Light-weight double-layer cylinder structure design method for additive manufacturing

Abstract

The invention relates to a lightweight double-layer cylinder structure design method for additive manufacturing, belongs to the field of additive manufacturing, and solves the problems that a traditional double-layer cylinder structure has many parts, is difficult to assemble, cannot give consideration to lightweight and additive manufacturing manufacturability, is large in overall topological optimization calculation amount and is difficult to manufacture. The method comprises the steps that the additive manufacturing direction is set, and a design domain and a non-design domain are divided; segmenting the design domain in the axial direction and the radial direction to obtain a plurality of periodically arranged minimum design units; in each minimum design unit, topological optimization is carried out by taking a minimum volume method as a target function, and functional load constraint, additive manufacturing self-forming constraint and symmetry constraint are applied; the optimized minimum design units are arrayed and combined to obtain an integral double-layer cylinder structure, and the closed cavity is processed; and finally, carrying out strength check and iterative optimization. According to the invention, the integrated and lightweight design of the double-layer cylinder structure is realized, the structural performance is ensured, and the feasibility of the additive manufacturing process is ensured.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and in particular to a lightweight double-layer cylinder structure design method for additive manufacturing. Background Technology

[0002] Double-walled tube structures, as a typical engineering structure, have wide applications in aerospace, energy, and chemical industries. They typically consist of an inner tube, an outer tube, and an intermediate sandwich structure. With the development of additive manufacturing technology, new process paths have been provided for the integrated forming of complex structures, bringing new opportunities for innovative structural design.

[0003] However, current design and manufacturing methods for double-walled cylindrical structures still have many shortcomings. Designs based on traditional manufacturing processes typically require the inner and outer cylinders, as well as the sandwich structure (such as reinforcing ribs and filling materials), to be manufactured separately and then assembled using welding, bolting, or other methods. This approach suffers from a large number of parts, complex connection processes, long production cycles, and high costs. Furthermore, constrained by traditional processes, the sandwich structure is limited in form, and design space is not fully utilized. While directly employing a holistic topology optimization method for additive manufacturing can yield high-performance lightweight structures, it involves enormous computational demands, geometrically complex optimization results, and may include numerous difficult-to-form overhanging structures, leading to a mismatch between manufacturability and design expectations. Summary of the Invention

[0004] Based on the above analysis, the present invention aims to provide a lightweight double-layer cylinder structure design method for additive manufacturing, in order to solve at least one of the many shortcomings of the current design and manufacturing methods for double-layer cylinder structures, such as the difficulty of assembling many parts, long design cycle, low overall topology optimization calculation efficiency, and poor manufacturability of the results.

[0005] On one hand, embodiments of the present invention provide a lightweight double-layer cylindrical structure design method for additive manufacturing, comprising the following steps:

[0006] S1. Set the additive manufacturing direction as the axis of the cylinder, and divide the structures that are in contact with the external structure for assembly or maintain functionality into non-design domains, and divide the remaining structures into design domains;

[0007] S2. Divide the design domain in the axial and radial directions to obtain multiple periodically arranged minimum design units;

[0008] S3. Within each of the minimum design units, topology optimization is performed using the minimum volume method as the objective function, and constraints are applied during the optimization process. The constraints include at least functional load constraints, additive manufacturing self-forming constraints, and symmetry constraints.

[0009] S4. Perform array and Boolean addition operations on the design domain part of the topology-optimized minimum design unit to obtain the double-layer cylinder design domain structure, and then combine it with the non-design domain structure to obtain the overall double-layer cylinder structure, and check and process the closed cavity.

[0010] S5. Perform strength verification on the overall double-layer cylinder structure. If the technical indicators are met, the design is completed; otherwise, return to step S2 to adjust the structure of the smallest design unit and perform iterative optimization.

[0011] Furthermore, in step S2, the smallest design unit is a sector-shaped block, the size of which is determined by the inner radius r, outer radius R, length d, axial segmentation number a and radial segmentation number b of the double-layer cylinder, the thickness is the difference between R and r, the height is d / b, the arc length of the inner diameter of the sector is 2πr / a, and the arc length of the outer diameter of the sector is 2πR / a.

[0012] Furthermore, the size of the minimum design unit must satisfy the self-forming constraint condition: d / b≥2πR / a.

[0013] Furthermore, in step S3, the objective function of the topology optimization is: minV(x)=∫Ωxi(ξ)dξ;

[0014] Where ξ represents the spatial coordinate vector within the design domain Ω; xi(ξ) is a function with spatial coordinate ξ as the independent variable, representing the relative density of the material at that coordinate, and its value range is a continuous variable [0,1]; when xi(ξ)=0, it means there is no material at coordinate ξ; when xi(ξ)=1, it means there is full material at coordinate ξ.

[0015] Furthermore, in step S3, the functional load constraint includes the input load and the corresponding constraint result;

[0016] The input load includes at least one of concentrated force, pressure, and temperature load;

[0017] The constraint results include at least one of the following: the maximum structural stress is less than the allowable material stress, and the maximum structural displacement is less than the maximum permissible displacement.

[0018] Furthermore, in step S3, the additive manufacturing self-forming constraint is: the normal vector n of any point on the structural surface and the additive manufacturing direction e Z The included angle θ satisfies: θ ≥ θ min , where θ min For the minimum self-forming angle, the additive manufacturing direction e Z The direction is vertically upward.

[0019] Furthermore, in step S3, the symmetry constraint ensures that the minimum design unit maintains geometric symmetry in both the axial and radial directions. Specifically, for any point i within the minimum design unit, the coordinates ξ... i =[x i ,y i ,z i ] T The coordinates of its symmetric point i' about the XZ plane are [x i ,-y i ,z i ] T The coordinates of the point i symmetric about the XY plane are [x i ,y i ,-z i ] T .

[0020] Furthermore, in step S4, the inspection and treatment of the closed cavity refers to: if the assembled overall double-layer cylinder structure has a closed cavity, then a powder cleaning hole or a liquid cleaning hole is opened on the closed cavity.

[0021] Furthermore, in step S5, the technical indicators include structural load-bearing capacity and weight requirements; the iterative optimization includes adjusting the topology optimization model of the smallest design unit based on the overall verification results, returning to step S2 to further remove materials.

[0022] Furthermore, this invention proposes a lightweight double-layer cylinder structure suitable for additive manufacturing, which is obtained according to the design method described above.

[0023] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0024] 1) This invention decomposes the double-layer cylinder structure into arrayable minimum design units and performs integrated topology optimization, and finally forms it in one step through additive manufacturing, thereby reducing the number of parts and assembly steps, shortening the manufacturing cycle, and reducing production costs.

[0025] 2) This invention performs topology optimization at the minimum design unit level with the goal of minimizing volume, enabling it to find the optimal material distribution for specific load-bearing conditions. Combined with subsequent overall iterative optimization, multiple rounds of weight reduction are achieved, with a weight reduction rate exceeding 85%, resulting in significant lightweighting effects.

[0026] 3) This invention simultaneously introduces additive manufacturing self-forming constraint and symmetry constraint into the topology optimization model. The self-forming constraint ensures that the optimized structure can be printed stably with little or no support, improving the manufacturing success rate and surface quality; the symmetry constraint ensures that the smallest unit can form a continuous and uniform overall structure after arraying, avoiding stress concentration, and at the same time, it allows optimization calculations to be performed on small units, improving optimization efficiency.

