Nested grid structure for regulating torque-axial force conversion and optimization design method

Abstract

The present application belongs to the field of structural mechanics nonlinear response regulation, and specifically provides a nested grid structure for regulating torque-axial force conversion and an optimization design method, establishes the configuration description of the nested grid of the inner and outer layers, generates a three-dimensional model by using CAD, carries out finite element quasi-static simulation under the given axial constraint and torsional loading conditions, extracts the torque-axial force relationship curve to construct a data set, trains a deep operator network proxy model based on the data set, realizes the rapid prediction from the structure parameters to the whole response curve, adopts the reverse parameter solving strategy of discrete configuration enumeration combined with continuous parameter gradient optimization to obtain the optimal structure parameters, and back-substitutes the optimization results into CAD / finite element for rechecking and verification, thereby forming a closed-loop design method of simulation data-proxy prediction-reverse optimization-high-fidelity rechecking. The present application realizes the programmable mapping between the torque input and the axial force output, and realizes the efficient reverse solution and programmable regulation of the target curve under the constraint conditions such as parameter boundary.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear response control in structural mechanics, specifically relating to a nested mesh structure and optimization design method for controlling torque-axial force conversion. Background Technology

[0002] Torque-axial force conversion mechanisms are widely used in clamping and locking, limit braking, force transmission and energy conversion, and are also commonly used in the assembly and maintenance of hydropower equipment for bolt pre-tightening, sealing and tightening, and load application. Existing engineering solutions mainly include screw pairs (lead screw and nut), wedge / inclined plane mechanisms, gear-connecting rod mechanisms, and friction clutches. The basic idea is to use geometric transmission or friction coupling to convert rotary input into axial displacement or axial force output. Although the above solutions are relatively mature, they generally suffer from problems such as a large number of structural components, sensitivity to assembly accuracy and clearance, efficiency decay and performance drift due to friction and wear, and difficulty in continuously programmable control of the response relationship. Especially when a specific "torque-axial force curve shape" (such as threshold type, segmented type, or directional difference type) is required, it often relies on complex mechanism superposition or additional control units, resulting in high system integration and maintenance costs.

[0003] In recent years, research on mesh structures, as a type of mechanical metamaterial, to achieve macroscopic equivalent performance control through element geometry design has been continuously developing. For example, by employing asymmetric configurations such as chiral elements and bending / curving beams, and utilizing their geometric nonlinearity under large deformation conditions, significant normal reaction forces can be generated under torsional loads, thereby achieving the coupled conversion between torque and axial reaction forces. However, existing related structures are mostly single-layer meshes or single-parameter systems with limited degrees of freedom in control, making it difficult to simultaneously achieve independent control of output amplitude, directional differences, and curve shape characteristics within the same structure. Furthermore, the inverse solution of the target curve usually relies on repeated simulation trial and error, resulting in low design efficiency and insufficient robustness.

[0004] The existing technologies for programmable control and target curve design of torque-axial force conversion structures have the following main defects: (1) Fixed mapping relationship and few adjustable dimensions. The torque-axial force relationship of traditional screw pairs, wedges and connecting rods is mainly determined by transmission geometry and friction interface, making it difficult to achieve target curve shaping such as threshold type, segmented type, saturation type or direction difference type without significantly increasing the complexity of the mechanism; (2) Insufficient stability and consistency. Contact friction, assembly gap and wear will cause the equivalent transmission parameter to drift, resulting in the output force and torque relationship fluctuating with the working condition, and poor repeatability; (3) Limited degree of freedom of control of single-layer mesh structure. The existing technologies mostly adopt single-layer mesh or single unit system, and the output amplitude, nonlinear range and directionality are often coupled with each other, making it difficult to achieve independent control of multiple indicators while meeting strength, stability and manufacturing constraints; (4) Low efficiency of reverse design. The solution of the target torque-axial force curve usually relies on repeated simulation trial and error or local search. When facing high-dimensional parameters and strong nonlinear response, the computational cost is high and it is easy to get trapped in local optimum. There is a lack of fast prediction and efficient optimization mechanism for the whole curve. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a nested mesh structure and optimization design method for regulating torque-axial force conversion, so as to realize programmable mapping between torque input and axial force output, and efficient reverse solution and programmable control of target curve.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a nested mesh structure optimization design method for regulating torque-axial force conversion, comprising the following steps: Step 1, Nested Mesh Structure Design and Simulation Calculation, includes the following sub-steps: S1-1, Parametric geometric modeling of structure: establishing nested mesh structures; S1-2, CAD Model Generation: Based on the structural design parameters modeled in step S1-1, the SolidWorks secondary development interface is used to realize the automated modeling and assembly generation of nested mesh structures. S1-3, Simulation Solution and Data Extraction: Perform numerical simulation analysis on the three-dimensional CAD model generated in step S1-2 to obtain the torsion-axial force conversion curve; Step 2, Torque-Axial Force Relationship Prediction and Inverse Optimization, includes the following sub-steps: S2-1, Proxy Model Training: A proxy model of the torque-axial force relationship is trained using a batch simulation data-driven approach. S2-2, Inverse Optimization Design: A reverse solution strategy combining discrete configuration enumeration and continuous parameter gradient optimization is employed to efficiently inversely determine the optimal structural parameter P based on the target torque-axial force curve. ; S2-3, Closed-loop verification: The optimal structural parameters P... Substitute back to step S1-2, regenerate the CAD model and perform high-fidelity finite element simulation verification, and form an iterative update mechanism through error feedback until the target accuracy requirements are met.

[0007] In a preferred embodiment, the structural parametric geometric modeling in step S1-1 includes the following steps: 1) Establish a parametric model of the nested cylindrical base panel: The nested cylinders are coaxially arranged along the same central axis, including an outer sleeve and an inner sleeve. The diameter of the central circle of the outer sleeve is... D 1. Wall thickness is w 1. The diameter of the center circle of the inner sleeve is D 2. Wall thickness is w 2. The axial height of both the outer sleeve and the inner sleeve is... H Both are coaxial and their end faces are flush; 2) Parametric generation of microstructures: The shape of the centerline of a single microstructure is described by a sine function, used to define the geometric profile of a bending / curved beam. The cross-sectional width of the microstructure is... w 3; Using one microstructure as the basic unit, four microstructures are generated through rotation operations, and connected at the endpoints in a rectangular pattern to form a grid unit. The four microstructures can be set with the same or different geometric parameters. 3) Grid cell array configuration and hierarchical assembly: End caps are respectively installed at the upper and lower axial ends of the outer sleeve and the inner sleeve, with an end cap thickness of [missing information]. h The outer mesh is arranged on the surface area of ​​the outer sleeve and consists of upper and lower mesh units. The upper and lower parts are respectively composed of... n 1× m One grid cell is periodically arranged along the circumferential and axial directions to form a hollow grid structure; the inner grid is arranged in the inner sleeve surface area and consists of upper and lower grid cells, the upper and lower parts being respectively composed of... n 2× m Two grid cells are arranged periodically.

