Topological optimization and additive manufacturing integrated system for lightweight mechanical structure

Abstract

The invention relates to the technical field of machine manufacturing, in particular to a lightweight mechanical structure topological optimization and additive manufacturing integrated system which comprises a structure topological optimization module, a finite element simulation module, a process parameter calculation module, a production and manufacturing module and a printing quality monitoring module. The process parameter calculation module establishes a mapping relation between a material space and a structure space based on a differential geometry theory, comprises a differential geometry characterization unit, a thermal deformation prediction and compensation unit and a process parameter mapping and optimization unit, realizes accurate conversion from a design domain to a manufacturing domain, and realizes accurate conversion from the design domain to the manufacturing domain through a curvature-driven thermal deformation compensation method. Active compensation of thermal deformation is realized from the geometric nature of the structure; a thermal-mechanical coupling process parameter self-adaptive control system under multi-manifold cross constraint is adopted, real-time monitoring and parameter adjustment in the manufacturing process are achieved, the problem that an existing topological optimization result is difficult to be directly applied to additive manufacturing is solved, and the manufacturing precision and the mechanical property of a lightweight mechanical structure are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical manufacturing, in particular to a lightweight mechanical structure topology optimization and additive manufacturing integrated system, which deeply integrates structural design optimization and additive manufacturing process, and realizes full-process digital control from structural design to manufacturing processing. BACKGROUND

[0002] With the increasing demand for lightweight structures in high-end manufacturing industries such as aerospace and automotive industries, topology optimization, as an important means to achieve lightweight structures, has been widely used in various mechanical structure designs. At the same time, additive manufacturing (3D printing) technology is becoming an ideal means to realize lightweight structure manufacturing due to its advantages of being able to manufacture complex structures, reducing assembly links, and shortening manufacturing cycle.

[0003] However, there is a clear technical gap between topology optimization and additive manufacturing. The traditional topology optimization process mainly focuses on structural mechanical properties, often ignoring manufacturing constraints such as thermal deformation and material property changes in the additive manufacturing process. The additive manufacturing process lacks feedback adjustment mechanisms for structural characteristics. This "design-manufacturing" separation mode makes it difficult to directly apply topology optimization results to additive manufacturing, and it is difficult to ensure manufacturing precision and structural performance, which seriously restricts the widespread application of lightweight structures.

[0004] In addition, the problem of thermal deformation in the additive manufacturing process has always been a key factor affecting manufacturing precision. Existing technologies mostly use empirical compensation or post-correction methods, lack active compensation mechanisms based on structural essential characteristics, and have limited compensation effect and poor adaptability.

[0005] Therefore, there is an urgent need for an integrated system that deeply integrates topology optimization and additive manufacturing, realizes full-process intelligent control from structural optimization to manufacturing processing, and improves the manufacturing precision and mechanical properties of lightweight structures. SUMMARY

[0006] The purpose of the present application is to provide a lightweight mechanical structure topology optimization and additive manufacturing integrated system, which establishes a bidirectional mapping relationship between topology optimization and additive manufacturing, realizes accurate conversion from the design domain to the manufacturing domain, solves the problem that topology optimization results are difficult to directly apply to additive manufacturing in the prior art, and improves the manufacturing precision and performance stability of lightweight structures.

[0007] The present application provides a lightweight mechanical structure topology optimization and additive manufacturing integrated system, which comprises:

[0008] A structural topology optimization module for topology optimization of a mechanical structure and generating an optimized structure scheme;

[0009] A finite element simulation module connected with the structure topology optimization module, used for performing mechanical performance analysis on the optimized structure scheme;

[0010] A process parameter calculation module connected with the structure topology optimization module and the finite element simulation module, the process parameter calculation module comprising:

[0011] A differential geometry representation unit used for constructing material space manifold and structure space manifold, and establishing mapping relationship between the two manifolds;

[0012] A thermal deformation prediction and compensation unit used for predicting thermal deformation trend based on structure curvature characteristics and generating compensation strategy;

[0013] A process parameter mapping and optimization unit used for generating optimal process parameters under multi-manifold intersection constraint;

[0014] A production manufacturing module connected with the process parameter calculation module, used for implementing additive manufacturing according to the process parameters;

[0015] A printing quality monitoring module connected with the production manufacturing module and the process parameter calculation module, used for monitoring manufacturing process and feeding monitoring data back to the process parameter calculation module.

[0016] As preferred, the structure topology optimization module comprises:

[0017] A structure parameter and manufacturing constraint input sub-module used for inputting structure material composition, structure load distribution, structure boundary condition and manufacturing constraint;

[0018] A topology optimization sub-module used for performing topology optimization calculation according to the structure parameters and manufacturing constraints;

[0019] A structure improvement sub-module used for performing manufacturability improvement on the topology optimization result;

[0020] A material selection sub-module used for selecting adaptive material according to the topology optimization result;

[0021] A performance evaluation sub-module used for evaluating mechanical performance of the mechanical structure;

[0022] An optimization scheme acquisition sub-module used for outputting final optimization scheme and process parameters.

[0023] As preferred, the differential geometry representation unit comprises:

[0024] A material space manifold construction component used for defining material space containing parameters such as density, strength and thermal conductivity, and introducing Riemann metric on the material space;

[0025] A structural space manifold construction component is configured to define a structural space including geometric shapes, topological connections and performance indicators, and introduce a Riemannian metric of the structural space.

[0026] A manifold mapping establishment component is configured to construct a mapping function from a material space to a structural space, and optimize the mapping relationship by a variational functional.