[0027] 4) The novel additive manufacturing double-layer cylinder structure obtained by this invention has an interlayer composed of periodically arrayed topology-optimized units, and the supporting skeleton within the unit is an integrated configuration that simultaneously satisfies load-bearing capacity, self-forming properties, and symmetry constraints. This configuration not only has high specific strength, but all its geometric features (such as X-shaped intersecting skeletons, tree-like skeletons, and their connecting walls) are stably printable forms, which can be directly used for lightweight additive manufacturing solutions, resolving the contradiction between high-performance lightweight design and additive manufacturing process adaptability.

[0028] 5) This invention actively avoids or addresses enclosed cavities in its design, and the periodic array forms regular, interconnected internal channels, allowing unmelted powder or cleaning fluid to be efficiently and thoroughly removed after printing. Compared to traditional complex internal cavity structures, this invention reduces the difficulty and time required for powder cleaning, ensures the cleanliness and consistency of parts, and improves product quality.

[0029] 6) Compared to the huge computational load of directly performing multi-constraint optimization on the overall structure, this method places the optimization object on a minimum periodic unit, reducing the scale by about a×b times, making topology optimization with complex process constraints feasible under normal computational conditions, greatly improving computational efficiency and possessing engineering practicality.

[0030] 7) The parametric modeling method of this invention solidifies design rules, such as the self-forming prediction formula d / b≥2πR / a, symmetry constraint settings, array logic, etc., into an automated process. This process can be encapsulated as a software module or design wizard, transforming the design of such specific structures from relying on personal experience into a repeatable and standardized operation, which can significantly improve the development speed and quality stability of products.

[0031] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0032] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0033] Figure 1 This is an overall schematic diagram of a lightweight double-layer cylinder structure for additive manufacturing.

[0034] Figure 2 This is a flowchart of the lightweight double-layer cylinder structure design method for additive manufacturing according to the present invention.

[0035] Figure 3 A schematic diagram of self-forming angle constraints in additive manufacturing;

[0036] Figure 4 A schematic diagram of the symmetry constraint for the minimum design unit (taking symmetry in the XZ and XY planes as an example);

[0037] Figure 5 This is a schematic diagram of the double-layer cylinder shape described in the specific implementation method;

[0038] Figure 6 This is a schematic diagram showing the dimensions of the smallest segmented unit in the embodiment;

[0039] Figure 7 This is a schematic diagram illustrating the loading constraints of the smallest design unit in the embodiment;

[0040] Figure 8 This is a schematic diagram of the result after topology optimization of the smallest design unit in the embodiment;

[0041] Figure 8a for Figure 8 Enlarged schematic diagram of the optimized minimum design unit;

[0042] Figure 9 This is a schematic diagram of the overall double-layer cylindrical design domain structure formed by arraying the optimized minimum design units;

[0043] Figure 10 This is a schematic diagram of the lightweight double-layer cylinder structure obtained after iterative optimization.

[0044] Figure 11 This is a schematic diagram of the stainless steel double-layer cylinder structure to be optimized in Example 2;

[0045] Figure 12 This is a schematic diagram of the minimum design unit obtained through topology optimization in Example 2;

[0046] Figure 12a for Figure 12 Enlarged schematic diagram of the optimized minimum design unit;

[0047] Figure 13This is a schematic diagram of the lightweight double-layer cylinder structure finally obtained in Example 2;

[0048] Figure 14 This is a schematic diagram of the final structure obtained in Comparative Example 1;

[0049] Figure 15 This is a schematic diagram of the final structure obtained in Comparative Example 2;

[0050] Figure 16 This is a schematic diagram of the final structure obtained in Comparative Example 3;

[0051] Figure 17 This is a schematic diagram comparing the results of additive manufacturing deformation simulation and deformation compensation for a double-layer tube structure in an application example of the present invention.

[0052] Figure label:

[0053] 1. Inner sleeve; 2. Outer sleeve; 3. Sandwich structure; 4. Inner skin; 5. Outer skin; 6. Filling structure; 7. Inner connecting wall; 8. Outer connecting wall; 9. X-shaped cross support frame; 9-1. Main load-bearing rib; 9-2. Auxiliary load-bearing rib; 10. Hollowed-out area; 11. Transition rounded corner. Detailed Implementation

[0054] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0055] Traditional double-layer tube structure design methods suffer from problems such as numerous parts, difficult assembly, and a disconnect between design and manufacturing. Directly employing overall topology optimization faces challenges such as low computational efficiency and poor manufacturability of the optimized results. Therefore, this invention aims to provide an innovative design method that balances performance, lightweight design, and manufacturing feasibility.

[0056] One specific embodiment of the present invention discloses a lightweight double-layer cylinder structure design method for additive manufacturing. For example... Figure 2 As shown, the method includes the following steps:

[0057] S1. Set the additive manufacturing direction as the axis of the cylinder, and divide the structures that are in contact with the external structure for assembly or maintain functionality into non-design domains, and divide the remaining structures into design domains;

[0058] S2. Divide the design domain in the axial and radial directions to obtain multiple periodically arranged minimum design units;

[0059] S3. Within each of the minimum design units, topology optimization is performed using the minimum volume method as the objective function, and constraints are applied during the optimization process. The constraints include at least functional load constraints, additive manufacturing self-forming constraints, and symmetry constraints.

[0060] S4. Perform array and Boolean addition operations on the design domain part of the topology-optimized minimum design unit to obtain the double-layer cylinder design domain structure, and then combine it with the non-design domain structure to obtain the overall double-layer cylinder structure, and check and process the closed cavity.

[0061] S5. Perform strength verification on the overall double-layer cylinder structure. If the technical indicators are met, the design is completed; otherwise, return to step S2 to adjust the structure of the smallest design unit and perform iterative optimization.

[0062] Specifically, in S1, the additive manufacturing direction is set and the design domain and non-design domain are divided. Considering that the additive manufacturing process is a layer-by-layer accumulation, the forming direction has a decisive influence on the self-support and final quality of the structure. In this embodiment, the additive manufacturing direction is set to the axial direction of the cylinder (i.e., the direction of the additive manufacturing). Figure 5 (The direction of extension of the middle cylinder). This choice aligns the macroscopic features of the structure with the printing direction, which helps reduce the need for supporting structures. Subsequently, the design domain is divided, such as... Figure 1 As shown: the inner sleeve 1 and outer sleeve 2, which are in contact with external structures or need to maintain specific functions (such as sealing surfaces and connecting threads), are classified as non-design domains, and their geometry remains unchanged during the optimization process; the sandwich structure 3 used for lightweight design is classified as a design domain. This classification ensures the accuracy of the product's critical interface dimensions while freeing up maximum design space for topology optimization.

[0063] Specifically, in S2, the design domain is divided axially and radially to obtain multiple periodically arranged minimum design units. To reduce the computational complexity of large-scale topology optimization and ensure the final structure has arrayable fabrication friendliness, this step involves regular partitioning of the design domain. For example... Figure 5 and Figure 6 As shown, let the inner radius of the double-layered cylinder be r, the outer radius be R, the length be d, and the circumferential arc be 2π. Divide the cylinder circumferentially (corresponding to radial division) into a parts and axially into b parts. Thus, each minimum design unit is a sector-shaped block with the following dimensions: thickness (Rr), height d / b, inner arc length of the sector 2πr / a, and outer arc length of the sector 2πR / a.