[0008] In a preferred embodiment, the lower grid cells in the outer grid are arranged in a mirror image or in the same direction as the upper grid cells, and the lower grid cells in the inner grid are arranged in a mirror image or in the same direction as the upper grid cells.

[0009] In the preferred embodiment, the specific process of generating the CAD model in step S1-2 is as follows: 1) Generate a two-dimensional mesh structure sketch in the unfolded plane based on the geometric parameters and array parameters of the nested mesh structure in step S1-1. The unfolded dimension of the outer cylindrical panel is π. D 1× HThe unfolded dimension of the inner cylindrical panel is π. D 2× H ; 2) Perform Boolean operations on the mesh structure on the unfolded plane and the corresponding cylindrical base panel unfolded sketch to obtain the intersecting sketch used to form the hollow area, forming a combined contour, and generating the corresponding panel entity / surface based on the combined contour; 3) By using wrapping or equivalent surface mapping, the unfolded sketch is mapped to the cylindrical surfaces of the outer and inner cylindrical panels to complete the construction of the mesh cutout feature on the cylindrical surface; 4) Based on parameters h The upper and lower end caps are automatically generated and stitched / merged with the cylindrical panel and mesh structure to form a complete three-dimensional nested mesh structure CAD model.

[0010] In the preferred embodiment, the specific process of simulation solution and data extraction in steps S1-3 is as follows: 1) Import the model into Abaqus / CAE for quasi-static simulation: Import the model into Abaqus / CAE, establish material parameters and set geometric nonlinearities, and perform quasi-static solution using the general static analysis step; set boundary conditions and loading methods: apply full constraints to the lower end face, set a reference point RP on the upper end face and associate the end face with the reference point through motion coupling, and apply a torsional angle in the range of -90° to +90° to the reference point. φ As a displacement-type boundary condition, its axial degree of freedom is constrained; local densification is carried out on the microstructure curved beam, the connection area and the end transition area; 2) Data Extraction: After the simulation is completed, the applied torque is obtained by extracting the reaction torque at the reference point RP through historical output. T The axial force output is obtained by extracting the axial reaction force at the reference point RP. F z , build F z ( φ )as well as F z ( T Curve data.

[0011] In the preferred embodiment, the specific process of training the surrogate model in step S2-1 is as follows: 1) Unify the configuration parameters of the outer and inner layers into a parameter vector P; 2) Extract the axial force curve for each sample within the torsion angle range [-90°, 90°], and normalize the torsion angle to... x ∈[-1, 1], and the sample curves are unified to a fixed sampling grid through interpolation. x grid =linspace(-1,1, Nx ),in, x grid Indicates the sampling points for the normalized torsion angle. N x The number of curve sampling points; the curve output is standardized and divided into training, validation and test sets; 3) Model Construction: A deep operator network is used as the surrogate model, with the structural parameter vector P as the input to the branch network and the normalized torsion angle sampling points as the input. x grid As input to the backbone network; 4) The network training uses mean squared error as the objective function and employs the Adam optimizer for iterative updates. After training, the model parameters and curve standardization parameters are saved. x grid This is used for subsequent reverse optimization design.

[0012] In a preferred embodiment, the curve standardization parameters include the mean and standard deviation.

[0013] In the preferred embodiment, in step 1) of step S2-1, the parameter vector P = [ t out , a out , b out , c out , d out , t in , a in , b in , c in , d in ],in t out , t in ∈{1, 2} represents the discrete configuration type of the outer and inner meshes, where 1 is the same orientation type and 2 is the mirror type. a out , b out , c out , d out For the continuous design variables of the four outermost microstructures; a in , b in , c in ,d in ) represents the continuous design variables for the four microstructures in the inner layer.

[0014] In the preferred embodiment, in step 3) of step S2-1, the input... x grid Introduce Fourier feature mapping.

[0015] In the preferred embodiment, in step 4) of step S2-1, N x Randomly selected from each curve sampling point N s Each point is involved in the loss calculation.

[0016] In the preferred embodiment, the reverse optimization design in step S2-2 includes the following steps: 1) Input the target curve as a discrete set of target points to obtain the target point set. ,in x i For normalized torsion angle sampling points, This corresponds to the target axial force value; 2) Using the parameter vector P as the design variable, an enumeration strategy is used to traverse all combinations of the discrete configuration variables; 3) For each discrete combination, the continuous variables are randomly initialized within the feasible interval, and the mean squared error loss function at the target point is minimized using the Adam gradient optimization method. The mean and standard deviation saved during the training phase are then de-standardized. 4) After each parameter update, perform interval pruning on the continuous variables, and obtain the optimal solution for the discrete combination by multiple random restarts; 5) Select the solution with the minimum global loss among all discrete combination optimal solutions as the optimal structure parameter P. .

[0017] In a preferred embodiment, the mean squared error loss function is expressed as follows: ; in, For the surrogate model at the target point x i The predicted output at that point.

[0018] In a preferred embodiment, the closed-loop verification in step S2-3 includes the following steps: 1) P Input the trained surrogate model and calculate the prediction curve. The network output is denormalized according to the mean and standard deviation saved during the training phase to obtain the axial force prediction curve under physical dimensions. 2) In the target discrete point set The prediction is performed again, and the mean square error at the target point and the goodness-of-fit index are calculated. R 2 Output the comparison results between the global prediction curve and the target discrete points; 3) P Returning to step one, the corresponding CAD model is regenerated and verified using Abaqus quasi-static simulation, extracting high-fidelity torque-axial force curves. It is then compared with the target curve and the proxy prediction curve. When the error exceeds the preset tolerance, P is adjusted. Add the corresponding samples to the dataset and update the surrogate model. Then repeat steps S2-2 and S2-3 until the target accuracy requirement is met.

[0019] This invention also provides a nested mesh structure for regulating torque-axial force conversion, designed using the above method. It includes an outer mesh and an inner mesh. The outer mesh is arranged on the cylindrical surface region of the outer sleeve and consists of upper and lower mesh units. The upper and lower parts are respectively composed of… n 1× m One grid cell is periodically arranged along the circumferential and axial directions to form a hollow grid structure; the inner grid is arranged in the inner sleeve surface area and consists of upper and lower grid cells, the upper and lower parts being respectively composed of... n 2× m Two grid cells are arranged periodically; both the outer and inner grids are composed of microstructures; the outer sleeve and the inner sleeve are coaxially nested and their end faces are flush.

