A helical gradient lattice structure design method and medium
By using a helical gradient lattice structure design method and leveraging logarithmic spiral functions and dual-lattice composite structures, porosity and connectivity are optimized, solving the problem of spatial performance regulation of existing lattice structures and achieving synergistic optimization of mechanical properties and biological functions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIVERSITY OF SCIENCE AND ENGINEERING
- Filing Date
- 2026-05-09
- Publication Date
- 2026-06-05
AI Technical Summary
Existing lattice structures are difficult to control in terms of porosity, relative density, and structural stiffness in space, making it difficult to meet the needs of practical engineering applications. Furthermore, the difference in connection with the rigid structure of natural bone leads to poor performance.
A spiral gradient lattice structure design method is adopted. By introducing a logarithmic spiral function to establish the array path, and combining it with a dual-lattice composite structure, the gradient changes of the support diameter and lattice unit size are designed to optimize the pore connectivity and distribution law, and a continuously changing three-dimensional model is constructed.
While ensuring structural stability, the mechanical properties and bioactivity of the helical gradient lattice structure were improved, promoting cell migration and bone tissue ingrowth, optimizing pore connectivity and distribution, and reducing stress concentration.
Smart Images
Figure CN122154251A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computer-based lattice structure design technology, specifically to a spiral gradient lattice structure design method and medium. Background Technology
[0002] In the biomedical field, porous structures are widely used in bone repair and bone replacement materials. In recent years, with the rapid development of additive manufacturing technology, especially the maturity of metal 3D printing technologies such as selective laser melting and electron beam melting, porous materials with complex internal topologies can be manufactured in a single unit, providing new technical means for the design of novel lightweight structural materials. Among these, lattice structures, due to their high specific strength, high specific stiffness, adjustable porosity, and good energy absorption performance, have gradually become an important research direction for lightweight structural design. By rationally designing the topology and spatial distribution of unit cells, precise control of overall mechanical properties can be achieved while ensuring structural lightweighting.
[0003] In existing research, various lattice topologies have been used to construct lattice materials, such as body-centered cubic (BCC), diamond, and rhombic dodecahedral (RD) structures. Among them, the diamond structure possesses good three-dimensional spatial connectivity, high porosity, and biocompatibility, providing good structural isotropic properties and showing good application potential in biomedical implants and porous material structures. The RD structure has a higher relative density than the diamond structure, exhibiting higher strength and better fatigue performance, making it suitable as a load-bearing area for bone scaffolds.
[0004] Currently, most crystal lattice structures are typically formed by periodic arrays of single unit cells in three-dimensional space or by uniform gradients of multiple structures. While uniform lattice structures offer good fabrication feasibility, their porosity, relative density, and structural stiffness remain largely consistent in space, making it difficult to meet the spatial control requirements of structural performance in practical engineering applications. Although uniform gradient array structures mimic the two-scale continuous structure of natural bone, the rigid structural connections and inherent properties of metallic materials differ significantly from natural bone, leading to large discrepancies between clinical applications and experimental research performance. Summary of the Invention
[0005] The technical problem to be solved by this application is to provide a design method and medium for a helical gradient lattice structure, which has the characteristics of improving the mechanical properties of the helical gradient lattice structure and optimizing the pore connectivity and distribution.
[0006] In a first aspect, one embodiment provides a method for designing a helical gradient lattice structure, comprising:
[0007] Construct the outer contour;
[0008] An array path for the parametric curves is established by introducing a logarithmic spiral function;
[0009] Establishing a bilattice composite structure as the basis for lattice structure growth;
[0010] The gradient design based on the aforementioned lattice composite structure includes: sequentially designing support parameters, lattice size parameters, and lattice porosity for each point in the array path; wherein, the support parameter design includes: constructing a support diameter function based on the principle that the support diameter gradually decreases from the outer region to the center region and a gradient function; and calculating the support diameter based on the support diameter function; the lattice size parameter design includes: constructing a lattice unit size function based on the principle that the pore size gradually increases from the outside to the inside and a gradient function; the lattice porosity design includes: calculating the lattice porosity based on the support diameter and the lattice unit size;
[0011] The kernel structure and peripheral structure of the interface;
[0012] Obtain the model obtained from the modeling process.
[0013] In one embodiment, constructing the outer contour includes: selecting a regular cylinder as the design space, and establishing a three-dimensional coordinate system with the center of the bottom surface of the cylinder as the origin, wherein the Z-axis is along the height direction of the cylinder.
[0014] In one embodiment, the step of introducing a logarithmic spiral function to establish an array path of parametric curves includes: introducing a logarithmic spiral parametric expression within the constructed outer contour design space to describe the spatial expansion path of the conch-like structure.
