Virtual simulation 3D printing interactive teaching method for popular science education

Abstract

This invention discloses a virtual simulation 3D printing interactive teaching method for science popularization education, belonging to the field of virtual simulation science popularization teaching technology. It includes acquiring user entity modeling commands and material selection parameters, generating a three-dimensional geometric topology through semantic parsing, mapping material parameters to a material physical property database to extract thermodynamic characteristic parameters, and fusing them to construct a multi-physics coupled printing process simulation model. The evolution data of the simulation model is input into a particle swarm optimization path planning engine to generate the optimal nozzle motion trajectory, driving a virtual rendering engine to output real-time printing animation. Learner interaction behavior is collected to update the boundary constraints of the three-dimensional geometric topology, iteratively generating corrected printing teaching feedback information from the simulation model. This invention improves the physical realism of 3D printing virtual simulation and achieves dynamic linkage between simulation and interaction in science popularization education.

Description

Technical Field

[0001] This invention belongs to the field of virtual simulation science popularization teaching technology, specifically a virtual simulation 3D printing interactive teaching method for science popularization education. Background Technology

[0002] Existing virtual simulation methods for 3D printing education in science popularization only process user-input entity modeling commands to generate simple 3D models. The virtual display remains at the geometric level; material selection parameters are not correlated with corresponding physical property databases; nozzle movement trajectories often use preset fixed paths; and the simulation process lacks dynamic optimization mechanisms. Current virtual simulation teaching does not collect learners' interactive behaviors; the constraints of the simulation model remain in their initial state and cannot be adjusted based on teaching interactions. The simulation model and the teaching interaction are independent of each other.

[0003] Conventional 3D printing virtual simulations only achieve single-geometric visualization, failing to integrate material thermodynamic properties to construct multi-physics coupled simulation models. The simulation process deviates from the actual physical changes observed in 3D printing, failing to demonstrate the correlation between material properties and the printing process to learners. Fixed path planning cannot adapt to the printing needs of different 3D structures and material parameters, resulting in insufficient rationality of the virtual printing trajectory. Learners cannot intervene in the simulation process through interactive operations, the simulation model cannot be iteratively updated, and teaching feedback cannot be dynamically corrected based on interactive behavior, making it difficult to meet the interactive and realistic simulation requirements of science education. This invention aims to achieve multi-physics coupled simulation construction that integrates 3D geometric topology and material thermodynamic parameters. It requires path planning for particle swarm optimization based on simulation evolution data, while simultaneously updating model boundary constraints and iterating the simulation model through learner interactive operations. Summary of the Invention

[0004] This invention aims to solve at least one of the technical problems existing in the prior art; Therefore, this invention proposes a virtual simulation 3D printing interactive teaching method for science popularization education, including: Obtain the solid modeling instructions and material selection parameters input by the user; The entity modeling instructions are semantically parsed to generate a three-dimensional geometric topology. The material selection parameters are mapped to a material physical property database to extract thermodynamic property parameters. By integrating the three-dimensional geometric topology and the thermodynamic property parameters, a multi-physics coupled printing process simulation model is constructed. The evolution data of the multiphysics coupled printing process simulation model is input into a path planning engine based on particle swarm optimization to generate the optimal nozzle motion trajectory. The virtual rendering engine is driven by the optimal nozzle motion trajectory to output a real-time printing process animation; Collect learners' interactive behavior in response to the real-time printing process animation, and update the boundary constraints of the three-dimensional geometric topology. Based on the changes in the boundary constraints, the multiphysics coupled printing process simulation model is iterated again to generate corrected printing teaching feedback information.

[0005] Furthermore, the entity modeling instructions are semantically parsed to generate a three-dimensional geometric topology, specifically including: The solid modeling instructions input by the user include sketch drawing trajectory, extrusion height value, and Boolean operation type; Identify the feature line segments in the sketch drawing trajectory and extract the endpoint coordinates and curvature extreme points; Based on the stretching height value, the feature line segment is vector-translated to construct an initial three-dimensional mesh framework; The Boolean operation types are parsed, including union, intersection, and difference operations. The initial three-dimensional mesh framework is geometrically merged or trimmed according to the Boolean operation type to form a closed three-dimensional geometric topology; Verify the manifold integrity of the three-dimensional geometric topology and remove overhanging edges and overlapping surfaces.