[0027] Preferably, the thermal distortion prediction and compensation unit comprises:

[0028] A thermal distortion-curvature relationship modeling component is configured to analyze the Gaussian curvature and mean curvature distribution of the structural surface, and establish a mapping relationship between the thermal distortion and the curvature.

[0029] A curvature-driven structure optimization component is configured to design a structural surface morphology evolution strategy based on the curvature distribution.

[0030] A thermal distortion prediction and compensation component is configured to predict a temperature field distribution based on the thermal analysis result, calculate the curvature change caused by the temperature field, and generate an active compensation scheme.

[0031] Preferably, the process parameter mapping and optimization unit comprises:

[0032] A multi-manifold space construction component is configured to define a thermal field manifold, a force field manifold and a process parameter manifold.

[0033] A cross-constraint measure space component is configured to define a cross measure between manifolds, and quantify the mutual influence between different parameters.

[0034] A geodesic parameter optimization component is configured to construct an energy functional in the parameter space and derive an optimal parameter trajectory.

[0035] An adaptive control component is configured to construct an error manifold based on real-time monitoring data, and calculate a parameter adjustment strategy.

[0036] Preferably, the finite element simulation module comprises:

[0037] A data input sub-module is configured to generate a finite element grid model and boundary conditions according to the optimized structure scheme.

[0038] A finite element simulation sub-module is configured to calculate stress distribution parameters and deformation distribution parameters of the structure.

[0039] A performance feedback sub-module is configured to generate mechanical structure performance parameters according to the finite element analysis result, and feed the performance parameters back to the structure topology optimization module and the process parameter calculation module.

[0040] Preferably, the production and manufacturing module comprises:

[0041] An optimization scheme input sub-module is configured to receive the mechanical structure parameters from the structure topology optimization module and the process parameters from the process parameter calculation module;

[0042] A manufacturing method selection sub-module is configured to select a manufacturing scheme according to the mechanical structure parameters and the process parameters;

[0043] An additive manufacturing sub-module is configured to perform additive manufacturing when the manufacturing scheme is additive manufacturing;

[0044] A subtractive manufacturing sub-module is configured to perform subtractive manufacturing when the manufacturing scheme is subtractive manufacturing;

[0045] An additive-subtractive hybrid manufacturing sub-module is configured to perform additive-subtractive hybrid manufacturing when the manufacturing scheme is hybrid manufacturing.

[0046] Preferably, the printing quality monitoring module comprises:

[0047] A material performance calculation sub-module is configured to calculate the material variation law and the material parameters after thermal deformation compensation during the manufacturing process according to the process parameters;

[0048] A printing process monitoring sub-module is configured to monitor the manufacturing process and obtain monitoring data, calculate the deviation from the expected state according to the monitoring data, and feed back the deviation to the process parameter calculation module for parameter adjustment.

[0049] Preferably, the parameter adjustment strategy adopted by the adaptive control assembly comprises:

[0050] An energy input control strategy is configured to dynamically adjust the energy density based on the material state tensor;

[0051] A scanning path planning strategy is configured to generate an adaptive scanning path based on the structure curvature distribution;

[0052] A printing speed regulation strategy is configured to dynamically adjust the printing speed based on the thermal gradient;

[0053] A material supply management strategy is configured to dynamically adjust the material supply rate based on the cross-sectional features.

[0054] Preferably, the data flow conversion mechanism established between the differential geometry characterization unit, the thermal deformation prediction and compensation unit, and the process parameter mapping and optimization unit comprises:

[0055] The differential geometry characterization unit transmits the material-structure mapping relationship and the curvature distribution data to the thermal deformation prediction and compensation unit;

[0056] The thermal deformation prediction and compensation unit transmits the predicted deformation field and the compensation strategy to the process parameter mapping and optimization unit;

[0057] The process parameter mapping and optimization unit delivers parameter optimization feedback information to the differential geometry characterization unit and the thermal deformation prediction and compensation unit.

[0058] The beneficial effects of the present application include:

[0059] 1. Through the material-structure mapping theory based on differential geometry, a multi-scale mapping mechanism from material micro characteristics to structure macro performance is established, breaking through the limitations of traditional linear mapping, which can accurately describe the nonlinear material behavior in the additive manufacturing process, and improve the accuracy of structure performance prediction;

[0060] 2. Through the curvature-driven thermal deformation compensation method, active compensation of thermal deformation is realized from the geometric essence of the structure, and compared with the traditional empirical compensation method, the manufacturing precision is improved by 45%-60%, especially in complex curved surface structures;

[0061] 3. Through the thermal-mechanical coupling process parameter adaptive control system under the constraint of multi-manifold intersection, real-time monitoring and parameter adjustment of the manufacturing process are realized, which improves the manufacturing process stability by more than 50%, and significantly reduces the waste rate;

[0062] 4. Through the cooperative work of each functional module, closed-loop control from design to manufacturing is realized, which improves the structure mechanical performance by 30%-40% while maintaining lightweight, especially in anisotropic material application scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 It is the overall architecture schematic diagram of the lightweight mechanical structure topology optimization and additive manufacturing integrated system of the present application;

[0064] Figure 2 It is the functional architecture schematic diagram of the structure topology optimization module of the present application;

[0065] Figure 3 It is the functional architecture schematic diagram of the process parameter calculation module of the present application;

[0066] Figure 4 It is the working flow schematic diagram of the differential geometry characterization unit of the present application;

[0067] Figure 5 It is the working flow schematic diagram of the thermal deformation prediction and compensation unit of the present application;

[0068] Figure 6 It is the working flow schematic diagram of the process parameter mapping and optimization unit of the present application;

[0069] Figure 7 It is the system data flow process schematic diagram of the present application. DETAILED DESCRIPTION

[0070] Reference is made to Figures 1-7 The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0071] Reference is made to Figure 1 The lightweight mechanical structure topology optimization and additive manufacturing integrated system provided by the present application comprises a structure topology optimization module 1, a finite element simulation module 2, a process parameter calculation module 3, a production manufacturing module 4 and a printing quality monitoring module 5.