[0020] In the preferred embodiment, the shape of the centerline of a single microstructure is described by a sine function. Using one microstructure as a basic unit, four microstructures are generated through a rotation operation. The four microstructures are connected at their endpoints in a rectangular pattern to form a single grid unit.

[0021] In a preferred embodiment, the lower grid cells in the outer grid are arranged in a mirror image or in the same direction as the upper grid cells, and the lower grid cells in the inner grid are arranged in a mirror image or in the same direction as the upper grid cells.

[0022] In a preferred embodiment, the geometric parameters of the four microstructures constituting a single grid cell can be set to be the same or different to achieve asymmetry within the cell and programmable mechanical response.

[0023] In a preferred embodiment, the diameter of the center circle of the outer sleeve is . D 1. Wall thickness is w 1. The diameter of the center circle of the inner sleeve is D 2. Wall thickness is w 2. The axial height of both the outer sleeve and the inner sleeve is...H Both are coaxial and their end faces are flush.

[0024] The nested mesh structure and optimization design method for regulating torque-axial force conversion provided by this invention have the following beneficial effects: 1. Strong control over torque-axial force relationship. Through the collaborative design of nested inner and outer meshes and segmented upper and lower units, combined with mirror / co-directional configuration, the torque-axial force relationship curve can be programmably controlled, effectively adjusting key features such as output amplitude, nonlinear range, and differences in positive and negative torsional directions.

[0025] 2. Expanded design space and easier to accommodate multiple constraints. Compared to single-layer mesh structures, this invention utilizes the decoupling of inner and outer layer parameters and the layer superposition mechanism to expand the achievable response space, making it easier to obtain torque-axial force curves that meet target performance under constraints such as strength, stability, and manufacturing, and improving the robustness and feasibility of the solution.

[0026] 3. Significantly improved reverse engineering efficiency. A surrogate model trained on simulation data enables rapid prediction of parameters and curves. Combined with discrete configuration enumeration and continuous parameter gradient optimization, it achieves rapid parameter calculation for the target curve, reducing repeated simulation trials, lowering computational costs, and improving optimization efficiency.

[0027] 4. A closed-loop verification mechanism is established, ensuring reliable and traceable results. Optimized parameters are substituted back into the high-fidelity finite element method for verification, and data and models are iteratively updated based on error feedback, forming a prediction-optimization-verification closed loop to improve design accuracy and engineering usability. Attached Figure Description

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram illustrating the parametric modeling and configuration composition of the nested mesh structure in an embodiment of the present invention; Figure 2 This is a simulation diagram illustrating torsional loading, boundary condition setting, and torque / axial force data extraction in an embodiment of the present invention. Figure 3 This is a schematic diagram showing the comparison of the response space between a single-layer mesh and a nested mesh in an embodiment of the present invention; Figure 4 This is a schematic diagram of the DeepONet proxy model structure in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the training convergence and prediction results of the proxy model in an embodiment of the present invention; Figure 6 This is a schematic diagram of the reverse optimization design process in an embodiment of the present invention; Figure 7 This is a schematic diagram of the reverse optimization results in an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0030] Example 1: A nested mesh structure optimization design method for regulating torque-axial force conversion includes two stages: structural design and simulation calculation, and prediction and inverse optimization design. First, based on parametric geometric modeling of the structure, a configuration description of the inner and outer nested meshes is established. A three-dimensional model is automatically generated using CAD, and quasi-static finite element simulation is performed under given axial constraints and torsional loading conditions to extract torque-axial force relationship curves and construct a dataset. Then, a DeepONet surrogate model is trained based on the dataset to achieve rapid prediction from structural parameters to the entire response curve. Under the condition of given discrete points of the target curve, the optimal structural parameters are obtained by the inverse parameter calculation strategy of "discrete configuration enumeration + continuous parameter gradient optimization". Finally, the optimization results are back-substituted into CAD / finite element for verification, forming a closed-loop design method of "simulation data - surrogate prediction - inverse optimization - high-fidelity verification".

[0031] Specifically, the following steps are included: Step 1: Nested Mesh Structure Design and Simulation. This section constructs a nested mesh structure with inner and outer coaxial elements based on parametric modeling. Geometric parameters are used to uniformly describe the structural configuration, element array, and inter-layer relationships, enabling automatic generation and repeatable updates of the structural geometry. Based on this, quasi-static finite element simulation is used to obtain the torque-axial force conversion response curve, providing high-quality data support for subsequent surrogate model training and inverse optimization.

[0032] Includes the following sub-steps: S1-1, Structural parametric geometric modeling.

[0033] First, a parametric model of the nested cylindrical base panel is established. The nested cylinders are coaxially arranged along the same central axis, including an outer sleeve and an inner sleeve: the central circle diameter of the outer sleeve is... D 1. Wall thickness is w 1; The diameter of the center circle of the inner sleeve is D 2. Wall thickness is w 2; The axial height of both the outer sleeve and the inner sleeve is HThe two layers are coaxial and their end faces are flush, forming a double-layered cylindrical base to support boundary constraints and mesh arrangement. Based on this, the parametric generation of microstructures (mesh beam elements) is performed. The shape of the centerline of a single microstructure is described by a sine function to define the geometric profile of a bending / curved beam; the cross-sectional width of the microstructure is... w 3 (Its thickness can be related to the thickness of the base panel or set as an independent parameter). Using one microstructure as a basic unit, four microstructures are generated through rotation, and connected at the endpoints according to a rectangular pattern to form a mesh unit; the four microstructures can be set with the same or different geometric parameters to achieve asymmetry within the unit and programmable mechanical response. Subsequently, the mesh unit array is configured and hierarchically assembled. End caps are respectively installed at the upper and lower axial ends of the outer sleeve and the inner sleeve, with an end cap thickness of [missing information]. h This is used to transfer the end loading interface and axial boundary constraints. The outer mesh is arranged on the cylindrical surface area of ​​the outer sleeve. The outer mesh consists of upper mesh element ① and lower mesh element ②, with the upper and lower parts respectively composed of... n 1× m A perforated mesh structure is formed by periodically arranging one mesh unit along the circumferential and axial directions. The lower mesh unit ② can be arranged as a mirror image or in the same direction as the upper mesh unit ① to control the deformation mode and axial reaction force difference in the positive / negative torsional directions. Further, an inner mesh is configured on the basis of the outer mesh. The inner mesh is arranged in the inner sleeve surface area and consists of an upper mesh unit ③ and a lower mesh unit ④. The upper and lower parts are respectively composed of… n 2× m Two grid cells are arranged periodically; wherein, the lower grid cell ④ can also be arranged in a mirror or in the same direction as the upper grid cell ③, so as to achieve independent control of the directionality and nonlinear response of the inner grid.