[0006] Furthermore, the material selection parameters are mapped to a material physical property database to extract thermodynamic property parameters, specifically including: The material selection parameters include a material name identifier and a filler density percentage; Retrieve entries from the material physical property database that match the material name identifier; Read the pre-stored melting point temperature, thermal conductivity coefficient, and shrinkage rate values ​​from the entry; The thermal conductivity coefficient is linearly interpolated and corrected based on the fill density percentage to generate an effective thermal conductivity coefficient. The combination of the melting point temperature, the shrinkage rate, and the effective thermal conductivity is defined as the thermodynamic characteristic parameter.

[0007] Furthermore, by integrating the three-dimensional geometric topology and the thermodynamic characteristic parameters, a multiphysics coupled printing process simulation model is constructed, specifically including: The three-dimensional geometric topology is divided into tetrahedral meshes to generate a finite element analysis mesh; The thermodynamic property parameters are assigned to each element node of the finite element analysis mesh; Define a heat source term that simulates the laser heating process of a printhead; A thermal stress constitutive equation is established, which relates temperature change to structural deformation displacement. The heat source term is coupled with the thermal stress constitutive equation to form the multi-physics coupled printing process simulation model.

[0008] Furthermore, the evolution data of the multiphysics-coupled printing process simulation model is input into a particle swarm optimization-based path planning engine to generate the optimal nozzle motion trajectory, specifically including: The contour curve of the cross section to be printed is derived from the multiphysics coupled printing process simulation model. Initialize the particle swarm, with each particle representing a candidate nozzle scanning path; Define a fitness function that includes path length cost and heat accumulation penalty term; The heat accumulation penalty term is calculated based on the local temperature history in the evolution data; The velocity and position of the particle swarm are iteratively updated until the fitness function converges. The converged particle position information is extracted and smoothed to obtain the optimal nozzle motion trajectory.

[0009] Furthermore, based on the optimal nozzle motion trajectory, the virtual rendering engine is driven to output a real-time printing process animation, specifically including: Analyze the discrete points and timestamps in the optimal nozzle motion trajectory; Generate a nozzle movement pose matrix based on the discrete points; The shader program is invoked to gradually accumulate material textures on the surface of the three-dimensional geometric topology according to the nozzle movement pose matrix. The color gradient rate of the simulated cooling and curing visual effect is determined by the thermal conductivity coefficient in the thermodynamic property parameters. The rendered frame sequence is encoded into the real-time printing process animation.

[0010] Furthermore, by collecting learners' interactive actions in response to the real-time printing process animation, the boundary constraints of the three-dimensional geometric topology are updated, specifically including: Monitor learners’ input device operations, including mouse click locations and keyboard shortcut commands; Identify the collision object at the mouse click location in the real-time printing process animation; The modification intent corresponding to the keyboard shortcut command is analyzed, and the modification intent includes undoing the previous step, rotating the viewing angle, or adding a support structure; When the modification is intended to add a support structure, a tapered support geometry is generated below the collision object; The conical support geometry is used as a new geometric constraint and incorporated into the boundary constraint conditions of the three-dimensional geometric topology.

[0011] Furthermore, based on the changes in the boundary constraints, the multiphysics coupled printing process simulation model is iterated again to generate corrected printing teaching feedback information, specifically including: The tapered support geometry in the boundary constraint conditions is converted into a finite element load boundary. The thermal stress distribution of the multiphysics coupled printing process simulation model was re-solved; Detect whether there are regions in the thermal stress distribution that exceed the material's yield strength; If there is a region exceeding the material's yield strength, generate the corrected printed teaching feedback information, which includes risk warning text and structural optimization suggestions; If there is no region exceeding the material yield limit, the corrected printing instruction feedback information, including printing time estimates and material usage statistics, is generated.