[0072] The structure topology optimization module 1 is used for topology optimization of the mechanical structure and generates an optimized structure scheme. The finite element simulation module 2 is connected with the structure topology optimization module 1 and is used for mechanical performance analysis of the optimized structure scheme. The process parameter calculation module 3 is connected with the structure topology optimization module 1 and the finite element simulation module 2 and is used for generating optimal process parameters based on the theory of differential geometry. The production manufacturing module 4 is connected with the process parameter calculation module 3 and is used for implementing additive manufacturing according to the process parameters. The printing quality monitoring module 5 is connected with the production manufacturing module 4 and the process parameter calculation module 3 and is used for monitoring the manufacturing process and feeding back the monitoring data to the process parameter calculation module 3.

[0073] The various modules of the present application will be described in detail below:

[0074] Reference is made to Figure 2 The structure topology optimization module 1 comprises a structure parameter and manufacturing constraint input submodule 11, a topology optimization submodule 12, a structure improvement submodule 13, a material selection submodule 14, a performance evaluation submodule 15 and an optimized scheme acquisition submodule 16.

[0075] The structure parameter and manufacturing constraint input submodule 11 is used for inputting structure material composition, structure load distribution, structure boundary conditions and manufacturing constraints. In a preferred embodiment of the present application, the input structure parameters include material characteristic parameters such as material density, elastic modulus and Poisson's ratio, as well as information such as the geometric boundary of the structure, load distribution and support position. The manufacturing constraints include minimum wall thickness constraints (usually set to 0.8mm-1.5mm, depending on the precision of the additive manufacturing equipment used), maximum overhang angle constraints (usually 45°), minimum feature size constraints and other manufacturability-related limitations.

[0076] The topology optimization submodule 12 is used for topology optimization calculation according to the structure parameters and manufacturing constraints. In the present application, the variable density method combined with the moving asymptote algorithm is preferably used for topology optimization, and the optimization objective is to minimize the structure mass under the given constraint conditions. Specifically, the mathematical model of topology optimization can be expressed as:

[0077]

[0078] ,

[0079] wherein: is the relative density at the design domain point ranging from 0 to 1 ; is the design domain; is the maximum volume fraction allowed, usually set as 30%-50% of the original volume; and are the maximum stress and allowable stress, respectively; and are the maximum displacement and allowable displacement, respectively. is usually set as 0.001 to avoid singularity problems in numerical calculation. The structure improvement submodule 13 is used to improve the manufacturability of the topology optimization result. This submodule mainly solves the common "checkerboard" phenomenon, discontinuous structure and non-compliance with manufacturing constraints in the direct result of topology optimization. Preferably, the density filtering and projection method combined with sensitivity analysis are used for structure improvement to ensure that the final structure meets the process requirements of additive manufacturing.

[0080] The material selection submodule 14 is used to select the appropriate material according to the topology optimization result. In the preferred embodiment of the present application, this submodule selects the most suitable material from the pre-set material library based on the mechanical requirements and thermal deformation characteristics of the structure. The material library includes common metal materials (such as aluminum alloy, titanium alloy, stainless steel, etc.), polymer materials and composite materials, and each material is recorded with detailed physical and mechanical performance parameters.

[0081] The performance evaluation submodule 15 is used to evaluate the mechanical performance of the mechanical structure. This submodule combines the optimized structure with the characteristics of the selected material, uses the finite element analysis method to evaluate the performance indicators of the structure in terms of static load, dynamic response, thermal deformation, etc. The performance evaluation result will be used as the basis for judging whether the structure needs further optimization.

[0082] The optimization scheme acquisition submodule 16 is used to output the final optimization scheme and process parameters. When the structure performance meets the design requirements, this submodule will generate a structure model file in a standard format (such as STL, STEP, etc.) and preliminary process parameter suggestions to provide basic data for the subsequent manufacturing process.

[0083] Referring to

[0084] , the finite element simulation module 2 includes a data input submodule 21, a finite element simulation submodule 22 and a performance feedback submodule 23. Figure 1

[0085] ​The data input sub-module 21 is configured to generate a finite element mesh model and boundary conditions according to the optimized structural scheme. In the preferred embodiment of the present application, an adaptive meshing technique is adopted to automatically refine the mesh in regions with complex geometric features (such as thin-walled, sharp corners, transition regions, etc.), thereby improving the analysis accuracy. For the thin-walled regions typical of lightweight structures, the mesh size is usually set to 1 / 3 to 1 / 5 of the wall thickness, ensuring the calculation accuracy.

[0086] The finite element simulation sub-module 22 is configured to calculate the stress distribution parameters and deformation distribution parameters of the structure. This sub-module supports multiple analysis types such as statics analysis, modal analysis, thermal analysis, and thermal-mechanical coupling analysis. Preferably, for additive manufacturing processes, the focus is on thermal-mechanical coupling analysis to predict the temperature field distribution, thermal stress distribution, and resulting deformation field during the manufacturing process.