[0034] S1-2, CAD Model Generation. Based on the structural design parameters modeled in step S1-1, the SolidWorks API is used to automate the modeling and assembly generation of nested mesh structures.

[0035] Specifically, firstly, based on the geometric parameters and array parameters of mesh elements ①, ②, ③, and ④ ( n 1, m 1, n 2, m (2 and mirror options) Generate a 2D mesh structure sketch in the unfolded plane, where the unfolded dimension of the outer cylindrical panel is π. D 1× H The unfolded dimension of the inner cylindrical panel is π. D 2× HSubsequently, Boolean operations are performed on the mesh structure on the unfolded plane and the corresponding unfolded sketch of the cylindrical base panel to obtain the intersecting sketch used to form the hollow area, forming a combined contour; and the corresponding panel solid / surface is generated based on this combined contour. Further, through wrapping or equivalent surface mapping, the unfolded sketch is precisely mapped to the cylindrical surfaces of the outer and inner cylindrical panels, completing the construction of the mesh hollow feature on the cylindrical surface, realizing the coaxial nesting configuration of the outer and inner meshes; finally, based on the parameters... h The system automatically generates upper and lower end caps and integrates them with the cylindrical panel and mesh structure to form a complete 3D nested mesh structure CAD model. This modeling process can be automatically reconstructed and updated according to design parameters, and outputs a standard 3D model file for subsequent simulation and manufacturing.

[0036] S1-3. Simulation Solution and Data Extraction. Numerical simulation analysis is performed on the 3D CAD model generated in step S1-2 to obtain the torsional-axial force conversion curve.

[0037] Specifically, the model was imported into Abaqus / CAE, material parameters were established, and geometric nonlinearity was set (NLGEOM=ON). A quasi-static solution was performed using the Static, General step to characterize the nonlinear mechanical response of the nested mesh under large deformation conditions. Boundary conditions and loading methods were as follows: Full constraints were applied to the lower end face to fix the structure (restricting triaxial translation and rotation); a reference point RP was set on the upper end face, and the end face was associated with the reference point through motion coupling, allowing the end face load and response to be uniformly output and extracted at the reference point. During loading, a torsional angle was applied to the reference point. φ As a displacement-type boundary condition, its axial degrees of freedom are constrained to form a predetermined axial boundary condition, thereby generating axial reaction force output during torsion. The loading range of the torsion angle is -90° to +90°, and incremental loading is used to obtain complete positive and negative torsional responses. In terms of mesh generation, the microstructure curved beam, connection region, and end transition region are locally refined, and mesh independence analysis is conducted by changing the element size to ensure that the torque and axial force response curves converge to the mesh scale. After simulation, the applied torque is obtained by extracting the reaction torque at the reference point RP through the history output. T The axial force output is obtained by extracting the axial reaction force at the reference point RP. F z Thus constructing F z ( φ )as well as F z ( T The curve data, such as curves, are used as the basis for subsequent training and reverse optimization of the proxy model.

[0038] Step 2: Torque-axial force relationship prediction and reverse optimization.

[0039] This section constructs a surrogate model of torque-axial force response based on the simulation data obtained in the first part, enabling rapid prediction of structural parameters to the entire response curve, thus replacing the costly finite element iterative calculation. Building upon this, a reverse solution strategy of discrete configuration enumeration + continuous parameter gradient optimization is adopted to efficiently inversely calculate the optimal structural parameters for the target curve. A closed-loop verification and iterative update mechanism is then established through high-fidelity simulation verification.

[0040] Includes the following sub-steps: S2-1, Proxy model training.

[0041] After establishing a parametric description of the nested mesh structure, a surrogate model of the torque-axial force relationship is trained using a batch simulation data-driven approach. Let the number of selectable microstructure types be... k Then a single grid cell consists of four microstructures, and the four microstructures can be selected independently, with the number of combinations being: k 4 Considering the choice of mirror / co-directional configuration for the upper and lower segmented elements (2 types), the configuration space of a single-layer mesh is 2. k 4 The nested mesh is formed by the independent combination of two sets of meshes, an outer layer and an inner layer, and the overall configuration space is expanded to (2). k 4 ) 2 This significantly improves the design freedom of realizing torque-axial force curves.

[0042] Based on the "parametric modeling—CAD generation—finite element simulation" process described in Part 1, the configuration space is sampled, sample structures are generated in batches, and their response curves are obtained to construct a training dataset. Specifically, the configuration parameters of the outer and inner layers are uniformly encoded into a parameter vector P=[ t out , a out , b out , c out , d out , t in , a in , b in , c in , d in ],in tout , t in ∈{1, 2} represents the discrete configuration type of the outer and inner meshes (1 for unidirectional type, 2 for mirror type), a out , b out , c out , d out )and( a in , b in , c in , d in ) represents the continuous design variables (corresponding to microstructure geometric parameters) for the four microstructures in the outer and inner layers. For each sample, the axial force curve is extracted within the torsion angle range [-90°, 90°], and the torsion angle is normalized to x ∈[-1, 1], and at the same time, the sample curves are unified to a fixed sampling grid through interpolation. x grid =linspace(-1,1, N x (Preferred) =2000) to form a consistent supervision signal. To improve training stability, the curve output is standardized (subtract the mean and divide the standard deviation), and the dataset is divided into training set, validation set, and test set at 70%, 15%, and 15% respectively.

[0043] In terms of model construction, DeepONet is used as a surrogate model, with the structural parameter vector P as the input to the branch network and normalized twist angle sampling points. x grid As input to the backbone network, it learns the operator mapping relationship from structural parameters to the entire axial force curve.

[0044] Preferably, to enhance the backbone network's ability to represent curve details and nonlinear features, the input... x grid Introduce Fourier feature mapping.

[0045] The network training uses mean squared error as the objective function, employs the Adam optimizer for iterative updates, and combines a learning rate decay strategy to improve convergence stability.

[0046] Furthermore, to reduce the computational burden of a single iteration and improve generalization ability, additional steps can be taken for each training sample. N xRandomly selected from each curve sampling point N s Points (preferred) N s =256) participates in the loss calculation, realizing random subsampling training of the curve. After training, the model parameters and the standardized parameters of the curve (mean, standard deviation) are saved. x grid This is used for subsequent reverse optimization design.