[0012] Furthermore, it also includes knowledge graph association steps, specifically including: Extract the feature keywords of the three-dimensional geometric topology; Input the aforementioned key features into the science popularization knowledge graph retrieval interface; The popular science knowledge graph retrieval interface returns physical principle descriptions and engineering application cases related to the feature keywords; The description of the physical principles and the engineering application examples are overlaid and displayed in the narration area of ​​the real-time printing process animation.

[0013] Furthermore, inputting the aforementioned feature keywords into the science popularization knowledge graph retrieval interface specifically includes: The feature keywords are expanded using synonyms to generate an expanded query term set; Traverse the extended query term set and match node names in the popular science knowledge graph; Calculate the relevance score between the matched nodes and the current teaching scenario; Filter nodes whose correlation scores are higher than a preset threshold and their adjacent relationships; Extract the text content from the nodes and their adjacency relationships, and encapsulate it into the physical principle description and the engineering application case.

[0014] Compared with the prior art, the beneficial effects of the present invention are: The three-dimensional geometric topology generated by semantic parsing of user entity modeling commands is fused with the thermodynamic property parameters extracted from the material physical property database by mapping material selection parameters to construct a multi-physics coupled printing process simulation model. This allows three-dimensional geometric information and material physical properties to participate in the simulation calculation simultaneously. The simulation process can reflect the physical changes of the interaction between structure and material in 3D printing. Virtual simulation is no longer limited to geometric shape display, but can fully reflect the influence of material thermodynamic properties on the printing process. The evolution logic of the simulation model is consistent with the physical process of actual printing, improving the physical matching degree of the virtual simulation process.

[0015] By inputting the evolution data of the multiphysics-coupled printing process simulation model into a path planning engine based on particle swarm optimization, the generation of the nozzle motion trajectory can be based on real-time simulation data. The trajectory generation results can be adapted to the printing requirements of corresponding 3D structures and material parameters, and the trajectory planning and simulation process form a data linkage. By collecting learners' interactive behaviors in the real-time printing animation and transforming them into boundary constraints of the 3D geometric topology, the multiphysics-coupled simulation model can be iterated again by changing the constraints. This allows the simulation model to dynamically adjust according to learners' interactive behaviors, and the simulation parameters and process states are updated synchronously with the changes in constraints. The corrected printing teaching feedback information is directly generated based on the iterated simulation model. The feedback content maintains a correspondence with learners' interactive operations, achieving real-time connection between the virtual simulation process and teaching interaction. The generation of teaching feedback is completed synchronously with the iteration of the simulation model, and interactive operations can directly affect the core simulation links, allowing virtual simulation and science popularization teaching to form an integrated operation. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the steps of the virtual simulation 3D printing interactive teaching method for science education as described in this invention. Figure 2 A flowchart for mapping material selection parameters to a physical property database to extract thermodynamic parameters; Figure 3 For 3D printing path planning-particle swarm optimization iterative convergence curve; Figure 4 Print the path convergence process diagram for the particle swarm optimization algorithm; Figure 5 This is for the optimal motion path planning of 3D printing nozzles based on particle swarm optimization. Detailed Implementation

[0017] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] See Figure 1 This invention provides a virtual simulation 3D printing interactive teaching method for science education, the specific method including: The system acquires entity modeling commands and material selection parameters input by the user via a graphical interface, parses the commands using natural language and graphical semantics, and generates corresponding 3D geometric topologies. Material selection parameters are mapped to a pre-built material physical property database, extracting corresponding thermodynamic properties. The generated 3D geometric topology and extracted thermodynamic properties are fused to construct a printing process simulation model that couples temperature and stress fields. Data generated during the simulation evolution of this multi-physics coupled printing process simulation model is input into a path planning engine based on particle swarm optimization, which calculates the optimal nozzle trajectory. Based on the optimal nozzle trajectory, a 3D virtual rendering engine is driven to output and display a dynamic animation of the printing process in real time. During the animation demonstration, the system continuously collects interactive actions from the learner via input devices; these actions are used to update the boundary constraints of the 3D geometric topology. Based on the updated boundary constraints, the system automatically iterates and solves the multi-physics coupled printing process simulation model again, and generates revised printing teaching feedback information based on the new solution results, which is then presented to the learner.