[0087] The performance feedback sub-module 23 is configured to generate mechanical structure performance parameters based on the finite element analysis results and feed the performance parameters back to the structural topology optimization module 1 and the process parameter calculation module 3. The performance parameters include but are not limited to: maximum stress (accurate to MPa), stress distribution uniformity (represented by standard deviation), maximum deformation (accurate to pm), deformation distribution, natural frequency (accurate to Hz), etc. These parameters will serve as the basis for optimization iteration and process parameter adjustment.

[0088] The process parameter calculation module 3 is the core innovative part of the present application, which establishes an accurate mapping between the topology optimization results and the additive manufacturing process parameters based on the theoretical framework of differential geometry, realizing seamless conversion from the design domain to the manufacturing domain. As shown in Figure 3 , this module includes a differential geometry characterization unit 31, a thermal deformation prediction and compensation unit 32, and a process parameter mapping and optimization unit 33.

[0089] The differential geometry characterization unit 31 is the basic component of the process parameter calculation module 3, which is configured to construct the material space manifold and the structure space manifold, and establish the mapping relationship between the two manifolds. Referring to Figure 4 , this unit includes a material space manifold construction component 311, a structure space manifold construction component 312, and a manifold mapping establishment component 313.

[0090] The material space manifold construction component 311 is configured to define a material space containing parameters such as density, strength, and thermal conductivity, and introduce a Riemannian metric on the material space. In the preferred embodiment of the present application, the material space is defined as a multi-dimensional parameter space M, whose coordinates represent the physical and mechanical properties of the material. For metal additive manufacturing, typical material parameters include density p (usually 2.7-8.0 g / cm³), elastic modulus E (usually 70-210 GPa), thermal conductivity k (usually 15-400 W / (m·K)), thermal expansion coefficient a (usually 10-25 x 10⁻6 (e.g., / K)

[0091] To describe the interaction relationships between material parameters, a Riemannian metric is introduced in the material space M. This metric defines the concepts of "distance" and "angle" in material space. Metric matrix The construction is based on the correlation analysis between material parameters, and can be expressed as:

[0092] ,

[0093] in: To measure the components of the tensor, the relationship between the i-th parameter and the j-th parameter in the material space is represented; These are structural performance indicators (such as strength, stiffness, etc.), representing the mechanical response of the structure. , These are material parameters, such as density and elastic modulus. The weighting coefficients reflect the importance of different performance indicators and are usually determined according to the specific application scenario. For example, in load-bearing structures, the weight of the strength indicator can be set to 0.6, the weight of the stiffness indicator can be set to 0.3, and the weight of the thermal deformation indicator can be set to 0.1. This indicates the performance metrics considered. Perform summation.

[0094] The structural space manifold building component 312 is used to define a structural space containing geometry, topological connections, and performance indicators, and introduces a Riemannian metric for the structural space. The structural space S is a multidimensional space describing the geometry and performance characteristics of the structure, and its coordinates represent the morphological features and performance indicators of the structure. In this invention, particular attention is paid to the curvature characteristics of the structural surface, and Gaussian curvature is introduced. and mean curvature As a key parameter characterizing structural morphology.

[0095] In structural space Introducing Riemannian metrics This metric matrix, used to describe the coupling relationship between structural parameters, can be represented as:

[0096] .

[0097] in: The metric tensor components in the structure space represent the structure parameters. and parameters The relationship between them; These are structural response indicators (such as displacement, stress, etc.), representing the behavior of a structure under external loads. , These are structural parameters, such as geometric dimensions and shape characteristics; is the weight coefficient, reflecting the importance of different structural response indicators, for example, for structures requiring high precision, the displacement index weight can be set to 0.7, and the stress index weight can be set to 0.3; represents all the considered structural response indicators are summed up.

[0098] The manifold mapping establishment component 313 is used to construct a mapping function from the material space to the structure space, and optimize the mapping relationship through a variational functional. The component establishes a mapping function between material properties and structural performance , which maps a point in the material space to a corresponding point in the structure space.

[0099] To optimize the mapping relationship, a variational functional is constructed , representing the "energy" of the mapping, and the ideal mapping should minimize this energy:

[0100] ,

[0101] wherein: is the energy functional of the mapping , used to evaluate the goodness of the mapping; is the stretching energy, representing the stretching deformation of the material space caused by the mapping, with the unit of J; is the bending energy, representing the bending deformation of the material space caused by the mapping, with the unit of J; is the distortion energy, representing the distortion deformation of the material space caused by the mapping, with the unit of J; , , is the weight coefficient, usually set to , , , which can be adjusted according to specific application requirements; represents the integration over the entire material space ; is the volume element in the material space.

[0102] The optimal mapping function is solved by numerical optimization methods (such as gradient descent method, conjugate gradient method, etc.), establishing an accurate correspondence between material properties and structural performance.

[0103] The thermal deformation prediction and compensation unit 32 is a key component for solving the problem of thermal deformation in the additive manufacturing process. It realizes accurate prediction and active compensation of thermal deformation by analyzing the internal relationship between structural curvature characteristics and thermal deformation. Referring to Figure 5 , the unit includes a thermal deformation-curvature relationship modeling component 321, a curvature-driven structure optimization component 322, and a thermal deformation prediction and compensation component 323.

[0104] The thermal deformation-curvature modeling component 321 is used to analyze the Gaussian curvature and mean curvature distribution of the structure surface, and to establish the mapping relationship between thermal deformation and curvature. In the present application, it is found that the thermal deformation mode of a structure has a close relationship with its curvature distribution, especially for thin-walled structures, this relationship is more significant.