[0015] In one embodiment, the establishment of the dual-lattice composite structure as the basis for lattice structure growth includes: the core region adopting a diamond lattice structure and the outer region adopting a rhombic dodecahedral structure.
[0016] In one embodiment, the step of sequentially designing the support parameters and lattice size parameters for each point in the array path includes:
[0017] Obtain the gradient control function for the spiral structure;
[0018] Based on the gradient control function, construct the support diameter function and the lattice unit size function, and calculate the porosity of the lattice structure.
[0019] In a second aspect, one embodiment provides a computer-readable storage medium storing a program that can be loaded by a processor and executed by any of the spiral gradient lattice structure design methods described in the above embodiments.
[0020] The beneficial effects of this invention are:
[0021] Because the growth base is based on a bilattice composite structure, it provides high porosity and good connectivity in the core region, while improving the overall stiffness and load-bearing capacity of the structure in the outer region. This allows the resulting bone tissue to both promote cell migration and angiogenesis, and enhance the overall stiffness and load-bearing capacity of the structure. By constructing a support diameter function based on the principle of gradually decreasing support diameter from the outer region to the center region and using a gradient function, the support diameter can be calculated. This allows for weight reduction while improving load-bearing capacity, thereby improving the mechanical properties of the helical gradient lattice structure. When applied to bone tissue engineering, this effectively guides cell migration and bone tissue ingrowth. Furthermore, by constructing a lattice unit size function based on the principle of gradually increasing pore size from the outside to the inside and using a gradient function, the lattice unit size can be calculated. This enhances the permeability and bioactivity of the structure when applied to bone tissue engineering, effectively guiding cell migration and bone tissue ingrowth. Thus, the continuous variation of porosity in space enables the lattice structure to possess both good mechanical properties and material transport capabilities, thereby optimizing pore connectivity and distribution patterns. When applied to bone tissue engineering, this effectively reduces stress concentration, promotes cell migration and bone tissue ingrowth, and achieves synergistic optimization of mechanical properties and biological functions. Attached Figure Description
[0022] Figure 1 This is a schematic flowchart of a spiral gradient lattice structure design method according to an embodiment of this application;
[0023] Figure 2 This is a schematic diagram of the helical gradient lattice structure distribution according to one embodiment of this application;
[0024] Figure 3 This application Figure 1 A schematic diagram of a method flow for one embodiment of step S40;
[0025] Figure 4 This is a schematic diagram of the structure of one embodiment of this application. Detailed Implementation
[0026] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of this application. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to this application are not shown or described in the specification. This is to avoid obscuring the core parts of this application with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.
[0027] Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various embodiments. At the same time, the steps or actions in the method description can be rearranged or adjusted in a manner obvious to those skilled in the art. Therefore, the various orders in the specification and drawings are only for the clear description of a particular embodiment and do not imply a necessary order, unless otherwise stated that a particular order must be followed.
[0028] The serial numbers assigned to components in this document, such as "first" and "second," are used only to distinguish the described objects and have no sequential or technical meaning. The terms "connection" and "linkage" used in this application, unless otherwise specified, include both direct and indirect connections (linkages).
[0029] To facilitate the explanation of the inventive concept of this application, the gradient lattice structure design technology will be briefly described below.
[0030] In nature, biological structures often evolve into highly optimized geometric forms through long-term evolution. Seashells are a typical example, with their overall structure exhibiting a logarithmic helix shape, characterized by self-similar expansion and continuous growth. During growth, this structure achieves layer-by-layer size increases and continuous morphological transitions, while simultaneously improving material utilization efficiency and ensuring structural stability.
[0031] Therefore, by introducing the golden spiral curve into the design of porous lattice structures and constructing a continuously changing spatial control function to regulate the geometric parameters of the lattice structure as a whole, it is expected to achieve the biomimetic distribution of the pore structure and the gradient optimization of mechanical properties, thereby taking into account both load-bearing capacity and osseointegration performance in the same structure.
[0032] Current common gradient lattice structure design methods achieve local optimization of structural performance by altering cell size, rod diameter, or cell topology to create a spatial gradient in relative density. However, the applicant's research found that most existing gradient lattice structures vary along a single direction, making it difficult to achieve layer-by-layer size increases and continuous morphological transitions. This makes it challenging to improve material utilization efficiency while maintaining structural stability, thus hindering effective guidance of cell migration and bone tissue ingrowth pathways and limiting the scaffold's osseointegration capabilities.