[0019] In one embodiment of the present invention, the solid modeling instructions input by the user include a sketch drawing trajectory, an extrusion height value, and a Boolean operation type. The system identifies feature line segments in the sketch drawing trajectory and extracts the endpoint coordinates and curvature extrema of these line segments. Based on the extrusion height value provided by the user, a vector translation operation is performed on the identified feature line segments to construct an initial 3D mesh framework. The system parses the Boolean operation type specified by the user, which includes union, intersection, and difference operations. The initial 3D mesh framework is then used to perform geometric merging or trimming calculations according to the parsed Boolean operation type, thereby forming a closed 3D geometric topology. The system verifies the manifold integrity of the 3D geometric topology and performs geometric cleanup operations to remove overhanging edges and overlapping surfaces. Regarding material processing, the material selection parameters include a material name identifier and a fill density percentage, see [link to relevant documentation]. Figure 2The system retrieves data entries from the material physical property database that exactly match the material name identifier. It reads the pre-stored melting point temperature, thermal conductivity, and shrinkage rate values ​​from these entries, and performs linear interpolation correction on the read thermal conductivity value based on the filler density percentage to generate an effective thermal conductivity value. The melting point temperature, shrinkage rate value, and effective thermal conductivity value are then combined to define the thermodynamic characteristic parameters used in this teaching simulation scenario.

[0020] In practice, the user-input entity modeling commands include a sketch trajectory, an extrusion height value, and a Boolean operation type. The sketch trajectory can be defined by a series of two-dimensional coordinate points. The extrusion height value is a positive real number in millimeters, and the Boolean operation type is an enumeration of values ​​specifying a geometric operation type. The system identifies feature segments in the sketch trajectory, extracts endpoint coordinates and curvature extrema. Feature segments are straight or curved lines with obvious geometric features in the trajectory. Endpoint coordinates are the start and end points of the feature segment on the two-dimensional plane, and curvature extrema are the points on the feature segment where the curvature function reaches a local maximum or minimum value. Based on the extrusion height value, the feature segments are vector-translated to construct an initial three-dimensional mesh framework. The direction of the vector translation is perpendicular to the plane where the sketch trajectory is located, and the translation magnitude is equal to the extrusion height value. After translation, the endpoints of the corresponding feature segments are connected to form mesh edges and mesh faces in three-dimensional space. The Boolean operation types are analyzed, including union, intersection, and difference operations. The initial 3D mesh framework is geometrically merged or trimmed according to these Boolean operation types to form a closed 3D geometric topology. In the Boolean difference operation, the initial 3D mesh framework is subtracted from a reference geometry, removing the overlapping portions of the initial 3D mesh framework with the reference geometry. The manifold integrity of the 3D geometric topology is verified, eliminating dangling edges and overlapping surfaces. Manifold integrity requires that each edge in the 3D geometric topology strictly belongs to two faces; dangling edges belong to only one face; and overlapping surfaces are completely coincident faces in 3D space.

[0021] In some embodiments, the material selection parameters include a material name identifier and a filler density percentage. The material name identifier is a string that uniquely identifies the material type, and the filler density percentage is a value between 0 and 100. Entries matching the material name identifier are retrieved from a material physical property database. This database is a relational database storing various inherent properties of materials, and the material name identifier is used as the primary key for the query. Pre-stored melting point temperature, thermal conductivity, and shrinkage rate values ​​are read from the entries. The melting point temperature is the phase transition temperature at which a material changes from a solid to a liquid state. The thermal conductivity is a measure of a material's ability to conduct heat, and the shrinkage rate is the percentage of volume shrinkage during cooling. A linear interpolation correction is performed on the thermal conductivity based on the filler density percentage to generate an effective thermal conductivity. This linear interpolation correction reflects the influence of the material's internal porous structure on its thermal conductivity. The linear interpolation process is understood to be implemented using the following formula:

[0022] in: Indicates the effective thermal conductivity. This represents the thermal conductivity of a material in a fully dense state. This indicates the percentage of filler density. The melting point temperature, shrinkage rate, and effective thermal conductivity are combined to define a thermodynamic property parameter, which is a data structure containing three physical quantities.

