabricated by laser powder bed fusion. J Manuf Process 76:559\u0026ndash;574. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jmapro.2022.02.035\u003c/span\u003e\u003cspan address=\"10.1016/j.jmapro.2022.02.035\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu J, Cheng D, Oo K, McCrimmon TL, Bai S (2024) Design and Additive Manufacturing of TPMS Heat Exchangers. Appl Sci 14(10):3970. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jmapro.2022.02.035\u003c/span\u003e\u003cspan address=\"10.1016/j.jmapro.2022.02.035\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTang W, Zhou H, Zeng Y, Yan M, Jiang C, Yang P et al (2023) Analysis on the convective heat transfer process and performance evaluation of Triply Periodic Minimal Surface (TPMS) based on Diamond, Gyroid and Iwp. Int J Heat Mass Transf 201:123642. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijheatmasstransfer.2022.123642\u003c/span\u003e\u003cspan address=\"10.1016/j.ijheatmasstransfer.2022.123642\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChallis VJ, Xu X, Zhang LC, Roberts AP, Grotowski JF, Sercombe TB (2014) High specific strength and stiffness structures produced using selective laser melting. Mater Design 63:783\u0026ndash;788. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.matdes.2014.05.064\u003c/span\u003e\u003cspan address=\"10.1016/j.matdes.2014.05.064\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYan K, Wang J, Li L, Deng H (2023) Numerical investigation into thermo-hydraulic characteristics and mixing performance of triply periodic minimal surface-structured heat exchangers. Appl Therm Eng 230:120748. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/B978-0-12-824438-8.00002-9\u003c/span\u003e\u003cspan address=\"10.1016/B978-0-12-824438-8.00002-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBrummer M, Raddatz KJ, Schmitt MM, Schlick G, Tobie T, Daub R et al (2023) Static load-carrying behavior and material properties of additively manufactured gears (PBF-LB/M, 16MnCr5). Rapid Prototyp J 29(11):117\u0026ndash;130. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1108/RPJ-02-2023-0035\u003c/span\u003e\u003cspan address=\"10.1108/RPJ-02-2023-0035\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMura A, Cur\u0026agrave; F, Pasculli L (2018) Optimisation methodology for lightweight gears to be produced by additive manufacturing techniques. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. ;232(19):3512\u0026ndash;23. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/0954406217737107\u003c/span\u003e\u003cspan address=\"10.1177/0954406217737107\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNguyen L, Nguyen K (2022) Lightweight Plastic Gear Body using Gyroid Structure for Additive Manufacturing. J Mach Eng. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.36897/jme/157077\u003c/span\u003e\u003cspan address=\"10.36897/jme/157077\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNestorovski B, Angeleska E, Avramov N (2023) Load carrying capacities of gears with a lattice structure body. MATEC Web of Conferences. ;387:02001. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1051/matecconf/202338702001\u003c/span\u003e\u003cspan address=\"10.1051/matecconf/202338702001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e\u0026Ccedil;alışkan Cİ, Khan HM, \u0026Ouml;zer G, Bulduk ME, Coşkun M (2025) Evaluation of Lattice Material Suitability for Additive Manufactured Gears under Compression Loads. Trans Indian Inst Met 78(2):36. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12666-024-03529-z\u003c/span\u003e\u003cspan address=\"10.1007/s12666-024-03529-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBulduk ME, \u0026Ccedil;alışkan Cİ, Coşkun M, \u0026Ouml;zer G, Ko\u0026ccedil; E (2022) Comparison of the effect of different topological designs and process parameters on mechanical strength in gears. Int J Adv Manuf Technol 119(9\u0026ndash;10):6707\u0026ndash;6716\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eF\u0026eacute;lix-Mart\u0026iacute;nez C, Piedra S, Perez-Barrera J, Gonz\u0026aacute;lez-Carmona JM, Franco Urquiza EA, G\u0026oacute;mez-Ortega A (2025) Lightweighting and performance analysis of a spur gear by implementing cellular structures and additive manufacturing. Int J Adv Manuf Technol 136(5\u0026ndash;6):2291\u0026ndash;2303. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-024-14977-8\u003c/span\u003e\u003cspan address=\"10.1007/s00170-024-14977-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWallat L, Altschuh P, Reder M, Nestler B, Poehler F (2022) Computational Design and Characterisation of Gyroid Structures with Different Gradient Functions for Porosity Adjustment. Materials 15(10):3730. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/ma15103730\u003c/span\u003e\u003cspan address=\"10.3390/ma15103730\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMaskery I, Aboulkhair NT, Aremu AO, Tuck CJ, Ashcroft IA (2017) Compressive failure modes and energy absorption in additively manufactured double gyroid lattices. Additive Manuf 16:24\u0026ndash;29. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.addma.2017.04.003\u003c/span\u003e\u003cspan address=\"10.1016/j.addma.2017.04.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFu J, Ding J, Qu S, Zhang L, Wang MY, Fu MW et al (2022) Improved light-weighting potential of SS316L triply periodic minimal surface shell lattices by micro laser powder bed fusion. Mater Design 222:111018. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.matdes.2022.111018\u003c/span\u003e\u003cspan address=\"10.1016/j.matdes.2022.111018\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMaskery I, Ashcroft IA (2020) The deformation and elastic anisotropy of a new gyroid-based honeycomb made by laser sintering. Additive Manuf 36:101548. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.addma.2020.101548\u003c/span\u003e\u003cspan address=\"10.1016/j.addma.2020.101548\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTeng F, Sun Y, Guo S, Gao B, Yu G (2022) Topological and Mechanical Properties of Different Lattice Structures Based on Additive Manufacturing. Micromachines 13(7):1017. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/mi13071017\u003c/span\u003e\u003cspan address=\"10.3390/mi13071017\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSzatkiewicz T, Laskowska D, Bałasz B, Mitura K (2022) The Influence of the Structure Parameters on the Mechanical Properties of Cylindrically Mapped Gyroid TPMS Fabricated by Selective Laser Melting with 316L Stainless Steel Powder. Materials 15(12):4352. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/ma15124352\u003c/span\u003e\u003cspan address=\"10.3390/ma15124352\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7772615/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7772615/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Additive Manufacturing (AM) enables the production of parts with complex structures, such as triply periodic minimal surfaces (TPMS), which have unique properties, for instance, a high strength-to-weight ratio. This study investigates the influence of TPMS lattice parameters, such as cell radius, cell height and thickness ratio between inner and outer side of the lattice, on the mechanical performance of spur gears. A series of 56 gears with unique gyroid lattices has been designed using nTop® and analysed via finite element simulation in Ansys Workbench. Results suggest that with a mass reduction of 50% in the body of the gear, the gear failure will still occur at the tooth, indicating potential for further mass reduction. Moreover, correlations between lattice parameters and stiffness and stress distribution have been identified. Study compares additionally stress distribution within the gear between various designs. Stress state is visualized as a fnction of a distance from axis of the gear.","manuscriptTitle":"Evaluation of TPMS Lattice Parameters on the Mechanical Properties of Lightweight Gears Produced by Additive Manufacturing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-05 08:39:08","doi":"10.21203/rs.3.rs-7772615/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2025-11-29T17:32:42+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-10-27T03:21:21+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-24T20:46:03+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-08T10:02:13+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2025-10-06T16:40:48+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"a62236af-e741-4f1d-a51a-92e9b79f401d","owner":[],"postedDate":"November 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-09T16:08:47+00:00","versionOfRecord":{"articleIdentity":"rs-7772615","link":"https://doi.org/10.1007/s00170-026-17811-5","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2026-03-06 15:59:57","publishedOnDateReadable":"March 6th, 2026"},"versionCreatedAt":"2025-11-05 08:39:08","video":"","vorDoi":"10.1007/s00170-026-17811-5","vorDoiUrl":"https://doi.org/10.1007/s00170-026-17811-5","workflowStages":[]},"version":"v1","identity":"rs-7772615","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7772615","identity":"rs-7772615","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}