[0047] S2-2, Inverse Optimization Design. A reverse solution strategy combining discrete configuration enumeration with continuous parameter gradient optimization is employed to efficiently inversely determine the optimal structural parameter P based on the target torque-axial force curve. .

[0048] After the surrogate model is trained and the network parameters are frozen, inverse optimization design is carried out focusing on the target torque-axial force relationship. First, the target curve is input as discrete target points to obtain the target point set. ,in x i For normalized torsion angle sampling points, This corresponds to the target axial force value. Subsequently, the structural parameter vector P described in the previous step is used as the design variable, where the discrete configuration variables (outer / inner layer type) are enumerated using an enumeration strategy to traverse all combinations. For each discrete combination, the remaining continuous variables are randomly initialized within a given feasible interval, and the Adam gradient optimization method is used to minimize the mean squared error loss function at the target point. in For the surrogate model at the target point x i The predicted output is calculated, and the model output is denormalized using the mean and standard deviation saved during the training phase to ensure that the optimization is performed within the physical dimensions. During the optimization iteration process, after each parameter update, interval pruning (clamping) is performed on the continuous variables to strictly satisfy the boundary constraints, and the optimal solution under the discrete combination is obtained through multiple random restarts; finally, the optimal solution with the minimum global loss among all the optimal solutions of discrete combinations is selected as the optimal structure parameter P. The output is used for subsequent closed-loop simulation verification and structure generation.

[0049] S2-3, Closed-loop verification. The optimal structural parameters P... Substitute back to step S1-2, regenerate the CAD model and perform high-fidelity finite element simulation verification, and form an iterative update mechanism through error feedback until the target accuracy requirements are met.

[0050] Specifically, firstly, P Input the trained surrogate model, using a fixed uniform sampling grid during the training phase. x gridCalculate the prediction curve The network output is then denormalized using the mean and standard deviation saved during the training phase to obtain the axial force prediction curve in physical dimensions. Subsequently, the target discrete point set... The prediction is performed again, and the mean squared error (MSE) at the target point and the goodness-of-fit index are calculated. R 2 Quantifying P It approximates the target curve; at the same time, it outputs the comparison results of the global predicted curve and the target discrete points, which can be used to intuitively verify the consistency between the curve shape and key feature points (peaks, inflection points, symmetrical / asymmetrical intervals, etc.).

[0051] Furthermore, to ensure the reliability of the reverse solution results of the surrogate model under the high-fidelity physical model, P Returning to the automated process of Part 1, the corresponding CAD model was regenerated and verified using Abaqus quasi-static simulation, extracting high-fidelity torque-axial force curves. The model is then compared with the target curve and the surrogate prediction curve to calculate indicators such as maximum absolute error and relative error. When the error exceeds the preset tolerance, the verification sample can be added to the dataset and the surrogate model can be updated. The second step of reverse optimization and the verification process of this step are repeated until the target accuracy requirements are met, thus forming a closed-loop design and verification mechanism of "target curve - reverse parameter calculation - simulation verification".

[0052] Example 2: In this embodiment, the present invention is illustrated using specific implementation examples.

[0053] (I) Nested mesh structure design and simulation calculation.

[0054] Step 1: Parametric Geometric Modeling of the Structure. First, a parametric model of the nested cylindrical foundation panel is established, as shown in the figure. Figure 1 As shown. The nested cylinders are coaxially arranged along the same central axis, including an outer sleeve and an inner sleeve: the central circle diameter of the outer sleeve is... D 1 = 63.66 mm, wall thickness is w 1 = 5mm; the diameter of the center circle of the inner sleeve is D 2=39.79mm, wall thickness is w 2=5mm; the axial height of both the outer and inner sleeves is 2=5mm. H =226mm, ensuring both are coaxial and have flush end faces, thus forming a double-layer cylindrical base to bear boundary constraints and mesh layout. Based on this, the parametric generation of microstructures (mesh beam elements) is performed. A sine function is used for each individual microstructure. Describe the shape of its centerline. Ais a variable parameter, representing the amplitude parameter of the sine function, used to define the geometric profile of the bending / curving beam; the cross-sectional width of the microstructure is... w 3 = 1mm (its thickness can be related to the thickness of the base panel or set as an independent parameter). Using one microstructure as a basic unit, four microstructures are generated through rotation, and connected at the endpoints according to a rectangular pattern to form a grid unit; the four microstructures can be set with the same or different geometric parameters to achieve asymmetry and programmable mechanical response within the unit. Subsequently, the grid unit array configuration and hierarchical assembly are performed. End caps are respectively installed at the upper and lower axial ends of the outer sleeve and the inner sleeve, with an end cap thickness of [missing information]. h =5mm, used to transfer the end loading interface and axial boundary constraints. The outer mesh is arranged on the cylindrical surface area of ​​the outer sleeve. The outer mesh consists of upper mesh unit ① and lower mesh unit ②, and the upper and lower parts are respectively composed of... n 1× m A perforated mesh structure is formed by periodically arranging 8×4 mesh units along the circumferential and axial directions. The lower mesh unit ② can be arranged as a mirror image or in the same direction as the upper mesh unit ① to control the deformation mode and axial reaction force difference under positive / negative torsional directions. Further, an inner mesh is configured on the outer mesh layer. The inner mesh is arranged in the inner sleeve surface area and consists of upper mesh unit ③ and lower mesh unit ④. The upper and lower parts are respectively composed of… n 2× m 2 = 5 × 4 grid units are arranged periodically; wherein, the lower grid unit ④ can also be arranged in a mirror or in the same direction relative to the upper grid unit ③, so as to achieve independent control of the directionality and nonlinear response of the inner grid.

[0055] The second step is CAD model generation. Based on the structural design parameters, the SolidWorks API (Secondary Development Interface) is used to automate the modeling and assembly of the nested mesh structure. Specifically, firstly, based on the geometric parameters and array parameters of mesh elements ①, ②, ③, and ④... n 1, m 1, n 2, m (2 and mirror options) Generate a 2D mesh structure sketch in the unfolded plane, where the unfolded dimension of the outer cylindrical panel is π. D 1× H The unfolded dimension of the inner cylindrical panel is π. D 2× HSubsequently, Boolean operations are performed on the mesh structure on the unfolded plane and the corresponding unfolded sketch of the cylindrical base panel to obtain the intersecting sketch used to form the hollow area, forming a combined contour; and the corresponding panel solid / surface is generated based on this combined contour. Further, through wrapping or equivalent surface mapping, the unfolded sketch is precisely mapped to the cylindrical surfaces of the outer and inner cylindrical panels, completing the construction of the mesh hollow feature on the cylindrical surface, realizing the coaxial nesting configuration of the outer and inner meshes; finally, based on the parameters... h The system automatically generates upper and lower end caps and integrates them with the cylindrical panel and mesh structure to form a complete 3D nested mesh structure CAD model. This modeling process can be automatically reconstructed and updated according to design parameters, and outputs a standard 3D model file for subsequent simulation and manufacturing.