[0033] In view of this, this application provides a design method and medium for a helical gradient lattice structure. Because the growth basis is based on a bilattice composite structure, it provides high porosity and good connectivity in the core region, while improving the overall stiffness and load-bearing capacity of the structure in the peripheral region. This allows the resulting bone tissue to both promote cell migration and angiogenesis, and also enhance the overall stiffness and load-bearing capacity of the structure. Based on the principle that the diameter of the support rods gradually decreases from the peripheral region to the central region and using a gradient function, a support rod diameter function is constructed to calculate the support rod diameter. This allows for a reduction in structural weight while improving load-bearing capacity, thereby improving the mechanical properties of the helical gradient lattice structure. When applied to bone tissue engineering, this effectively guides cell migration and bone tissue ingrowth. Furthermore, based on the principle that the pore size gradually increases from the outside to the inside and using a gradient function, a lattice unit size function is constructed to calculate the lattice unit size. This enhances the permeability and bioactivity of the structure when applied to bone tissue engineering, effectively guiding cell migration and bone tissue ingrowth. Thus, the continuous variation of porosity in space enables the lattice structure to possess both good mechanical properties and material transport capabilities, thereby optimizing pore connectivity and distribution patterns. When applied to bone tissue engineering, this effectively reduces stress concentration, promotes cell migration and bone tissue ingrowth, and achieves synergistic optimization of mechanical properties and biological functions.
[0034] This application provides an embodiment of a spiral gradient lattice structure design method; please refer to [reference needed]. Figure 1 ,include:
[0035] Step S10: Construct the outer contour.
[0036] As one embodiment of this application, a regular cylinder is selected as the design space, and a three-dimensional coordinate system (such as a Cartesian coordinate system) is established with the center of the bottom surface of the cylinder as the origin of the coordinate system, wherein the Z-axis is along the height direction of the cylinder.
[0037] In a specific embodiment, the following description uses a porous metal scaffold for bone tissue engineering with a 3D-printed conch-like gradient crystal structure as an example. As a specific embodiment for constructing the outer contour, the selected cylinder has a diameter of 40 mm and a height of 40 mm.
[0038] Step S20: Introduce the logarithmic spiral function to establish the array path of the parametric curve.
[0039] As one embodiment of this application, step S20 includes: introducing a logarithmic spiral parametric expression within the constructed outer contour design space to describe the spatial expansion path of the conch-like structure. In one embodiment, the logarithmic spiral parametric expression can be expressed as:
[0040]
[0041] Where X(t), Y(t), and Z(t) represent the coordinate components of the X-axis, Y-axis, and Z-axis, respectively; t represents the number of rotations parameter, 0≤t≤1, and when t=0, it represents a planar spiral; a represents the preset starting radius; b represents the preset spiral growth rate, which determines the expansion speed of the spatial expansion path; c represents the total height of the spiral; θ represents the rotational radian of the spiral; and e represents the natural base.
[0042] Based on the above parametric formula, the radial expansion rate of the helix can be controlled, so that the lattice structure exhibits a continuous and gradually expanding distribution in space, thereby simulating the morphological law of the layer-by-layer growth of biological structures.
[0043] In a specific embodiment, following a logarithmic spiral with a strict golden ratio, b=0.306, a=5, c=40, t=1, θ=2π·t=2π, all in mm.
[0044] Step S30: Establish a bilattice composite structure as the basis for lattice structure growth.
[0045] In one embodiment of this application, please refer to Figure 2 The dual-lattice composite structure employs a diamond lattice structure in its core region and a rhombic dodecahedral structure in its outer region. The diamond lattice structure in the core region provides high porosity and good connectivity, enabling the resulting bone tissue to promote cell migration and angiogenesis. The rhombic dodecahedral structure in the outer region enhances the overall stiffness and load-bearing capacity of the structure.
[0046] Furthermore, Boolean operations can be used to achieve a continuous transition between the two lattice structures in space, so that there are no obvious interface abrupt changes between different regions, thereby avoiding stress concentration problems.
[0047] Step S40: Gradient design is performed based on the lattice composite structure.
[0048] Step S40 includes: sequentially designing the support parameters, lattice size parameters, and porosity of the lattice structure for each point in the array path. The support parameter design includes: constructing a support diameter function based on the principle that the support diameter gradually decreases from the outer region to the center region and using a gradient function; and calculating the support diameter based on the support diameter function. The lattice size parameter design includes: constructing a lattice unit size function based on the principle that the pore size gradually increases from the outside to the inside and using a gradient function. The lattice structure porosity design includes: calculating the porosity of the lattice structure based on the support diameter and the lattice unit size.