[0064] It should be noted that, in order to ensure that the optimized structure within the unit has good self-forming properties during additive manufacturing (i.e., to avoid excessively large overhanging surfaces), this embodiment applies constraints to the segmentation dimensions, namely, formula (1):

[0065] d / b≥2πR / a(1)

[0066] This condition ensures that the vertical dimension (construction direction) of the unit is not less than its maximum circumferential dimension, geometrically pre-determining a "tall and slender" unit that is conducive to self-support, rather than a "flat" unit. If this condition is not met, the subsequently optimized structure is very likely to have areas that violate the self-forming angle, leading to manufacturing failure or the need to add a lot of supports, increasing costs and post-processing difficulty.

[0067] Specifically, in S3, topology optimization with multiple constraints is performed within each minimum design unit.

[0068] First, the topology optimization method employs the minimum volume method, aiming to find the material distribution scheme that minimizes the structural volume (i.e., minimizes the weight) while satisfying all constraints. Its objective function is given by formula (2):

[0069] minV(x)=∫ Ω xi(ξ)dξ (2)

[0070] Here, minV(x) represents the optimization objective of minimizing the structural volume, and V(x) represents the optimized structural volume. Ω represents the design domain for topology optimization, which in this method refers to the minimum design unit. xi(ξ) is a design variable representing the relative density of the material at spatial coordinate point ξ within the design domain Ω, and its value ranges from 0 to 1. xi(ξ) = 0 represents removing the material at this point, and xi(ξ) = 1 represents retaining the material at this point. The physical meaning of the integral operation ∫Ωxi(ξ)dξ is to calculate the total amount of material within the design domain Ω, and its value is equal to the structural volume V(x).

[0071] Secondly, three types of constraints are applied during the topology optimization process: functional load constraints, additive manufacturing self-forming constraints, and symmetry constraints.

[0072] To ensure that the optimization results meet the product's technical specifications, functional load constraints are first applied. Functional load constraints include two aspects: load input and result limitations.

[0073] Firstly, load input: defined according to the actual working conditions of the product, including but not limited to concentrated force, pressure, temperature field, etc., its mathematical expression is shown in formula (3):

[0074]

[0075] Where S represents the sum of input loads; Fi represents concentrated force loads; Pi represents pressure loads; and Ti represents temperature loads.

[0076] Secondly, the results are limited: the corresponding constraint results include, but are not limited to, structural stress, displacement, temperature, etc., to ensure that it has sufficient strength, stiffness and other properties, and its mathematical expression is shown in formula (4):

[0077]

[0078] Where U represents the set of constraint results; σ max σ represents the calculated maximum stress of the structure under load. t Representative material allowable stress; l max l represents the calculated maximum displacement of the structure under load. t T represents the maximum allowable displacement of the structure. max The highest temperature calculated for the structure under thermal load is represented by T. t This represents the highest operating temperature allowed by the material or design.

[0079] By using functional load constraints, the feasible domain of the optimized design is directly limited at the physical level, ensuring the basic mechanical performance of the final topology.

[0080] Furthermore, to ensure that the designed structure can be formed using additive manufacturing, additive manufacturing self-forming constraint is applied. Additive manufacturing self-forming constraint refers to the angular constraint formed by the angle between the surface of the additive structure and the forming direction (usually the vertical direction).

[0081] According to formula (2), the spatial coordinates of any point in the structure are: ξ=[x,y,z] T The normal vector of this point is denoted as n = [n x ,n y ,n z ] T The forming direction is denoted as: e Z =[0,0,1] T (i.e., the vertically upward direction). Let θ be the forming angle of any point, then θ is the vector n and e. Z The included angle, such as Figure 3 As shown. The self-forming constraint is given by formula (5):

[0082]

[0083] Where θ min The minimum self-forming angle (e.g., 45°, 50°, 55°, 60°, 65°).

[0084] In this invention, the minimum self-forming angle θ min The minimum self-forming angle θ is a key process parameter, and its specific value depends on the additive manufacturing technology, material type, and process conditions (such as laser power, powder thickness, and temperature). It can be determined based on engineering experience.min For example, in the selective laser melting (SLM) process for metallic materials, θ min The angle is typically selected between 40° and 50°, preferably 45°; in the fused deposition modeling (FDM) process for polymer materials, θ min The angle is typically chosen to be between 30° and 45°, with 37° being the preferred option. The principle for determining this angle is that at this angle, the structure can be successfully formed during the printing process without the need for additional supports or with minimal support.

[0085] The self-forming constraint of additive manufacturing is directly integrated into the optimization algorithm, guiding material distribution to avoid steep overhanging areas that are difficult to form. Without this constraint, the optimization algorithm may only pursue the theoretically optimal force transmission path, generating structures with a large number of horizontal or large overhang angles. These structures either require numerous supports during printing or collapse directly, leading to manufacturing failure.

[0086] Furthermore, to ensure that the designed minimum unit structure can be uniformly distributed in both the axial and radial directions and form a continuous overall structure through periodic array, symmetry constraints are applied.

[0087] by Figure 4 For example, let the coordinates of any point i be ξi=[x i ,y i ,z i ] T Then the constraint formula for maintaining symmetry of the minimum design unit in both the axis and the radial direction is (6):

[0088]

[0089] like Figure 4 As shown. After applying this constraint, the optimized element structure (such as...) Figure 8 As shown, these units naturally possess periodicity. A significant advantage of this approach is that when these units are arrayed, their boundaries can perfectly align, forming a continuous, smooth overall structure (such as...). Figure 9 As shown in the figure, this avoids stress concentration caused by discontinuities between elements. At the same time, it decomposes a large overall optimization problem into countless identical smaller problems, resulting in an order-of-magnitude improvement in computational efficiency.

[0090] For example, according to Figure 7 The constraint conditions are applied as shown. Specifically, according to formula (3), the functional load constraint is the product's load-bearing condition, namely: bearing external pressure P1 and internal pressure P2, with the corresponding fixed constraints denoted as P01 and P02; according to formula (4), the constraint calculation result requirement is: maximum stress σ max<Titanium alloy yield strength; constrain the self-forming angle θ ≥ 45° according to formula (5); constrain the minimum unit structure to be symmetrical in the XZ and XY directions according to formula (6).

[0091] In this embodiment, as a composite pressure-resistant structure, the design requires that the maximum stress should not cause plastic deformation of the structure; that is, the allowable stress is the yield strength of the material, serving as the upper limit of the stress constraint. Those skilled in the art will understand that in practical engineering applications, the stress constraint can be set as the allowable stress of the material according to specific safety specifications and requirements. The allowable stress is generally the yield strength or tensile strength of the material. When considering additional safety factors, the yield strength or tensile strength can be divided by a safety factor f greater than 1.

[0092] like Figure 8 , Figure 8a , Figure 12 and Figure 12a As shown, after three rounds of topology optimization calculations, the ideal minimum optimization design unit geometry is obtained:

[0093] The first structure is as follows Figure 8 , Figure 8a As shown, the skeleton structure is composed of an inner connecting wall, an outer connecting wall and an X-shaped cross support frame (including main load-bearing ribs). The four ends of the X-shaped cross support frame are connected to the ends of the inner connecting wall and the outer connecting wall respectively, forming a hollow area between the frames. The whole structure is a sandwich structure with both support and lightweight characteristics.

[0094] The second structure is as follows: Figure 12 and Figure 12a As shown, based on the first structure, an additional auxiliary load-bearing rib structure is added to the X-shaped cross-support frame (including the main load-bearing rib). The hollow area is more compact, and the transition between the connecting wall and the frame is smoothly connected by the transition rounded corner, which further enhances the local load-bearing performance.