[0056] The third step is simulation and data extraction. For example... Figure 2 As shown, numerical simulation analysis is performed on the 3D CAD model generated in the second step to obtain the torsional-axial force conversion curve. Specifically, the model is imported into Abaqus / CAE, material parameters are established and geometric nonlinearity is set (NLGEOM=ON), and a quasi-static solution is performed using the Static, General step to characterize the nonlinear mechanical response of the nested mesh under large deformation conditions. The boundary conditions and loading methods are as follows: full constraints are applied to the lower end face to fix the structure (restricting triaxial translation and triaxial rotation); a reference point RP is set on the upper end face, and the end face is associated with the reference point through motion coupling, so that the end face load and response can be uniformly output and extracted at the reference point. During the loading process, a torsional angle is applied to the reference point. φ As a displacement-type boundary condition, its axial degrees of freedom are constrained to form a predetermined axial boundary condition, thereby generating axial reaction force output during torsion. The loading range of the torsion angle is -90° to +90°, and incremental loading is used to obtain complete positive and negative torsional responses. For mesh generation, local refinement is applied to the microstructure curved beam, connection areas, and end transition areas. Mesh independence analysis is conducted by changing the element size to ensure that the torque and axial force response curves converge to the mesh scale. Mesh quality is evaluated using Skewness, ensuring that the maximum Skewness value does not exceed 0.75. After simulation, the applied torque is obtained by extracting the reaction torque at the reference point RP through the history output. T The axial force output is obtained by extracting the axial reaction force at the reference point RP. F z Thus constructing F z ( φ )as well as F z ( TThe curve data, such as curves, are used as the basis for subsequent training and reverse optimization of the proxy model.

[0057] (II) Torque-Axial Force Relationship Prediction and Inverse Optimization Method The first step is surrogate model training. After establishing a parametric description of the nested mesh structure, a surrogate model of the torque-axial force relationship is trained using a batch simulation data-driven approach. Assuming the number of selectable microstructure types is 3, the corresponding microstructure generation function... A If the values ​​are 1, 2, and 3, then a single grid cell consists of four microstructures, and these four microstructures can be selected independently, resulting in a total of 3 combinations. 4 Considering the choice of mirror / co-directional configuration for the upper and lower segmented elements (2 types), the configuration space of a single-layer mesh is 2. 3 4 The nested mesh is formed by the independent combination of two sets of meshes, an outer layer and an inner layer, and the overall configuration space is expanded to (2). 3 4 ) 2 This significantly improves the design freedom for realizing torque-axial force curves. Simulation results show that nested meshes increase the design space by 88% compared to single-layer meshes. Figure 3 As shown.

[0058] Based on the "parametric modeling—CAD generation—finite element simulation" process described in Part 1, the configuration space is sampled, sample structures are generated in batches, and their response curves are obtained to construct a training dataset. Specifically, the configuration parameters of the outer and inner layers are uniformly encoded into a parameter vector P=[ t out , a out , b out , c out , d out , t in , a in , b in , c in , d in ],in t out , t in ∈{1, 2} represents the discrete configuration type of the outer and inner meshes (1 for unidirectional type, 2 for mirror type), a out , b out , c out ,d out )and( a in , b in , c in , d in ) represents the continuous design variables (corresponding to microstructure geometric parameters) for the four microstructures in the outer and inner layers. For each sample, the axial force curve is extracted within the torsion angle range [-90°, 90°], and the torsion angle is normalized to x ∈[-1, 1], and at the same time, the sample curves are unified to a fixed sampling grid through interpolation. x grid =linspace(-1,1, N x (Preferred) =2000) to form a consistent supervision signal. To improve training stability, the curve output is standardized (subtract the mean and divide the standard deviation), and the dataset is divided into training set, validation set, and test set according to 70%, 15%, and 15% respectively.

[0059] In terms of model construction, DeepONet is used as a surrogate model, such as... Figure 4 As shown, the structural parameter vector P is used as the input to the branch network, and the normalized torsion angle sampling points are used. x grid As input to the backbone network, the operator mapping relationship from structural parameters to the entire axial force curve is learned. Preferably, to enhance the backbone network's ability to represent curve details and nonlinear features, the input... x grid We introduce Fourier feature mapping, with 8 Fourier features, a hidden layer width of 256, and a basis function dimension (output cardinality) of [value missing]. K =128, residual block number is 4. Network training uses mean squared error as the objective function and adopts Adam optimizer for iterative updates, with an initial learning rate of 1×10. -3 A StepLR learning rate decay strategy (step size 40, decay coefficient 0.5) is adopted to improve convergence stability, with a batch size of 64 and 100 training epochs. Furthermore, to reduce the computational burden per iteration and improve generalization ability, a learning rate decay strategy can be implemented for each training sample. N x Randomly selected from each curve sampling point N s Points (preferred) N s=256) participates in the loss calculation, realizing random subsampling training of the curve. After training, the model parameters and the standardized parameters of the curve (mean, standard deviation) are saved. x grid This is used for subsequent reverse optimization design. For example... Figure 5 As shown, the results indicate that the surrogate model training process is stable and converges, and its prediction performance is excellent. R 2 =0.9982).