[0049] In one embodiment of this application, please refer to Figure 3 The support parameters, lattice size parameters, and porosity of the lattice structure are designed sequentially for each point in the array path, including:
[0050] Step S401: Obtain the gradient control function of the spiral structure.
[0051] As one embodiment of this application, the gradient control function of the spiral structure can be expressed as:
[0052]
[0053]
[0054] Where x, y, and z represent the coordinates on the X-axis, Y-axis, and Z-axis, respectively. The gradient control function for the spiral structure, 0≤ ≤1, where r represents the radius of the helical structure. This indicates the maximum radius of the preset spiral structure.
[0055] In the specific implementation of this application, when When = 0, it corresponds to a rhombic dodecahedral structure. When =1, it corresponds to the diamond crystal lattice structure.
[0056] Step S402: Construct the support diameter function and lattice unit size function based on the gradient control function, and calculate the porosity of the lattice structure.
[0057] In one embodiment of this application, the support rod diameter function can be expressed as:
[0058]
[0059] in, The function representing the diameter of the support rod in three-dimensional coordinates. and These represent the minimum and maximum preset diameters of the support rod, respectively.
[0060] In practice, the minimum diameter of the support rod is 0.2 mm, and the maximum diameter is 0.3 mm.
[0061] Based on the above support rod diameter function, since 0 ≤ The value ≤1 ensures that the diameter of the designed support rod gradually decreases from thick to thin from the outer periphery to the center, which can reduce the structural weight while improving the load-bearing capacity. This can improve the mechanical properties of the helical gradient lattice structure and effectively guide cell migration and bone tissue ingrowth when applied to bone tissue engineering.
[0062] In one embodiment of this application, the lattice unit size function can be expressed as:
[0063]
[0064] in, This represents a function of lattice unit size in three-dimensional coordinates. and These represent the minimum and maximum values of the preset lattice unit size, respectively.
[0065] In practice, the minimum size of the lattice unit is 1.0 mm and the maximum size is 2.0 mm.
[0066] Based on the above lattice unit size function, since 0≤ The value ≤1 allows the size of the designed lattice unit to gradually decrease from the inside out, which can enhance the permeability and bioactivity of the structure when applied to bone tissue engineering, and effectively guide cell migration and bone tissue ingrowth pathways.
[0067] The porosity of a crystal lattice structure is determined by its relative density, and can be expressed as:
[0068]
[0069]
[0070] in, Represents the porosity function. denoted by ; g represents the relative density function; is a coefficient determined by the material properties; d represents the diameter of the support rod; and L represents the size of the lattice unit.
[0071] For relative density, which is the ratio of the total volume of the unit cell support to the total volume of the unit cell, it is proportional to the square of the ratio of the support diameter to the lattice unit size. Based on the support diameter and lattice unit size obtained above, it can be seen that the scheme of this application can realize the continuous change of porosity in space, so that the lattice structure has good mechanical properties and material transport capacity at the same time, thereby optimizing the pore connectivity and distribution law. When applied to bone tissue engineering, it effectively reduces stress concentration, promotes cell migration and bone tissue ingrowth, and achieves synergistic optimization of mechanical properties and biological functions.
[0072] Step S50: Connect the kernel structure and peripheral structure of the interface.
[0073] In the specific implementation of this application, the implicit modeling method based on scalar field driving of ntop software is adopted. The gradient control function is integrated with the support parameters, lattice size parameters and porosity of the lattice structure to generate a continuously changing three-dimensional lattice structure model. Thus, the geometry of nodes and supports can be controlled by the Boolean union operation of ntop software, ensuring the continuity of the lattice structure in topology and geometry, and avoiding the problems of node mismatch and connection discontinuity commonly found in traditional discrete modeling methods.
[0074] Step S60: Obtain the model obtained from the modeling process.
[0075] For specific implementation details, please refer to... Figure 4 The completed crystal structure model is exported as a standard 3D model file. The blue area represents the diamond array structure, while the surrounding areas represent a rhombic dodecahedral structure. Selective laser melting (SLM) is used for fabrication, employing Ti6Al4V titanium alloy powder. The structure is integrally formed through layer-by-layer melting and deposition. This process can precisely achieve the geometric details of complex lattice structures while ensuring the structure's mechanical properties and forming accuracy.
[0076] Based on the above specific embodiments, the mechanical properties and structural characteristics of the prepared gradient lattice structure were tested, and experimental data were obtained. During the loading test, no obvious stress concentration phenomenon was observed in the structure, and the overall stress was uniform, demonstrating good structural stability and fatigue resistance, meeting the requirements for bone tissue ingrowth and nutrient transport.