[0095] Specifically, in step S4, arraying, combination, and powder cleaning are performed. The smallest design unit (design domain only) obtained from step S3 is arrayed axially and radially according to the initial division quantities a and b, and then merged into a continuous double-layer cylinder design domain structure through Boolean addition. Next, this structure is combined with the non-design domains (inner and outer cylinders) retained in step S1 to obtain the complete double-layer cylinder structure. Finally, the closed cavities must be checked and processed. If there are closed cavities that cannot be connected to the outside, powder cleaning holes or liquid cleaning holes need to be opened at appropriate locations to ensure that unmelted or uncured raw materials (such as metal powder or photosensitive resin) can be thoroughly cleaned after printing. This is a critical process step to ensure the internal quality of additively manufactured parts. If this step is ignored, residual raw materials will affect the performance of the parts and may even lead to the scrapping of the parts.

[0096] Specifically, in step S5, strength verification and iterative optimization are performed. The overall strength of the 3D model obtained in step S4 is verified (e.g., through finite element analysis). If the verification results meet all technical indicators (e.g., load-bearing capacity, weight, etc.), the design is complete. If not (e.g., stress margin remains, allowing for further weight reduction; or displacement exceeds limits, requiring reinforcement), the iterative optimization loop begins. For example, if the overall stress level is low, step S2 can be returned to, and the objective function or constraints in the topology optimization model of the smallest design unit can be adjusted (e.g., further reducing the volume fraction) for a new round of more aggressive lightweight design. This two-level "unit-to-system" iterative mechanism allows the design to quickly converge to the optimal solution that satisfies performance requirements while achieving maximum lightweighting.

[0097] The design method of this invention provides a lightweight double-layer cylinder structure suitable for additive manufacturing, such as... Figure 6 As shown:

[0098] It includes an inner sleeve and an outer sleeve arranged coaxially, and a sandwich structure located between the two; the sandwich structure is composed of a plurality of topology optimization units arranged in a periodic array in the circumferential and axial directions; each topology optimization unit is a fan-shaped block, which includes an inner connecting wall connected to the outer wall of the inner sleeve, an outer connecting wall connected to the inner wall of the outer sleeve, and a filling structure connecting the inner connecting wall and the outer connecting wall.

[0099] The filling structure is an integrated support frame obtained by topology optimization after simultaneously applying functional load constraints, additive manufacturing self-forming constraints, and symmetry constraints. The support frame is symmetrical about at least one plane within the sector-shaped block, and the angles between all its exposed surfaces and the vertical direction of additive manufacturing are not less than a preset minimum self-forming angle θ. min .

[0100] Specifically, the sandwich structure is not a traditional homogeneous filler or simple ribs, but rather a periodic arrangement of designed minimum units with specific functions and process attributes. This achieves a balance between structural performance, lightweighting, and additive manufacturing processability.

[0101] In the additive manufacturing process, selective laser melting technology is used to deposit the lightweight double-layer cylinder structure layer by layer along the cylinder axis (usually set as the vertical printing direction). Crucially, this is achieved by simultaneously introducing a self-forming angle θ during the unit optimization stage. min The constraints ensure that the angle between all exposed surfaces of the supporting frame and the construction direction is not less than θ. minThis allows the molten pool area below the inclined surface to receive sufficient support from the solidified material above during the printing process, avoiding defects such as collapse and spheroidization caused by excessive overhang angle, reducing the risk of printing failure and post-processing costs.

[0102] Meanwhile, the symmetry of the supporting skeleton within the fan-shaped units and the periodic array of the entire sandwich structure result in a more uniform distribution of thermal stress during the printing process, helping to reduce deformation and cracking tendencies. This not only makes the mechanical properties of the structure more uniformly distributed and avoids localized stress anomalies, but also makes subsequent mechanical analysis, performance evaluation, and process parameter optimization simpler and more accurate, improving design efficiency and reliability.

[0103] The inner and outer connecting walls serve as key force transmission interfaces between the sandwich structure and the inner and outer sleeves. Their smooth transition or integrated design ensures that the load can be continuously and with low loss transmitted between components, laying the foundation for the high load-bearing efficiency of the overall structure.

[0104] Based on this solid force transmission foundation, unit-level topology optimization can spontaneously form a material layout distributed along an efficient force flow path while satisfying mechanical constraints such as stress and displacement, thereby eliminating redundant materials. Furthermore, this efficient unit configuration is extended to the whole through periodic array, ultimately achieving the unity of extreme lightweighting and high performance of the double-layer tube structure on a global scale.

[0105] The structure of this invention achieves integrated molding, eliminating weak points at the connection interface and assembly stress, drastically reducing the number of parts and significantly shortening the manufacturing cycle. The periodic symmetrical structure of this invention not only brings better structural stability and predictable mechanical behavior due to its regular array characteristics, but also, due to its numerous interconnected hollow areas and the avoidance or treatment of closed cavities in the design, allows for efficient and thorough cleaning of unmelted powder after printing, ensuring the internal cleanliness and functional integrity of the parts.

[0106] Furthermore, the supporting frame can be in an X-shaped cross-bracing configuration. This configuration includes a main load-bearing rib extending radially along a fan shape, which directly undertakes the main task of radial load transfer between the inner and outer sleeves. Symmetrically extending auxiliary load-bearing ribs enhance the structure's shear and torsional stiffness. Specifically, all rib connections to the connecting walls and rib intersections are provided with transition fillets, which effectively eliminate sharp corners and significantly reduce the stress concentration factor in these critical areas, thereby achieving lightweighting while further improving the structure's fatigue life and static load-bearing capacity. In additive manufacturing, fillets also facilitate molten pool flow, reduce thermal stress concentration, and have a positive effect on improving forming quality.

[0107] Furthermore, the supporting frame can also have a tree-like topology. The main load-bearing ribs, extending axially, directly connect the inner and outer sleeves and provide the primary axial stiffness. Secondary load-bearing ribs branching from these ribs extend symmetrically to both sides and connect to the connecting walls, thereby distributing the load. This configuration achieves excellent lateral stability and lightweighting while ensuring axial strength.

[0108] Furthermore, the dimensions of the topology optimization unit must satisfy the constraint: d / b ≥ 2πR / a; where d is the axial length of the double-layer cylinder, R is the outer radius of the outer sleeve, a is the number of circumferential arrays, and b is the number of axial arrays. This formula ensures that the height of the unit in the axial direction (construction direction) is not less than its circumferential outer arc length, thereby avoiding excessively thin or overhanging sheet-like structures during unit printing.

[0109] Furthermore, the sandwich structure does not contain completely enclosed cavities, or has powder-cleaning or liquid-cleaning holes on existing enclosed cavities. After completing the structural design, the enclosed cavities must be inspected and treated. If the sandwich structure contains completely enclosed cavities from which powder cannot flow out on its own, powder-cleaning or liquid-cleaning holes must be opened at its lowest point or a suitable location. In the optimal design, through reasonable topology optimization and arraying, an internally interconnected open porous structure can be directly formed, thus eliminating the need for additional hole-opening steps.

[0110] Furthermore, the double-layer cylindrical structure is a one-piece molded part, made of metal or alloy materials using selective laser melting additive manufacturing technology. One-piece molding not only eliminates assembly errors and loss of connection strength, but also enables the creation of complex, lightweight internal structures that are impossible with traditional processes, fully leveraging the technological advantages of additive manufacturing.