[0023] Optionally, data comparison can be achieved by changing the input value of the filler density percentage. For example, when the filler density percentage is 30%, the effective thermal conductivity calculated by the formula is 0.075 watts per meter Kelvin; when the filler density percentage is 80%, the effective thermal conductivity is 0.20 watts per meter Kelvin. Comparing the effective thermal conductivity values ​​under different filler density percentages can intuitively demonstrate the influence of the material's internal structure on its thermal properties. In some embodiments, the entries in the material physical property database also include parameters such as material density and specific heat capacity, but the combination of thermodynamic property parameters only selects melting point temperature, shrinkage rate, and effective thermal conductivity.

[0024] In one embodiment of the present invention, the construction of a multiphysics-coupled printing process simulation model begins with tetrahedral meshing of the generated three-dimensional geometric topology to generate a finite element analysis mesh for numerical calculation. The thermodynamic properties obtained in the above embodiment, including melting point temperature, effective thermal conductivity, and shrinkage rate, are assigned to each element node in the finite element analysis mesh. A heat source term is defined to simulate the laser heating process of the printing nozzle, and this heat source term is dynamically distributed in space according to the nozzle position and time. A thermal stress constitutive equation describing the material behavior is established, which relates the temperature change at each node during the simulation process to the resulting structural deformation displacement. The dynamic heat source term is coupled with the thermal stress constitutive equation to form a solvable multiphysics-coupled printing process simulation model, which can simultaneously calculate temperature diffusion and structural stress evolution during the printing process.

[0025] In practical implementation, constructing a multiphysics coupled printing process simulation model begins with tetrahedral meshing of the generated 3D geometric topology. This meshing process discretizes the internal space of the 3D geometric topology into a series of interconnected tetrahedral elements, generating a finite element analysis mesh for numerical calculations. The nodes of the finite element analysis mesh store spatial coordinates, and the tetrahedral elements record the connection relationships between nodes. Thermodynamic property parameters are assigned to each node of the finite element analysis mesh. This assignment process involves associating melting point temperature, effective thermal conductivity, and shrinkage rate as attribute data to each mesh node, ensuring that each node possesses complete material thermodynamic properties. A heat source term is defined, simulating the laser heating process of the printing nozzle. In space, the heat source term is a heat flux density distribution function that varies with time and moves with the nozzle position. A thermal stress constitutive equation is established, relating temperature change to structural deformation displacement. This equation describes the relationship between thermoelastic stress and strain caused by uneven material heating.

[0026] In some embodiments, the heat source term is defined as a Gaussian heat source model, which has a central peak heat flux density and radial attenuation characteristics. Its heat flux density distribution matches the laser spot shape and power of the printhead. The parameters of the heat source term include laser power, spot radius, and scanning speed. Laser power determines the total input energy, spot radius determines the heat distribution range on the material surface, and scanning speed determines the residence time of heat at a specific location. The heat source term is coupled with the thermal stress constitutive equation to form a multi-physics coupled printing process simulation model. The coupling process is manifested in the temperature field solution being used as a load input into the thermal stress constitutive equation, thereby calculating the structural stress and deformation induced by the non-uniform temperature field. The structural deformation may, in turn, weakly affect the thermal boundary conditions, forming a two-way weak coupling relationship. The mathematical expression of the multi-physics coupled printing process simulation model includes energy conservation equations and momentum conservation equations, and its solution process typically employs sequentially coupled finite element analysis.

[0027] Alternatively, the thermal stress constitutive equation can be expressed in the following form:

[0028] in: Represents the second-order Cauchy stress tensor. This represents the fourth-order elastic stiffness tensor. This represents the second-order total strain tensor. Indicates the coefficient of thermal expansion of a material. This represents the difference between the current temperature and the reference temperature. This represents the second-order Kronecker delta function. Coefficient of thermal expansion. Data can be obtained from a material physical property database or derived from shrinkage rate values. In some embodiments, data comparison can be conducted on the thermodynamic properties of different materials. For example, comparing polylactic acid with a melting point of 220 degrees Celsius with acrylonitrile-butadiene-styrene copolymer with a melting point of 260 degrees Celsius, under the same heat source, the differences in temperature field distribution and thermal stress field distribution at the finite element analysis mesh nodes are observed. The material with the higher melting point reaches a relatively lower peak temperature at the same location, and the generated thermal stress distribution pattern also differs.