[0077] Based on the above scheme, a layer-by-layer increase in porosity and a continuous transition at the interface of the two-layer structure (diamond array structure and rhombic dodecahedral structure) were achieved. While ensuring structural stability, the material utilization efficiency was improved, the cell migration and bone tissue ingrowth pathways were effectively guided, and the osseointegration capacity of the scaffold was optimized.
[0078] One embodiment of this application provides a computer-readable storage medium storing a program, the stored program including methods that can be loaded by a processor and processed in any of the above embodiments.
[0079] Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer programs, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or external hard drive, etc., and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.
[0080] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.
Claims
1. A method for designing a helical gradient lattice structure, characterized in that, include: Construct the outer contour; An array path for the parametric curves is established by introducing a logarithmic spiral function; Establishing a bilattice composite structure as the basis for lattice structure growth; The gradient design based on the aforementioned lattice composite structure includes: sequentially designing support parameters, lattice size parameters, and lattice porosity for each point in the array path; wherein, the support parameter design includes: constructing a support diameter function based on the principle that the support diameter gradually decreases from the outer region to the center region and a gradient function; and calculating the support diameter based on the support diameter function; the lattice size parameter design includes: constructing a lattice unit size function based on the principle that the pore size gradually increases from the outside to the inside and a gradient function; the lattice porosity design includes: calculating the lattice porosity based on the support diameter and the lattice unit size; The kernel structure and peripheral structure of the interface; Obtain the model obtained from the modeling process.
2. The spiral gradient lattice structure design method as described in claim 1, characterized in that, The construction of the outer contour includes: selecting a regular cylinder as the design space, and establishing a three-dimensional coordinate system with the center of the bottom surface of the cylinder as the origin, wherein the Z-axis is along the height direction of the cylinder.
3. The spiral gradient lattice structure design method as described in claim 1, characterized in that, The aforementioned introduction of a logarithmic spiral function to establish an array path of parametric curves includes: introducing a logarithmic spiral parametric expression within the constructed outer contour design space to describe the spatial expansion path of the conch-like structure.
4. The spiral gradient lattice structure design method as described in claim 3, characterized in that, The logarithmic spiral parameterization expression includes: Where X(t), Y(t), and Z(t) represent the coordinate components of the X-axis, Y-axis, and Z-axis, respectively; t represents the number of rotations parameter, 0≤t≤1, and when t=0, it represents a planar spiral; a represents the preset starting radius; b represents the preset spiral growth rate, which determines the expansion speed of the spatial expansion path; c represents the total height of the spiral; θ represents the rotational radian of the spiral; and e represents the natural base.
5. The spiral gradient lattice structure design method as described in claim 1, characterized in that, The establishment of a dual-lattice composite structure as the basis for lattice structure growth includes: the core region adopting a diamond lattice structure and the outer region adopting a rhombic dodecahedral structure.
6. The spiral gradient lattice structure design method as described in claim 1, characterized in that, The sequential design of support parameters and lattice size parameters for each point in the array path includes: Obtain the gradient control function for the spiral structure; Based on the gradient control function, construct the support diameter function and the lattice unit size function, and calculate the porosity of the lattice structure.
7. The spiral gradient lattice structure design method as described in claim 6, characterized in that, The support rod diameter function includes: Where x, y, and z represent the coordinates on the X-axis, Y-axis, and Z-axis, respectively. The function representing the diameter of the support rod in three-dimensional coordinates. and These represent the preset minimum and maximum values of the support rod diameter, respectively. The gradient control function for the spiral structure, 0≤ ≤1, where r represents the radius of the helical structure. This indicates the maximum radius of the preset spiral structure.
8. The spiral gradient lattice structure design method as described in claim 6, characterized in that, The lattice unit size function includes: Where x, y, and z represent the coordinates on the X-axis, Y-axis, and Z-axis, respectively. This represents a function of lattice unit size in three-dimensional coordinates. and These represent the minimum and maximum values of the preset lattice unit size, respectively; The gradient control function for the spiral structure, 0≤ ≤1, where r represents the radius of the helical structure. This indicates the maximum radius of the preset spiral structure.
9. The spiral gradient lattice structure design method as described in claim 6, characterized in that, The method for calculating the porosity of a crystal structure based on the support diameter and the size of the crystal unit includes: Where x, y, and z represent the coordinates on the X-axis, Y-axis, and Z-axis, respectively. Represents the porosity function. denoted by ; g represents the relative density function; is a coefficient determined by the material properties; d represents the diameter of the support rod; and L represents the size of the lattice unit.
10. A computer-readable storage medium, characterized in that, The medium stores a program that can be loaded by a processor and executed as the spiral gradient lattice structure design method as described in any one of claims 1 to 9.