[0111] To achieve rapid and reliable design of lightweight double-walled structures and avoid reliance on trial and error, this invention further provides a parametric modeling method highly compatible with this structure. This method encodes design objectives, performance requirements, and process constraints into an automated computational process, ensuring controllability at every step from basic input to final model output.

[0112] Specifically, a parametric modeling method for generating the above-described additive manufacturing double-layer cylinder structure includes the following steps:

[0113] Step 1: Parameter input and domain division: Input the inner radius r, outer radius R, and axial length d of the double-layer cylinder structure. Set the area corresponding to the inner sleeve and outer sleeve as the non-design domain, and set the area between them as the design domain for generating the sandwich structure.

[0114] Step 2: Periodic unit division: Based on the preset number of circumferential divisions a and the number of axial divisions b, the design domain is divided into a×b identical sector-shaped unit bases;

[0115] Step 3: Element-Constrained Topology Optimization: For a single sector-shaped element matrix, topology optimization calculations are performed with the goal of minimizing material volume, and the following constraints are applied simultaneously during the optimization process:

[0116] a) Functional constraints: Apply working condition loads and limit the maximum stress of the optimized structure to not exceed the allowable stress of the material and / or the maximum displacement to not exceed the allowable value;

[0117] b) Process constraints: The angle between the normal vector of all surfaces of the optimized structure and the vertical additive manufacturing direction shall not be less than the minimum self-forming angle θmin;

[0118] c) Geometric symmetry constraint: Ensure that the optimized element structure is symmetric about at least one coordinate plane within the sector element matrix;

[0119] Step 4: Array modeling: The unit structure obtained by optimization in step 3 is arrayed according to the number of circumferential divisions a and the number of axial divisions b, and a complete digital model of the sandwich structure is generated by Boolean union operation.

[0120] Step 5: Overall Verification and Iteration: Perform mechanical performance verification on the overall digital model including the sandwich structure, inner sleeve and outer sleeve. If the verification result meets the design requirements, output the final structural model; otherwise, return to step 3 to adjust the optimization parameters or return to step 2 to adjust the segmentation parameters a and b, and perform iterative design.

[0121] This parametric modeling method decomposes a large-scale, highly complex overall structural optimization problem into optimizing a representative minimum periodic element. Specifically, during element optimization, functional constraints, manufacturability constraints, and geometric symmetry constraints are applied equally and simultaneously. This ensures that the final element configuration possesses efficiency, additive manufacturing feasibility, and geometric symmetry from the outset, laying the foundation for subsequent periodic arrays.

[0122] This method is typically implemented in computer-aided engineering software platforms that integrate topology optimization modules. First, in step 1, the user or system inputs basic parameters via a graphical interface or script. The software automatically generates the initial geometry of the double-layered cylinder and completes the domain partitioning based on these parameters. Next, in step 2, during element partitioning, the system essentially creates a periodic mesh template for subsequent finite element analysis. Finally, in step 3, mature topology optimization algorithms such as the Variable Density Method (SIMP), level set method, or evolutionary structure optimization method are used as the basic solver.

[0123] Unlike traditional topology optimization which only considers mechanical response, this method, in each iteration, not only calculates the stress, strain energy, or displacement of the element under a given load, but also calculates the geometric normal of each element surface in parallel and determines in real time whether its angle with the preset construction direction (usually the Z-axis) satisfies θ. min The requirements are as follows: Simultaneously, by applying mirror-symmetric boundary conditions or directly imposing symmetry relationships on the design variables, the material distribution during the optimization process is forced to satisfy symmetry. These process and geometric constraints are typically integrated into the optimization model in the form of penalty functions, filtering techniques, or direct constraints, thereby driving the material distribution to evolve in a direction that simultaneously satisfies performance, manufacturability, and arrayability.

[0124] Once the optimization converges, step 4 is performed to obtain a clear element solid model through threshold extraction (e.g., density > 0.5). Subsequently, the elements are automatically expanded into a complete sandwich structure using the software's array copying and Boolean operation functions. Finally, step 5 involves performing an independent, typically more refined, finite element analysis on the generated overall model to verify whether it truly meets the global performance indicators, forming a closed-loop iterative process.

[0125] Compared to the traditional sequential design process of first optimizing performance and then making process improvements, this method avoids performance losses caused by forced modifications to the optimal structure to meet manufacturability requirements through simultaneous optimization. Compared to directly performing topology optimization on the entire complex double-layer tube structure with multiple constraints (as shown in Comparative Example 3), the unitization strategy of this method reduces the scale of design variables and constraints by approximately a×b times, making complex constraint optimization problems that were originally almost infeasible due to huge computational costs efficient and solvable. This solves the core pain point of long computation time for large-scale structural optimization in engineering practice.

[0126] Compared with the traditional approach of first optimizing performance and then fixing the process, this method optimizes simultaneously and embeds process constraints (such as self-forming angle) at the algorithm level. This ensures that all optimizations meet manufacturability requirements, prevents the design of unmanufacturable or high-risk configurations, and achieves a match between design and process.

[0127] More importantly, compared to the conventional approach of directly performing large-scale constraint optimization on the entire structure, the unitization strategy of this method reduces the design variables and constraint scale by about a×b times, making topology optimization under complex constraints not only computationally infeasible but also highly efficient and feasible. This not only solves the problem of long time consumption in large-scale optimization but also liberates designers from tedious trial and error. Only a few key parameters need to be input, and subsequent processes such as partitioning, optimization, arraying, and verification can be completed automatically or semi-automatically. As a result, the design cycle of lightweight structures that meet complex requirements is significantly shortened from the level of days / weeks to the level of hours.

[0128] This simultaneous optimization allows the algorithm to automatically explore the optimal solution that simultaneously satisfies mechanical performance, lightweight objectives, and process constraints within the global design space. This overcomes the difficulty of balancing multiple objectives in manual iteration, resulting in a design scheme with superior overall performance. Ultimately, this complete parametric process can be packaged into a dedicated software plugin or design wizard, allowing expert experience, such as constraint settings and parameter ranges, to be solidified and reused. This promotes the establishment of standardized and regulated additive manufacturing processes within enterprises, improving the consistency and reliability of quality.

[0129] Furthermore, the geometric symmetry constraint mentioned in step 3 specifically means making the optimized unit structure symmetric about the XZ plane and XY plane of the sector unit matrix.

[0130] Specifically, applying XZ plane symmetry (usually corresponding to a radial symmetry plane) ensures that the optimized element structure is mirrored on both sides. This allows adjacent elements to fit perfectly together on their corresponding sides when arrayed circumferentially, forming continuous inner and outer connecting walls. Applying XY plane symmetry (usually corresponding to an axial symmetry plane) ensures that the elements are also mirrored on both the top and bottom sides, allowing for seamless stacking when arrayed axially. This dual symmetry constraint is not only a geometric requirement but also implies that the force flow path is symmetrically distributed within the element, thus ensuring that the overall structure formed by this element array has highly uniform mechanical properties.

[0131] Accordingly, the present invention provides a design method for a lightweight double-layer cylinder structure, the design method comprising using the aforementioned parametric modeling method to obtain the aforementioned additive manufacturing double-layer cylinder structure.

[0132] Furthermore, after obtaining the double-layer cylindrical structure model, the closed cavities in the model need to be inspected and processed. An automated cavity detection algorithm can scan the model to identify completely enclosed mesh areas without openings connecting to the outside. For detected closed cavities, the system can prompt the designer to manually add cleaning holes, or automatically generate minimum-sized holes according to preset rules (such as at the lowest point of the cavity).