[0105] The Gaussian curvature of the structure surface and the mean curvature are defined respectively as:

[0106] , ,

[0107] wherein: is the Gaussian curvature, representing the intrinsic geometric property of the surface, with the unit of ; is the mean curvature, representing the extrinsic geometric property of the surface, with the unit of ; and are the principal curvatures, representing the bending degree of the surface along two orthogonal principal directions at a point, with the unit of .

[0108] The mapping relationship between thermal deformation and curvature can be expressed as:

[0109] ,

[0110] wherein: is the deformation vector at point , representing the displacement caused by thermal deformation, with the unit of ; and are the Gaussian curvature and the mean curvature at point respectively; is the temperature field, representing the temperature at point , with the unit of ; is the temperature gradient, representing the spatial variation rate of the temperature field, with the unit of ; is the mapping function, representing the relationship between curvature, temperature and deformation.

[0111] In practical applications, this mapping relationship is obtained through finite element analysis and experimental data fitting. For a typical metal additive manufacturing process, the relationship between thermal deformation and curvature can be approximated as:

[0112] ,

[0113] wherein: is the deformation at point , with the unit of ; to is the fitting coefficient, obtained by fitting the experimental data and the finite element analysis results; is the average curvature, unit is ; is the Gaussian curvature, unit is ; is the modulus of temperature gradient, unit is . For typical aluminum alloy structures, the reference values of these coefficients are: , , , , , , (unit corresponds to each term).

[0114] The curvature-driven structure optimization component 322 is used to design the structure surface morphology evolution strategy based on the curvature distribution. Based on the mapping relationship between thermal deformation and curvature, the curvature distribution of the structure is adjusted to achieve active control of thermal deformation.

[0115] To achieve this goal, a curvature flow equation is designed to describe the evolution of the structure surface morphology:

[0116] ,

[0117] wherein: represents the change rate of the structure surface with the evolution parameter , describing the evolution process of the surface morphology; is the surface gradient operator, representing the gradient calculated on the surface; is the curvature-based energy functional, representing the good or bad degree of the surface morphology; is the Gaussian curvature; is the average curvature.

[0118] The energy functional is defined as:

[0119] ,

[0120] wherein: is the energy functional, used to evaluate the good or bad degree of the surface morphology; and are the target average curvature and Gaussian curvature, respectively, obtained by reverse calculation from the thermal deformation prediction results; and are the weight coefficients, usually set to , , reflecting the relative importance of the average curvature and the Gaussian curvature in the thermal deformation control; represents the surface of the entire structure is integrated over the surface of the structure; is the area element on the surface.

[0121] The thermal distortion prediction and compensation component 323 is used to predict the temperature field distribution based on the thermal analysis results, calculate the curvature change caused by the temperature field, and generate an active compensation scheme. This component first predicts the temperature field distribution during the manufacturing process based on the thermal analysis results of the additive manufacturing process:

[0122] ,

[0123] where: is the temperature at point at time , in C; is the ambient temperature (usually 20-25 C), in C; is the temperature rise caused by the manufacturing process, in C, obtained by thermal analysis simulation.

[0124] Then, according to the temperature field prediction results, the curvature change caused by the temperature is calculated:

[0125] .

[0126] .

[0127] where: and are the changes in Gaussian curvature and mean curvature, respectively, in and ; is the temperature change, in ; is the modulus of the temperature gradient, in ; to are material-related coefficients, for aluminum alloy, typical values are , , , (the units correspond to each term).

[0128] Finally, the reverse curvature adjustment scheme is generated to achieve pre-compensation for thermal distortion:

[0129] ,

[0130] ,

[0131] where: and is the compensated curvature distribution, units are and ; and is the original curvature distribution, units are and ; and is the curvature variation, units are and ; and is the compensation coefficient, usually set as , , slightly larger than to consider the material nonlinear behavior.

[0132] The process parameter mapping and optimization unit 33 is a key component to convert design requirements into specific process parameters. It realizes the collaborative optimization of thermal field, force field and process parameters by establishing a multi-manifold cross-constrained framework. Referring to Figure 6 , this unit includes a multi-manifold space construction component 331, a cross-constrained measure space component 332, a geodesic parameter optimization component 333 and an adaptive control component 334.

[0133] The multi-manifold space construction component 331 is used to define the thermal field manifold, the force field manifold and the process parameter manifold. This component regards the thermal field, the force field and the process parameters in the additive manufacturing process as different manifold spaces respectively, and establishes their mathematical descriptions.

[0134] The thermal field manifold T describes the temperature distribution and thermal flow dynamics, and its points represent different temperature field configurations. The force field manifold F represents the stress distribution and deformation state, and its points represent different force field configurations. The process parameter manifold P contains energy input, scanning speed, path and other parameters, and its points represent different parameter configurations.

[0135] Appropriate measures are introduced on these manifolds, for example, on the process parameter manifold, the measure can be defined as:

[0136] ,

[0137] where: is the measure between points and on the process parameter manifold, representing their "distance"; and are two points on the process parameter manifold, representing two different parameter configurations; and are the first and second derivatives of the measure function at point and point , respectively. one coordinate component represents a specific process parameter (e.g. laser power, scanning speed, etc.); is a weight matrix, reflecting the relative importance of different parameters; represents the summation over all parameter combinations.

[0138] The cross-constrained measure space component 332 is used to define the cross measure between manifolds, quantifying the mutual influence between different parameters. This component constructs the cross measure , which is a probabilistic measure describing the correspondence between points on different manifolds.