[0060] The second step is reverse optimization design. After the surrogate model is trained and the network parameters are frozen, reverse optimization design is carried out focusing on the target torque-axial force relationship. For example... Figure 6 As shown, the target curve is first input as discrete target points to obtain a set of target points. ,in x i For normalized torsion angle sampling points, This corresponds to the target axial force value. In this embodiment, we take... {(1.0, -8.0), (0.6667, -7.5), (0.3333, -5.0), (0.0, 0.0), (-0.3333, 6.5), (-0.6667, 14.0), (-1.0, 20.0)} and In the two cases {(1.0, 3.0), (0.75,0.0), (0.5, -1.8), (0.25, -1.0), (0.0, 0.0), (-0.25, -1.0), (-0.5, -1.8), (-0.75, 0.0), (-1.0, 3.0)}, the structural parameter vector described in the previous step is used as the design variable. The discrete configuration variables (outer / inner type) are enumerated using all combinations. For each discrete combination, the remaining continuous variables are randomly initialized within the given feasible interval [0.3, 3.0], and the Adam gradient optimization method is used to minimize the mean squared error loss function at the target point. in For the surrogate model at the target point x i The predicted output is calculated, and the model output is destandardized using the mean and standard deviation saved during the training phase to ensure that the optimization is performed within the physical units. The optimization uses the Adam gradient method to iteratively update continuous variables (in this embodiment, the learning rate is 1×10⁻⁶). -2Each restart iteration has 300 steps. After each parameter update, interval pruning (clamping) is performed on the continuous variables to strictly satisfy the boundary constraints. The optimal solution for the discrete combination is obtained through 5 random restarts. Finally, the solution with the minimum global loss among all the optimal solutions of the discrete combinations is selected as the optimal structure parameter P. The results are [2, 1.981, 2.398, 2.519, 2.498, 1, 2.992, 1.715, 1.359, 1.184] and [1, 0.566, 1.992, 1.559, 0.793, 1, 2.743, 0.988, 1.838, 2.208], which are used for subsequent closed-loop simulation verification and structure generation.

[0061] The third step is closed-loop verification. Based on the optimal structural parameters P obtained in the second step... The reverse design results are then validated and output in a closed-loop manner. Specifically, P is first... Input the trained surrogate model, using a fixed uniform sampling grid during the training phase. x grid Calculate the prediction curve The network output is then denormalized using the mean and standard deviation saved during training to obtain the axial force prediction curve in physical dimensions. Subsequently, predictions are performed again on the target discrete point set, and the mean squared error (MSE) and goodness-of-fit index at the target points are calculated. R 2 Quantifying P The results show that the goodness of fit for approximating the target curve is 0.9999 and 0.9991, indicating excellent optimization results. Figure 7 As shown. At the same time, the comparison results of the global prediction curve and the target discrete points are output to intuitively verify the consistency between the curve shape and key feature points (peaks, inflection points, symmetrical / asymmetrical intervals, etc.).

[0062] Furthermore, to ensure the reliability of the reverse solution results of the surrogate model under the high-fidelity physical model, P Returning to the automated process of Part 1, the corresponding CAD model was regenerated and verified using Abaqus quasi-static simulation, extracting high-fidelity torque-axial force curves. The model is then compared with the target curve and the surrogate prediction curve to calculate indicators such as maximum absolute error and relative error. When the error exceeds the preset tolerance, the verification sample can be added to the dataset and the surrogate model can be updated. The second step of reverse optimization and the verification process of this step are repeated until the target accuracy requirements are met, thus forming a closed-loop design and verification mechanism of "target curve - reverse parameter calculation - simulation verification".

[0063] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A nested mesh structure optimization design method for regulating torque-axial force conversion, characterized in that, Includes the following steps: Step 1, Nested Mesh Structure Design and Simulation Calculation, includes the following sub-steps: S1-1, Parametric geometric modeling of structure: establishing nested mesh structures; S1-2, CAD Model Generation: Based on the structural design parameters modeled in step S1-1, the SolidWorks secondary development interface is used to realize the automated modeling and assembly generation of nested mesh structures. S1-3, Simulation Solution and Data Extraction: Perform numerical simulation analysis on the three-dimensional CAD model generated in step S1-2 to obtain the torsion-axial force conversion curve; Step 2, Torque-Axial Force Relationship Prediction and Inverse Optimization, includes the following sub-steps: S2-1, Proxy Model Training: A proxy model of the torque-axial force relationship is trained using a batch simulation data-driven approach. S2-2, Inverse Optimization Design: A reverse solution strategy combining discrete configuration enumeration and continuous parameter gradient optimization is employed to efficiently inversely determine the optimal structural parameter P based on the target torque-axial force curve. ; S2-3, Closed-loop verification: The optimal structural parameters P... Substitute back to step S1-2, regenerate the CAD model and perform high-fidelity finite element simulation verification, and form an iterative update mechanism through error feedback until the target accuracy requirements are met.

2. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 1, characterized in that, The parametric geometric modeling of the structure in step S1-1 includes the following steps: 1) Establish a parametric model of the nested cylindrical base panel: The nested cylinders are coaxially arranged along the same central axis, including an outer sleeve and an inner sleeve. The diameter of the central circle of the outer sleeve is... D 1. Wall thickness is w 1. The diameter of the center circle of the inner sleeve is D 2. Wall thickness is w 2. The axial height of both the outer sleeve and the inner sleeve is... H Both are coaxial and their end faces are flush; 2) Parametric generation of microstructures: The shape of the centerline of a single microstructure is described by a sine function, used to define the geometric profile of a bending / curved beam. The cross-sectional width of the microstructure is... w 3; Using one microstructure as the basic unit, four microstructures are generated through rotation operations, and connected at the endpoints in a rectangular pattern to form a grid unit. The four microstructures can be set with the same or different geometric parameters. 3) Grid cell array configuration and hierarchical assembly: End caps are respectively installed at the upper and lower axial ends of the outer sleeve and the inner sleeve, with an end cap thickness of [missing information]. h The outer mesh is arranged on the surface area of ​​the outer sleeve and consists of upper and lower mesh units. The upper and lower parts are respectively composed of... n 1× m One grid cell is periodically arranged along the circumferential and axial directions to form a hollow grid structure; the inner grid is arranged in the inner sleeve surface area and consists of upper and lower grid cells, the upper and lower parts being respectively composed of... n 2× m Two grid cells are arranged periodically.

3. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 2, characterized in that, The lower grid cells in the outer grid are arranged in a mirror image or in the same direction as the upper grid cells, and the lower grid cells in the inner grid are arranged in a mirror image or in the same direction as the upper grid cells.

4. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 2, characterized in that, In step S1-2, the specific process of generating the CAD model is as follows: 1) Generate a two-dimensional mesh structure sketch in the unfolded plane based on the geometric parameters and array parameters of the nested mesh structure in step S1-1. The unfolded dimension of the outer cylindrical panel is π. D 1× H The unfolded dimension of the inner cylindrical panel is π. D 2× H ; 2) Perform Boolean operations on the mesh structure on the unfolded plane and the corresponding cylindrical base panel unfolded sketch to obtain the intersecting sketch used to form the hollow area, forming a combined contour, and generating the corresponding panel entity / surface based on the combined contour; 3) By using wrapping or equivalent surface mapping, the unfolded sketch is mapped to the cylindrical surfaces of the outer and inner cylindrical panels to complete the construction of the mesh cutout feature on the cylindrical surface; 4) Based on parameters h The upper and lower end caps are automatically generated and stitched / merged with the cylindrical panel and mesh structure to form a complete three-dimensional nested mesh structure CAD model.

5. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 1, characterized in that, In steps S1-3, the specific process of simulation solution and data extraction is as follows: 1) Import the model into Abaqus / CAE for quasi-static simulation: Import the model into Abaqus / CAE, establish material parameters and set geometric nonlinearities, and perform quasi-static solution using the general static analysis step; set boundary conditions and loading methods: apply full constraints to the lower end face, set a reference point RP on the upper end face and associate the end face with the reference point through motion coupling, and apply a torsional angle in the range of -90° to +90° to the reference point. φ As a displacement-type boundary condition, its axial degree of freedom is constrained; local densification is carried out on the microstructure curved beam, the connection area and the end transition area; 2) Data Extraction: After the simulation is completed, the applied torque is obtained by extracting the reaction torque at the reference point RP through historical output. T The axial force output is obtained by extracting the axial reaction force at the reference point RP. F z , build F z ( φ )as well as F z ( T Curve data.

6. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 1, characterized in that, In step S2-1, the specific process of training the surrogate model is as follows: 1) Unify the configuration parameters of the outer and inner layers into a parameter vector P; 2) Extract the axial force curve for each sample within the torsion angle range [-90°, 90°], and normalize the torsion angle to... x ∈[-1, 1], and the sample curves are unified to a fixed sampling grid through interpolation. x grid =linspace(-1,1, N x ),in, x grid Indicates the sampling points for the normalized torsion angle. N x The number of curve sampling points; the curve output is standardized and divided into training, validation and test sets; 3) Model Construction: A deep operator network is used as the surrogate model, with the structural parameter vector P as the input to the branch network and the normalized torsion angle sampling points as the input. x grid As input to the backbone network; 4) The network training uses mean squared error as the objective function and employs the Adam optimizer for iterative updates. After training, the model parameters and curve standardization parameters are saved. x grid This is used for subsequent reverse optimization design.

7. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 6, characterized in that, The curve standardization parameters include the mean and standard deviation.

8. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 6, characterized in that, In step 1) of step S2-1, the parameter vector P=[ t out , a out , b out , c out , d out , t in , a in , b in , c in , d in ],in t out , t in ∈{1, 2} represents the discrete configuration type of the outer and inner meshes, where 1 is the same orientation type and 2 is the mirror type. a out , b out , c out , d out For the continuous design variables of the four outermost microstructures; a in , b in , c in , d in ) represents the continuous design variables for the four microstructures in the inner layer.

9. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 6, characterized in that, In step 3) of step S2-1, the input... x grid Introduce Fourier feature mapping.

10. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 6, characterized in that, In step 4) of step S2-1, N x Randomly selected from each curve sampling point N s Each point is involved in the loss calculation.

11. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 6, characterized in that, The reverse optimization design in step S2-2 includes the following steps: 1) Input the target curve as a discrete set of target points to obtain the target point set. ,in x i For normalized torsion angle sampling points, This corresponds to the target axial force value; 2) Using the parameter vector P as the design variable, an enumeration strategy is used to traverse all combinations of the discrete configuration variables; 3) For each discrete combination, the continuous variables are randomly initialized within the feasible interval, and the mean squared error loss function at the target point is minimized using the Adam gradient optimization method. The mean and standard deviation saved during the training phase are then de-standardized. 4) After each parameter update, perform interval pruning on the continuous variables, and obtain the optimal solution for the discrete combination by multiple random restarts; 5) Select the solution with the minimum global loss among all discrete combination optimal solutions as the optimal structure parameter P. .

12. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 11, characterized in that, The expression for the mean square error loss function is: ； in, For the surrogate model at the target point x i The predicted output at that point.

13. The nested mesh structure optimization design method for regulating torque-axial force conversion according to claim 1, characterized in that, The closed-loop verification in step S2-3 includes the following steps: 1) P Input the trained surrogate model and calculate the prediction curve. The network output is denormalized according to the mean and standard deviation saved during the training phase to obtain the axial force prediction curve under physical dimensions. 2) In the target discrete point set The prediction is performed again, and the mean square error at the target point and the goodness-of-fit index are calculated. R 2 Output the comparison results between the global prediction curve and the target discrete points; 3) P Returning to step one, the corresponding CAD model is regenerated and verified using Abaqus quasi-static simulation, extracting high-fidelity torque-axial force curves. It is then compared with the target curve and the proxy prediction curve. When the error exceeds the preset tolerance, P is adjusted. Add the corresponding samples to the dataset and update the surrogate model. Then repeat steps S2-2 and S2-3 until the target accuracy requirement is met.

14. A nested mesh structure for regulating torque-axial force conversion, characterized in that, It includes an outer grid and an inner grid. The outer grid is arranged on the surface area of ​​the outer sleeve and consists of upper and lower grid units. The upper and lower parts are respectively composed of... n 1× m One grid cell is periodically arranged along the circumferential and axial directions to form a hollow grid structure; the inner grid is arranged in the inner sleeve surface area and consists of upper and lower grid cells, the upper and lower parts being respectively composed of... n 2× m Two grid cells are arranged periodically; both the outer and inner grids are composed of microstructures; the outer sleeve and the inner sleeve are coaxially nested and their end faces are flush.

15. A nested mesh structure for regulating torque-axial force conversion according to claim 14, characterized in that, The shape of the centerline of a single microstructure is described by a sine function. Using one microstructure as a basic unit, four microstructures are generated through rotation. The four microstructures are connected at their endpoints in a rectangular pattern to form a single grid unit.

16. A nested mesh structure for regulating torque-axial force conversion according to claim 14, characterized in that, The lower grid cells in the outer grid are arranged in a mirror image or in the same direction as the upper grid cells, and the lower grid cells in the inner grid are arranged in a mirror image or in the same direction as the upper grid cells.

17. A nested mesh structure for regulating torque-axial force conversion according to claim 14, characterized in that, The geometric parameters of the four microstructures that make up a single grid cell can be set to be the same or different to achieve asymmetry within the cell and programmable mechanical response.

18. A nested mesh structure for regulating torque-axial force conversion according to claim 14, characterized in that, The central circle diameter of the outer sleeve is D 1. Wall thickness is w 1. The diameter of the center circle of the inner sleeve is D 2. Wall thickness is w 2. The axial height of both the outer sleeve and the inner sleeve is... H Both are coaxial and their end faces are flush.

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