[0133] Furthermore, the parametric modeling method described above can be enriched and expanded according to actual needs when it is implemented.

[0134] For example, in the element optimization in step 3, the objective function is not limited to minimum volume. When stiffness needs to be controlled, minimum flexibility (i.e., maximum stiffness) can be used as the objective, or multi-objective optimization can be adopted. Considering complex working conditions, a weighted combination of multiple load conditions can be applied to ensure that the optimized structure has good robustness to various load conditions. In addition, frequency constraints can be introduced to avoid resonance with the working environment, or thermal stress constraints can be introduced to optimize the performance of the structure under temperature fields.

[0135] Furthermore, a flexible decision-making framework is provided for the iteration in step 5. When the overall verification does not meet the requirements, returning to step 3 to adjust the optimization parameters is suitable for fine-tuning, such as slightly relaxing displacement constraints or adjusting the load size. Returning to step 2 to adjust the partitioning parameters a and b is suitable for more fundamental modifications. For example, when it is found that the element size is too large, resulting in excessive local stress, the values ​​of a or b can be increased, and smaller, denser elements can be used for re-optimization. This usually yields a more refined and better-performing structure, but it will correspondingly increase the computational load.

[0136] Regarding parameter selection, the minimum self-shaping angle θ min The setting of θ is not a fixed value, but should be considered a key process parameter related to the specific printing process and material properties. For most metal powder bed melting processes, θ min A good balance between reliable forming and design freedom can be achieved within the range of 35° to 50°. Setting it too low may lead to unstable quality of the overhang surface; setting it too high will excessively restrict material distribution and sacrifice lightweight potential. Preferably, it is set to 45°.

[0137] In addition, the sector-shaped unit matrix divided in step 2 can be solid in the initial state or preset as a mesh with initial pores to accelerate optimization convergence.

[0138] For step 4, in addition to simple translation and arraying, minor adaptive adjustments can be made during arraying based on the boundary conditions of the overall model (such as fading at the end units) to further improve overall performance or manufacturability. The addition of these features enables this parametric modeling method to adapt to more complex and refined design requirements.

[0139] The present invention will be described in more detail below through specific embodiments. These embodiments are merely descriptions of the best implementation of the invention and do not limit the scope of the invention in any way.

[0140] Example 1

[0141] A titanium alloy double-layer cylinder (such as Figure 5 As shown, it withstands internal and external pressure loads. It is designed according to the method of this invention.

[0142] S1. Set the axial direction as the construction direction. The inner sleeve and outer sleeve are outside the design domain, while the interlayer is within the design domain. The inner sleeve thickness is 2mm, and the outer sleeve thickness is 3mm.

[0143] S2. Let r = 110mm, R = 150mm, d = 300mm. Set a = 24, b = 6. The calculated element height d / b = 50mm, and the outer diameter arc length 2πR / a ≈ 39.25mm, satisfying the self-forming pre-constraint of d / b ≥ 2πR / a. The minimum design element for the sector shape is obtained.

[0144] S3. Perform topology optimization within the cell.

[0145] The objective is to minimize the volume: minV(x)=∫ Ω xi(ξ)dξ(2);

[0146] Constraints include: functional load constraints and result limitations.

[0147]

[0148] Internal pressure P2 = 10 MPa, external pressure P1 = 1.5 MPa; maximum stress σ max <800MPa (In this case, the allowable stress is the yield strength of the titanium alloy).

[0149] Self-shaping constraint:

[0150]

[0151] Self-forming angle θ min =45°.

[0152] Symmetry constraints:

[0153]

[0154] Apply symmetric constraints to the XZ and XY planes.

[0155] After optimization, the following was obtained: Figure 8 The unit structure shown is the smallest fan-shaped design unit corresponding to Example 1. It consists of an inner connecting wall (arc-shaped, matching the curvature of the inner sleeve's arc surface), an outer connecting wall (arc-shaped, matching the curvature of the outer sleeve's arc surface), and an X-shaped cross-support skeleton. The double-arc connecting walls are arranged along the inner and outer arc contours of the fan-shaped unit. The core load-bearing X-shaped cross-support skeleton (including main load-bearing rib 9-1 and auxiliary load-bearing rib 9-2) strictly follows the symmetry constraints of the XZ and XY planes, forming a mirror-extended double X-shaped combination with the unit's central axis as the symmetry reference (not two independent structures, but a symmetrical extension of the same skeleton). The two ends of its ribs are diagonally connected between the double-arc connecting walls, forming a symmetrically distributed fan-shaped hollow area. Transition rounded corners are provided at each structural connection to reduce stress concentration. Finally, an integrated load-bearing structure of "arc-shaped double walls + symmetrical X-shaped cross-support skeleton" is formed, which ensures both uniform stress distribution and fully meets the self-forming constraints of additive manufacturing.

[0156] S4. Array and combine the above optimized units according to parameters a=24 and b=10 to obtain the following... Figure 9 The overall structure: This structure is Figure 8The fan-shaped unit has a direct array configuration. The support structure inside the interlayer is a densely distributed X-shaped cross support skeleton with double-sided arc-shaped connecting walls. The material distribution is relatively full, and the overall weight is 8.34 kg. Inspection confirmed that there is no completely sealed cavity, so there is no need to open additional powder cleaning holes.

[0157] S5. The overall check found that the stress margin was too large (there were redundant load-bearing areas with low stress in some ribs). Return to the S2 stage and further reduce the material usage in non-core load-bearing areas in the element optimization: simplify the original X-shaped cross support frame into a simplified structure of "segmented axial main ribs + locally obliquely connected auxiliary ribs", retain the axial load-bearing segments of the main load-bearing ribs, remove the redundant cross parts of the auxiliary load-bearing ribs, and only retain the material corresponding to the core load transmission path.

[0158] After two rounds of iterative optimization, the final structure is obtained (e.g. Figure 10 The number and volume of its supporting ribs have been further reduced, resulting in an overall weight of 7.56 kg (compared to...). Figure 9 The structure is reduced in weight by approximately 0.78 kg, and stress is concentrated in the core support ribs. The stress distribution is highly matched with the load path, while simultaneously meeting the requirements for strength, deformation, and process constraints.

[0159] The final double-layer cylindrical structure designed significantly reduced its weight from 52.19 kg in the original model to 7.56 kg, a weight reduction of 85.51%. Considering that the thinnest part of the structure is already 1.5 mm, further weight reduction would affect the reliability of additive manufacturing processes, and the current weight fully meets the design requirements, so optimization was stopped here. After overall strength verification, its maximum stress is 364 MPa, meeting the requirement of titanium alloy materials having an allowable stress below 800 MPa. This structure is a single part and can be directly integrally formed through additive manufacturing, featuring a short design cycle and excellent manufacturability.

[0160] Example 2

[0161] A certain stainless steel double-walled cylinder (e.g.) Figure 11 As shown, it withstands internal pressure and external temperature loads. It is designed according to the method of this invention.

[0162] S1. Set the axial direction as the construction direction. The inner sleeve and outer sleeve are outside the design domain, while the interlayer is within the design domain. The inner sleeve thickness is 2mm, and the outer sleeve thickness is 3mm.