[0139] Specifically, the cross measure can be represented as a joint probability distribution:

[0140] ,

[0141] where: is the cross measure, representing the probability density of the thermal field state , the force field state , and the process parameter ; is a point on the thermal field manifold , representing a specific temperature field configuration; is a point on the force field manifold , representing a specific force field configuration; is a point on the process parameter manifold , representing a specific parameter configuration; represents the probability; , , represent the infinitesimal regions on the corresponding manifolds, respectively.

[0142] Based on the cross measure, the entropy function is defined to characterize the uncertainty of the system:

[0143] ,

[0144] where: is the entropy function, quantifying the uncertainty of the system, with the unit of bits (bit); is the cross measure; represents the natural logarithm; represents the integration over the Cartesian product of the three manifold spaces.

[0145] The geodesic parameter optimization component 333 is used to construct an energy functional in the parameter space and derive the optimal parameter trajectory. This component constructs an energy functional characterizing the goodness of the parameter trajectory: where: For energy functionals, evaluate parameter trajectories The degree of superiority or inferiority, expressed in J; For curves in parameter space, These are the parameters of the curve; The kinetic energy term of the curve is a measure on the manifold using process parameters. Calculation, representing the "rate" of parameter change; This is the potential energy term, representing the quality of the parameter configuration; the smaller the value, the better the configuration. Indicates in the parameter Integrate within the range of 0 to 1.

[0146] The Euler-Lagrange equation is derived using the variational method to describe the optimal parameter trajectory.

[0147] ,

[0148] in: For parameters Regarding curve parameters The second derivative of represents the acceleration of the parameter; The Christopher notation represents the connection coefficient of the process parameter manifold, describing the local geometric properties of the surface; and For parameters and about The first derivative of represents the rate of change of the parameter; For measuring tensors The reverse; Potential energy Regarding parameters The partial derivative of represents the gradient of the potential energy field.

[0149] The adaptive control component 334 is used to construct an error manifold based on real-time monitoring data and calculate parameter adjustment strategies. This component first constructs the error manifold based on the real-time monitoring data. , indicating the deviation between the actual state and the expected state:

[0150] ,

[0151] in: For a moment The error vector represents the deviation between the actual state and the expected state; This refers to the actual state, including monitoring parameters such as temperature and deformation; The expected state is the ideal parameter value predicted by the model.

[0152] Then, the geodesic line is calculated on the error manifold to determine the optimal correction direction:

[0153] ,

[0154] where: is the error component of the second order derivative with respect to time ; is the Christoffel symbol on the error manifold; and is the error component and of the first order derivative with respect to time .

[0155] Finally, based on the calculation results of the geodesic line, the parameter adjustment strategy is generated:

[0156] ,

[0157] where is the parameter adjustment amount, indicating the correction needed for the process parameters; is the step coefficient, usually set to 0.1-0.5, which can be dynamically adjusted according to the error size; is the error gradient with respect to the parameter, indicating the sensitivity of the error to the parameter change.

[0158] The production and manufacturing module 4 is an execution unit for implementing additive manufacturing, referring to Figure 1 , which includes an optimization scheme input submodule 41, a manufacturing method selection submodule 42, an additive manufacturing submodule 43, a subtractive manufacturing submodule 44, and an additive-subtractive hybrid manufacturing submodule 45.

[0159] The optimization scheme input submodule 41 is used to receive the mechanical structure parameters from the structural topology optimization module 1 and the process parameters from the process parameter calculation module 3. This submodule parses and preprocesses the structural geometric data (usually in STL format) and process parameters (including energy input, scanning speed, scanning path, etc.) to prepare for the subsequent manufacturing process.

[0160] The manufacturing method selection submodule 42 is used to select the manufacturing scheme according to the mechanical structure parameters and process parameters. According to the complexity of the structure, the precision requirement and the material characteristics, this submodule intelligently selects the most suitable manufacturing method. Generally, for high-complexity lightweight structures, additive manufacturing is preferred; for functional surfaces that require high surface quality, additive-subtractive hybrid manufacturing may be selected.

[0161] The additive manufacturing submodule 43 is used to perform additive manufacturing when the manufacturing scheme is additive manufacturing. This submodule supports multiple additive manufacturing technologies, including selective laser melting (SLM), electron beam melting (EBM), laser stereolithography (LSF), etc. According to the parameters provided by the process parameter calculation module 3, the power, scanning speed and path of the energy source (such as laser, electron beam) and the supply rate of the powder / silica are controlled to achieve high-precision additive manufacturing.

[0162] The subtractive manufacturing submodule 44 is used to perform subtractive manufacturing when the manufacturing scheme is subtractive manufacturing. This submodule is mainly used to manufacture parts with high manufacturing precision requirements and relatively simple structures, or as a finishing step after additive manufacturing.

[0163] The additive-subtractive hybrid manufacturing submodule 45 is used to perform additive-subtractive hybrid manufacturing when the manufacturing scheme is hybrid manufacturing. This hybrid manufacturing method combines the complex structure forming capability of additive manufacturing and the high precision characteristics of subtractive manufacturing, and is suitable for parts that require both complex internal structure and high surface quality.

[0164] The print quality monitoring module 5 is a key component to ensure manufacturing quality, as described in Figure 1 , which includes a material performance calculation submodule 51 and a print process monitoring submodule 52.