[0029] In one embodiment of the present invention, when generating the optimal nozzle motion trajectory, the cross-sectional profile curve of the current layer to be printed is derived from the solution results of the multiphysics coupled printing process simulation model. A particle swarm is initialized, where the position information of each particle represents a candidate nozzle scanning path. A fitness function is defined to evaluate the merits of each path. This fitness function includes a path length cost and a heat accumulation penalty term, which is calculated based on the local temperature history in the simulation model evolution data. By iteratively updating the velocity and position information of all particles in the particle swarm, the particles move towards the direction with better fitness until the fitness function of the entire particle swarm converges to a stable state. The path information represented by the particle with the best fitness after convergence is extracted, and after smoothing and filtering, the final optimal nozzle motion trajectory is obtained. When outputting the real-time printing process animation, the system parses the discrete points and corresponding timestamp sequences contained in the optimal nozzle motion trajectory, and generates the nozzle's movement pose matrix in virtual space based on the discrete points. The graphics shader program is invoked to progressively add material deposition textures to the surface of the 3D geometric topology, according to the positions indicated by the nozzle movement pose matrix. The visual effect of material cooling and solidification is simulated synchronously; the color gradation rate of this cooling and solidification visual effect is determined by the thermal conductivity coefficient, a thermodynamic property parameter. Finally, the time-series rendered frame images are encoded into a continuous real-time printing process animation.

[0030] In practical implementation, when generating the optimal nozzle trajectory, the cross-sectional profile curve of the current layer to be printed is derived from the solution results of the multiphysics coupled printing process simulation model. This profile curve is defined by a series of ordered two-dimensional or three-dimensional coordinate points, representing the boundary shape that the current printing layer needs to fill. A particle swarm containing a preset number of individuals is initialized. Each particle in the swarm represents a candidate nozzle scanning path, and each candidate path consists of a sequence of coordinates representing the position of the nozzle center point. A fitness function is defined to evaluate the merits of each candidate nozzle scanning path. The fitness function includes a path length cost and a heat accumulation penalty. The path length cost is the total length of the candidate nozzle scanning path, and the heat accumulation penalty is calculated based on the local temperature history in the evolution data of the multiphysics coupled printing process simulation model. The local temperature history is the sequence of temperature changes experienced by material points during the printing process over time. It can be understood that the calculation of the heat accumulation penalty accumulates the overheating risk value of areas on the nozzle scanning path that are repeatedly heated in a short period of time or whose adjacent areas have already been heated.

[0031] In some embodiments, the specific mathematical form of the fitness function is as follows:

[0032] in: This represents the fitness function value; a smaller value indicates a better path. Indicates the total length of the candidate nozzle scanning path; and These are preset weighting coefficients used to balance the impact of path length cost and heat accumulation penalty. This represents the number of points used for discretization evaluation of the candidate nozzle scanning path; It is a thermal accumulation penalty function, the value of which depends on the location. Current simulated temperature at [location] and its temperature history The velocity and position of the particle swarm are iteratively updated until the fitness function converges. The update rule follows the standard particle swarm optimization algorithm. Each particle adjusts its motion direction and step size based on its individual best position and the swarm's best position. The converged particle position information is extracted and smoothed to obtain the optimal nozzle trajectory. The smoothing process uses spline curve fitting to eliminate sharp corners in the path and ensure the smoothness of the nozzle trajectory.

[0033] Optionally, see Table 1, which shows an exemplary data comparison of how the fitness function value changes with the number of iterations during a single particle swarm optimization iteration.