[0163] S2. Take r = 75mm, R = 115mm, d = 400mm. Set a = 24, b = 8. Calculate the element height d / b = 50mm, and the outer diameter arc length 2πR / a ≈ 30.09mm, satisfying the self-forming pre-constraint of d / b ≥ 2πR / a. The minimum design element for the sector shape is obtained.

[0164] S3. Perform topology optimization within the cell.

[0165] The goal is to minimize the volume, as shown in formula (2).

[0166] Constraints include: functional load constraints, such as those in formulas (3) and (4).

[0167] Internal pressure P1 = 20 MPa, external temperature load T1 = 323 K; maximum stress σ max <600MPa (in this case, the allowable stress is the tensile strength of stainless steel), maximum deformation <10mm.

[0168] Self-forming constraint: as shown in formula (5).

[0169] Self-forming angle θ min =45°.

[0170] Symmetry constraints: as shown in formula (6).

[0171] After cell partitioning and topology optimization, the following is obtained: Figure 12 The unit structure shown is based on a tree-like topology and consists of a main load-bearing rib extending axially (Z-direction) and multiple auxiliary load-bearing ribs extending obliquely from the main load-bearing rib. The main load-bearing rib is arranged radially along the fan-shaped design domain. Its inner diameter side is tightly connected to the inner sleeve (non-design domain) through the inner connecting wall (arc-shaped), and its outer diameter side is connected to the outer sleeve (non-design domain) through the outer connecting wall (arc-shaped), forming the main path for load transfer from the inner and outer sleeves to the interlayer. The auxiliary load-bearing ribs are symmetrically distributed on both sides of the main load-bearing rib. One end is fixed to the main load-bearing rib, and the other end is connected to the inner connecting wall and the outer connecting wall, respectively. The inclination angle of all auxiliary load-bearing ribs is ≥45°, which fully meets the self-forming constraint of additive manufacturing and can effectively enhance the lateral stiffness and deformation resistance of the structure.

[0172] Will Figure 12 The optimized units are arrayed with circumferential a=24 and axial b=8, and the final optimized structure is obtained after overall performance verification, such as... Figure 13 As shown, the final structure retains the core load-bearing characteristics of the tree-like topological unit. The original double-layer cylinder weighed 74.97 kg, which was reduced to 20.94 kg after optimization, showing a significant weight reduction effect. After testing, its maximum stress was 585 MPa, which is controlled within the allowable value of 600 MPa, and the maximum deformation was less than the upper limit of the constraint of 10 mm, which fully meets the usage requirements. Moreover, there is no closed cavity in the interlayer, which makes powder cleaning convenient after additive manufacturing and has good additive manufacturing processability.

[0173] Application examples

[0174] This application focuses on a lightweight titanium alloy double-layer cylinder. Its design goals and initial parameters are the same as those in Example 1 (inner radius r = 110 mm, outer radius R = 150 mm, length d = 300 mm, material is Ti-6Al-4V).

[0175] The parametric design modeling process is as follows:

[0176] Step S1. Parameter Input and Domain Division: In the topology optimization software platform, input the inner radius r = 110mm, outer radius R = 150mm, and axial length d = 300mm of the double-layer cylinder structure. Set the functional inner sleeve (thickness 2mm) and outer sleeve (thickness 3mm) areas as non-design domains, and set the sandwich area between them as the design domain for generating the sandwich structure.

[0177] Step S2. Periodic element division: Set the number of circumferential divisions a = 24 and the number of axial divisions b = 10. Based on these parameters, the system automatically discretizes the design domain uniformly in the circumferential and axial directions, dividing it into a total of 24 × 10 = 240 identical sector-shaped element bases.

[0178] Step S3. Element-Constrained Topology Optimization: For a single sector-shaped element matrix, initiate topology optimization iterations with the objective of minimizing material volume. During the optimization process, the following constraints are applied simultaneously:

[0179] a) Functional constraints: Apply working condition loads, including internal pressure P2 = 10 MPa and external pressure P1 = 1.5 MPa, and limit the maximum stress of the optimized structure to no more than 800 MPa and the maximum displacement to no more than the design allowable value.

[0180] b) Process constraints: The angle between the normal vector of all outer surfaces of the optimized structure and the vertical additive manufacturing direction (Z-axis) is limited to no less than the minimum self-forming angle θ. min =45°.

[0181] c) Geometric symmetry constraint: Force the optimization to make the element structure symmetric about the XZ plane and XY plane of the sector element matrix.

[0182] After multiple rounds of iterative convergence, the following was extracted: Figure 8 The optimized unit shown is an integrated structure consisting of an inner connecting wall, an outer connecting wall, and an X-shaped cross support skeleton connecting the two, with transition rounded corners generated at the skeleton connections.

[0183] Step S4. Array Modeling: The single unit structure optimized in Step S3 is arrayed circumferentially and axially according to a=24 and b=10. Through Boolean union operations, the 240 units are seamlessly spliced ​​together to generate a complete digital model of the sandwich structure. This model is then combined with the inner and outer sleeve models outside the design domain to obtain... Figure 10 The digital model of the overall double-layer cylindrical lightweight structure is shown.

[0184] Step S5. Overall Verification and Iteration: An independent finite element analysis was performed on the overall model obtained in Step S4. The first round of verification revealed a low structural stress level, indicating room for further weight reduction. Therefore, we returned to Step S3, adjusting the optimization parameters while maintaining the original constraints to further eliminate materials along non-core load-bearing paths. After a second round of optimization and arraying, the final model was obtained, with a theoretical weight of 7.56 kg and a verified maximum stress of 364 MPa, meeting all design requirements. The design is now complete.

[0185] The additive manufacturing process is as follows:

[0186] Step M1. Import the final 3D model into the slicing software and position it according to the direction of the self-forming angle constraint in the design. Because self-forming constraints are used in the structural design, no additional support is needed inside the double-layered cylindrical sandwich structure, allowing for direct forming and good manufacturability. Next, perform additive manufacturing process simulation on the additive model. Deformation compensation is performed on the model using the simulation deformation data to improve forming accuracy. The initial deformation simulation and the simulation results after deformation compensation are shown below. Figure 17 As shown, the double-layer cylinder designed in this invention has good structural rigidity, small and uniform deformation, and can achieve high-precision forming directly through deformation compensation, making it suitable for additive manufacturing. A layer thickness of 80μm was set, and a partitioned scanning strategy was used to generate manufacturing instructions.

[0187] Step M2. Selective laser melting equipment was used for printing with Ti-6Al-4V powder. Main process parameters: laser power 320W, scanning speed 1200mm / s. After printing, the parts were separated by wire cutting, cleaned with high-pressure airflow and ultrasonic cleaning, and the supports and end faces were removed and precision milled to obtain solid parts. Inspection showed that the sandwich structure had good internal connectivity, no powder residue, and met cleanliness requirements.

[0188] The final additive manufacturing accuracy of the physical object's outer contour is ±0.2mm. Due to this high accuracy, no further machining of the outer shape is required. The measured weight is 7.62kg, with an error of only 0.8% compared to the design value, resulting in a weight reduction rate of 85.4%. The hydrostatic test shows that the part exhibits no leakage or permanent deformation under both 1.5MPa internal pressure and 10MPa external pressure, and the strain monitoring values ​​are all within the elastic range.

[0189] Comparative Example 1

[0190] For the same double-layer cylinder, without performing the segmentation in step S2, topology optimization is directly performed on the entire sandwich region. Furthermore, during the optimization process, only the same functional load constraints as in Example 1 are applied; no additive manufacturing self-forming constraints or symmetry constraints (such as...) are introduced. Figure 14 (As shown).