[0165] The material performance calculation submodule 51 is used to calculate the material variation law and material parameters after thermal deformation compensation during the manufacturing process according to the process parameters. Based on the principles of material science and thermodynamics, this submodule combines real-time process parameters to predict the microstructure, mechanical properties and geometric deformation of the material during additive manufacturing. For example, for metal additive manufacturing, this submodule can predict the microstructure, phase composition, residual stress and other microscopic properties, as well as the resulting changes in macroscopic mechanical properties.

[0166] The print process monitoring submodule 52 is used to monitor the manufacturing process and obtain monitoring data, calculate the deviation from the expected state according to the monitoring data, and feed the deviation back to the process parameter calculation module 3 for parameter adjustment. This submodule monitors key parameters in the printing process in real time through various sensors (such as infrared cameras, high-speed cameras, force sensors, etc.), including melt pool size (usually 0.1-0.5mm), temperature distribution (metal materials usually 1400-1600°C), cooling rate (usually 10 5 °C / s), etc. After processing the monitoring data, the deviation from the expected state is calculated to form a closed-loop control system.

[0167] Referring to Figure 7 , the data flow and collaborative work process between the modules in the system are as follows:

[0168] Firstly, the structure topology optimization module 1 receives the structure parameters and manufacturing constraints input by the user, performs topology optimization calculation, and generates a preliminary optimized structure scheme.

[0169] Then, the finite element simulation module 2 receives the optimized structure scheme, establishes a finite element model, performs mechanical performance analysis, and feeds back the analysis results to the structure topology optimization module 1 and the process parameter calculation module 3.

[0170] Next, the process parameter calculation module 3, based on the optimized structure scheme and the finite element analysis results, applies differential geometry theory to construct the material-structure mapping relationship, predicts the thermal deformation trend and generates compensation strategies, and optimizes the process parameter configuration. Among them, the differential geometry representation unit 31 transmits the material-structure mapping relationship and curvature distribution data to the thermal deformation prediction and compensation unit 32; the thermal deformation prediction and compensation unit 32 transmits the predicted deformation field and compensation strategies to the process parameter mapping and optimization unit 33; the process parameter mapping and optimization unit 33 transmits parameter optimization feedback information to the differential geometry representation unit 31 and the thermal deformation prediction and compensation unit 32.

[0171] Subsequently, the production manufacturing module 4 receives the optimized structure scheme and process parameters, selects the appropriate manufacturing method, and executes the additive manufacturing or hybrid manufacturing process.

[0172] Finally, the printing quality monitoring module 5 monitors the manufacturing process in real time, obtains monitoring data, calculates the deviation from the expected state, and feeds back the deviation to the process parameter calculation module 3, forming a closed-loop control system.

[0173] The application effect of the system of the present application is illustrated by a specific embodiment as follows.

[0174] An aircraft engine support needs to be designed and manufactured for lightweight. The support is a typical load-bearing structure, and the original design weight is 2.5 kg, and the material is TC4 titanium alloy. The process of lightweight design and manufacturing using the system of the present application is as follows:

[0175] Firstly, in the structure topology optimization module 1, the structure parameters (including geometric boundaries, load conditions, support positions, etc.) and manufacturing constraints (minimum wall thickness of 1.2 mm, maximum overhang angle of 45°) of the support are input. Through topology optimization calculation, an optimized structure scheme with a volume reduction of 42% is obtained.

[0176] Then, in the finite element simulation module 2, statics analysis and modal analysis are performed on the optimized structure scheme to verify that it meets the strength requirement (maximum stress of 685 MPa, less than the material yield strength of 950 MPa) and stiffness requirement (maximum deformation of 0.28 mm, less than the allowable deformation of 0.5 mm).

[0177] Then, in the process parameter calculation module 3, the differential geometry characterization unit 31 establishes the mapping relationship between the TC4 titanium alloy material characteristics and the bracket structure performance. Through the thermal deformation prediction and compensation unit 32, the curvature distribution of the bracket surface is analyzed, the thermal deformation trend (the maximum deformation is expected to be 0.35mm) is predicted, and the compensation strategy is generated. The process parameter mapping and optimization unit 33 optimizes the process parameter configuration under the multi-manifold intersection constraint framework, including laser power (180W), scanning speed (900mm / s), scanning path (adaptive path based on curvature), etc.

[0178] Subsequently, in the production and manufacturing module 4, the selective laser melting (SLM) technology is selected for manufacturing. During the manufacturing process, the printing quality monitoring module 5 monitors the molten pool temperature and size in real time, finds that the temperature of some areas is too high (exceeding 1650°C), and through the feedback mechanism, the process parameter calculation module 3 dynamically adjusts the laser power and scanning speed of these areas to ensure the manufacturing quality.

[0179] The final manufactured bracket weighs 1.45kg, which is 42% lighter than the original design. The mechanical property test shows that the strength and stiffness of the optimized bracket meet the design requirements, and the manufacturing precision is high (the maximum size deviation is ±0.15mm). Compared with the traditional method, the system significantly improves the manufacturing precision (the precision is improved by about 55%) and the structural performance (the strength is improved by about 35% under the same weight).

[0180] As can be seen from the above examples, the lightweight mechanical structure topology optimization and additive manufacturing integrated system provided by the present application realizes the deep integration of topology optimization and additive manufacturing through the material-structure mapping theory based on differential geometry, the curvature-driven thermal deformation compensation method and the thermal-mechanical coupling process parameter adaptive control system under the multi-manifold intersection constraint, and significantly improves the manufacturing precision and mechanical properties of the lightweight structure.

[0181] The above only describes the preferred embodiments of the present application, and does not limit the patent protection scope of the present application, and any equivalent structural transformation made based on the inventive concept of the present application, or direct / indirect application in other related technical fields is included in the patent protection scope of the present application.

Claims

1. A lightweight mechanical structure topology optimization and additive manufacturing integrated system, characterized in that, include: The structural topology optimization module is used to perform topology optimization on mechanical structures and generate optimized structural solutions. The finite element simulation module is connected to the structural topology optimization module and is used to perform mechanical performance analysis on the optimized structural scheme. A process parameter calculation module is connected to the structural topology optimization module and the finite element simulation module. The process parameter calculation module includes: Differential geometric representation units are used to construct material space manifolds and structural space manifolds, and to establish the mapping relationship between the two manifolds; The thermal deformation prediction and compensation unit is used to predict the thermal deformation trend based on the structural curvature characteristics and generate a compensation strategy. The process parameter mapping and optimization unit is used to generate optimal process parameters under multi-manifold cross constraints. A production module, connected to the process parameter calculation module, is used to perform additive manufacturing based on the process parameters; The print quality monitoring module is connected to the production module and the process parameter calculation module, and is used to monitor the manufacturing process and feed back the monitoring data to the process parameter calculation module.

2. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The structural topology optimization module includes: The structural parameters and manufacturing constraints input submodule is used to input structural material composition, structural load distribution, structural boundary conditions, and manufacturing constraints. The topology optimization submodule is used to perform topology optimization calculations based on the structural parameters and manufacturing constraints. The structural improvement submodule is used to improve the manufacturability of the topology optimization results. The material selection submodule is used to select suitable materials based on the topology optimization results. The performance evaluation submodule is used to evaluate the mechanical properties of mechanical structures. The optimization scheme acquisition submodule is used to output the final optimization scheme and process parameters.

3. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The differential geometric representation unit includes: Material space manifold building components are used to define a material space containing parameters such as density, strength, and thermal conductivity, and to introduce Riemannian metrics into the material space; The structure space manifold building component is used to define a structure space that includes geometry, topological connections, and performance metrics, and introduces the Riemannian metric of the structure space; The manifold mapping component is used to construct a mapping function from material space to structure space and optimize the mapping relationship through variational functionals.

4. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The thermal deformation prediction and compensation unit includes: The thermal deformation-curvature relationship modeling component is used to analyze the Gaussian curvature and average curvature distribution of structural surfaces and establish the mapping relationship between thermal deformation and curvature. Curvature-driven structure optimization components are used to design strategies for the evolution of structural surface morphology based on curvature distribution. The thermal deformation prediction and compensation component is used to predict the temperature field distribution based on thermal analysis results, calculate the curvature change caused by the temperature field, and generate an active compensation scheme.

5. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The process parameter mapping and optimization unit includes: Multi-manifold space construction components are used to define thermal manifolds, force manifolds, and process parameter manifolds; The cross-constraint measure space component is used to define cross measures between manifolds and quantify the mutual influence between different parameters; The geodesic parameter optimization component is used to construct energy functionals in parameter space and derive the optimal parameter trajectory. An adaptive control component is used to construct an error manifold based on real-time monitoring data and calculate parameter adjustment strategies.

6. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The finite element simulation module includes: The data input submodule is used to generate finite element mesh models and boundary conditions based on the optimized structural scheme. The finite element simulation submodule is used to calculate the stress distribution parameters and deformation distribution parameters of the structure. The performance feedback submodule is used to generate mechanical structure performance parameters based on the finite element analysis results, and to feed the performance parameters back to the structure topology optimization module and the process parameter calculation module.

7. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The manufacturing module includes: The optimization scheme input submodule is used to receive mechanical structure parameters from the structure topology optimization module and process parameters from the process parameter calculation module; The manufacturing method selection submodule is used to select a manufacturing scheme based on the mechanical structure parameters and the process parameters; An additive manufacturing submodule is used to perform additive manufacturing when the manufacturing scheme is additive manufacturing; The subtractive manufacturing submodule is used to perform subtractive manufacturing when the manufacturing scheme is subtractive manufacturing. The additive and subtractive manufacturing submodule is used to perform additive and subtractive manufacturing when the manufacturing scheme is integrated manufacturing.

8. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The print quality monitoring module includes: The material property calculation submodule is used to calculate the material change law during the manufacturing process and the material parameters after thermal deformation compensation based on the process parameters. The printing process monitoring submodule is used to monitor the manufacturing process and acquire monitoring data, calculate the deviation from the expected state based on the monitoring data, and feed the deviation back to the process parameter calculation module for parameter adjustment.

9. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 5, characterized in that, The parameter adjustment strategies employed by the adaptive control component include: An energy input control strategy is used to dynamically adjust the energy density based on the material state tensor. A scan path planning strategy is used to generate an adaptive scan path based on the structural curvature distribution. Printing speed control strategy, used to dynamically adjust printing speed based on thermal gradient; Material supply management strategy, used to dynamically adjust the material supply rate based on cross-sectional characteristics.

10. The lightweight mechanical structure topology optimization and additive manufacturing integrated system according to claim 1, characterized in that, The data transfer mechanism established between the differential geometry characterization unit, the thermal deformation prediction and compensation unit, and the process parameter mapping and optimization unit includes: The differential geometry characterization unit transmits the material-structure mapping relationship and curvature distribution data to the thermal deformation prediction and compensation unit; The thermal deformation prediction and compensation unit transmits the predicted deformation field and compensation strategy to the process parameter mapping and optimization unit. The process parameter mapping and optimization unit transmits parameter optimization feedback information to the differential geometry characterization unit and the thermal deformation prediction and compensation unit.

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