[0191] The optimized structure has a theoretical weight of 6.98 kg and a maximum stress of 790 MPa, which meets the mechanical performance requirements and is slightly lighter than the embodiment of this invention. However, the calculation time for overall topology optimization using this method is much longer than that of the method of this invention, increasing the time by more than 10 times. Moreover, the optimized structure has a complex and irregular shape, with many areas violating the 45° self-forming angle, making it unsuitable for direct additive manufacturing. If forced to print, a large number of support structures need to be added, greatly increasing the cost and post-processing difficulty, and even leading to manufacturing failure.

[0192] Comparative Example 2

[0193] Using traditional design and manufacturing methods, the double-layered cylinder features an internal structure with evenly distributed longitudinal reinforcing ribs. The separately manufactured inner and outer cylinders, along with the reinforcing ribs, are assembled by welding. Figure 15 As shown.

[0194] The final optimized part weighed 11.15 kg, heavier than the 7.56 kg of Example 1 (e.g., Figure 16 (As shown). Its maximum stress is 495 MPa, which meets the strength requirements, but the maximum stress is higher than that of this invention, and the lightweight effect is not as good as that of this invention. In addition, this method has the disadvantages of having a large number of parts (26), numerous manufacturing processes, and a long assembly cycle.

[0195] Comparative Example 3

[0196] For the same double-layer cylinder, without performing the segmentation in step S2, the entire sandwich region is directly subjected to topology optimization, but during the optimization process, the same three constraints as in Example 1 (functional load constraint, self-forming constraint and symmetry constraint) are applied simultaneously.

[0197] Optimized structure (e.g.) Figure 16 As shown in the figure, its theoretical weight is 8.67 kg and the maximum stress is 259 MPa. Although it meets the requirements of mechanical properties and self-forming properties, the calculation time for overall topology optimization is much longer than that of the method of this invention, with the time consumption increasing by more than 15 times. Moreover, the optimized structural morphology can only satisfy the radial symmetry of the overall structure, resulting in a larger scale and weaker rigidity of the optimized structure, which is prone to deformation in additive manufacturing. Compared with the regular and periodic structure obtained in Example 1 of this invention, it has disadvantages in terms of structural stability and manufacturing process.

[0198] The following table summarizes the optimization and test results of the embodiments, application examples, and comparative examples of the present invention:

[0199] Table 1

[0200]

[0201]

[0202] Note: "-" indicates that the item is not applicable or has not been tested.

[0203] As shown in Table 1, the solution of this invention achieves optimal overall performance in terms of lightweighting, computational efficiency, and process adaptability. Compared to Comparative Example 1, although the theoretical weight reduction rate of this invention is slightly lower, it solves the problem of its inability to be manufactured due to violation of process constraints and reduces computation time by more than 10 times. Compared to Comparative Example 3, which is also manufacturable, this invention improves computational efficiency by more than 15 times while maintaining a similar weight reduction rate, and its structure presents a regular periodic array, avoiding the drawbacks of easy deformation and unpredictability of the overall optimized structure. Compared to the traditional Comparative Example 2, this invention has significant advantages in weight reduction and integrated design. The measured results of the application example (weight 7.62 kg, weight reduction of 85.4%) are highly consistent with the design value, verifying the reliability and practicality of this invention.

[0204] In summary, the structure and method proposed in this invention solve the problems of low computational efficiency, poor manufacturability, and structural irregularity inherent in traditional topology optimization. It achieves a balance between lightweight structure, additive manufacturing adaptability, and macroscopic regularity, providing a solution for the integrated design and manufacturing of high-performance complex structures.

[0205] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A lightweight double-layer cylinder structure design method for additive manufacturing, characterized in that, Includes the following steps: S1. Set the additive manufacturing direction as the axis of the cylinder, and divide the structures that are in contact with the external structure for assembly or maintain functionality into non-design domains, and divide the remaining structures into design domains; S2. Divide the design domain in the axial and radial directions to obtain multiple periodically arranged minimum design units; S3. Within each of the minimum design units, topology optimization is performed using the minimum volume method as the objective function, and constraints are applied during the optimization process. The constraints include at least functional load constraints, additive manufacturing self-forming constraints, and symmetry constraints. S4. Perform array and Boolean addition operations on the design domain part of the topology-optimized minimum design unit to obtain the double-layer cylinder design domain structure, and then combine it with the non-design domain structure to obtain the overall double-layer cylinder structure, and check and process the closed cavity. S5. Perform strength verification on the overall double-layer cylinder structure. If the technical indicators are met, the design is completed; otherwise, return to step S2 to adjust the structure of the smallest design unit and perform iterative optimization.

2. The design method according to claim 1, characterized in that, In step S2, the smallest design unit is a sector-shaped block, the size of which is determined by the inner radius r, outer radius R, length d, axial segmentation number a and radial segmentation number b of the double-layer cylinder, the thickness is the difference between R and r, the height is d / b, the arc length of the inner diameter of the sector is 2πr / a, and the arc length of the outer diameter of the sector is 2πR / a.

3. The design method according to claim 2, characterized in that, The dimensions of the minimum design unit must satisfy the self-forming constraint: d / b ≥ 2πR / a.

4. The design method according to claim 1, characterized in that, In step S3, the objective function for topology optimization is: minV(x)=∫ Ω x i (ξ)dξ; Where ξ represents the spatial coordinate vector within the design domain Ω; x i (ξ) is a function with spatial coordinate ξ as its independent variable, representing the relative density of the material at that coordinate, and is a continuous variable with a value range of [0,1]. When x i When (ξ) = 0, it indicates that there is no material at coordinate ξ; when x i When (ξ) = 1, it means that the material at coordinate ξ is full.

5. The design method according to claim 1, characterized in that, In step S3, the functional load constraint includes the input load and the corresponding constraint result; The input load includes at least one of concentrated force, pressure, and temperature load; The constraint results include at least one of the following: the maximum structural stress is less than the allowable material stress, and the maximum structural displacement is less than the maximum permissible displacement.

6. The design method according to claim 1, characterized in that, In step S3, the additive manufacturing self-forming constraint is: the normal vector n of any point on the structural surface and the additive manufacturing direction e. Z The included angle θ satisfies: θ ≥ θ min , where θ min For the minimum self-forming angle, the additive manufacturing direction e Z The direction is vertically upward.

7. The design method according to claim 1, characterized in that, In step S3, the symmetry constraint is to ensure that the minimum design unit maintains geometric symmetry in both the axial and radial directions. Specifically, for any point i within the minimum design unit, the coordinates ξ... i =[x i ,y i ,z i ] T The coordinates of its symmetric point i' about the XZ plane are [x i ,-y i ,z i ] T The coordinates of the point i symmetric about the XY plane are [x i ,y i ,-z i ] T .

8. The design method according to claim 1, characterized in that, In step S4, the inspection and treatment of the closed cavity refers to: if the assembled overall double-layer cylinder structure has a closed cavity, then a powder cleaning hole or a liquid cleaning hole is opened on the closed cavity.

9. The design method according to claim 1, characterized in that, In step S5, the technical indicators include structural load-bearing capacity and weight requirements; the iterative optimization includes adjusting the topology optimization model of the smallest design unit based on the overall verification results, returning to step S2 to further remove materials.

10. A lightweight double-layer cylinder structure suitable for additive manufacturing, characterized in that, The structure is obtained by the design method according to any one of claims 1 to 9.

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