[0034] Table 1: Examples of Fitness Function Value Changes During Particle Swarm Optimization

[0035] When outputting a real-time printing process animation, the system analyzes the discrete points and corresponding timestamp sequences contained in the optimal printhead motion trajectory. The discrete points are spatial points sampled at fixed interpolation intervals after trajectory smoothing, and the timestamp sequence defines the relative or absolute time of the printhead reaching each discrete point. Based on the discrete points, a printhead pose matrix in virtual space is generated. This pose matrix is ​​a 4x4 transformation matrix that defines the printhead's position and orientation in three-dimensional space. The graphics shader program is invoked to progressively accumulate material deposition textures on the surface of the three-dimensional geometric topology according to the positions indicated by the printhead pose matrix. The material deposition textures are dynamically calculated and rendered to the frame buffer by vertex and fragment shader programs. In some embodiments, the visual effect of material cooling and solidification is simulated synchronously. The color gradation rate of the cooling and solidification visual effect is determined by the thermal conductivity coefficient in the thermodynamic property parameters. Materials with high thermal conductivity coefficients appear to cool from the high-temperature color during printing to the ambient color faster in the animation. It can be understood that the color gradation is implemented in the shader program through time-based linear interpolation, and the interpolation speed parameter is inversely proportional to the thermal conductivity coefficient. The time-series rendered frame images are encoded into a continuous real-time printing process animation. The encoding process uses a video encoding library to compress a series of ordered bitmap images into a video stream file or to stream the video directly in the graphical interface.

[0036] See Figure 3 In the path planning stage of the virtual simulation 3D printing interactive teaching method for science popularization education, the iterative convergence characteristics of the particle swarm optimization algorithm are quantitatively characterized by this convergence curve. Specifically, after deriving the contour curve of the cross-section to be printed from the multi-physics coupled printing process simulation model, the particle swarm is initialized, with each particle representing a candidate nozzle scanning path. A fitness function is defined, including path length cost and thermal accumulation penalty term. The thermal accumulation penalty term is calculated based on the local temperature history in the simulation evolution data; a smaller fitness function value indicates a better path planning scheme. The velocity and position of the particle swarm are iteratively updated until the fitness function converges. The curve visually illustrates the evolution of the optimal fitness value (solid line) and the average fitness value (dashed line) during the iteration process: In the early stage of iteration (0-10 iterations), both types of fitness values ​​decrease rapidly, reflecting the process of the particle swarm rapidly exploring and selecting high-quality paths in the solution space; in the middle stage of iteration (10-30 iterations), the rate of decrease slows down, and the particle swarm gradually converges towards the global optimal region; in the later stage of iteration (30-50 iterations), both types of fitness values ​​tend to stabilize, with the optimal fitness value finally converging to approximately 89.5 and the average fitness value converging to approximately 94.5. This verifies the effectiveness and convergence of the particle swarm optimization algorithm in 3D printing nozzle path planning and provides a quantitative basis for generating the optimal nozzle motion trajectory.

[0037] In one embodiment of the present invention, when collecting learner interaction behavior, the system monitors the learner's input device operations, including mouse click locations and keyboard shortcut commands. The system identifies the 3D collision object corresponding to the mouse click location in the real-time printing process animation and analyzes the specific modification intent corresponding to the keyboard shortcut commands. The modification intent includes undoing the previous step, rotating the viewing angle, or adding a support structure. When the analyzed modification intent is to add a support structure, the system automatically generates a conical support geometry below the identified collision object. This conical support geometry is used as a new geometric constraint and incorporated into the boundary constraint condition set of the original 3D geometric topology. When generating the corrected printing teaching feedback information, the system converts the newly added conical support geometry in the boundary constraint conditions into the loads and boundary conditions required for finite element analysis, re-solves the updated multiphysics coupled printing process simulation model, and obtains new thermal stress distribution data. The system detects whether there are regions in the new thermal stress distribution data that exceed the material yield limit. If there are regions that exceed the material yield limit, the system generates corrected printing teaching feedback information containing risk warning text and specific structural optimization suggestions. If there is no region exceeding the material's yield strength, then a revised printing instruction feedback message is generated, including estimated printing time and material usage statistics.

[0038] In practice, when collecting learners' interactive actions on the real-time printing animation, the system monitors the learners' input device operations, including mouse clicks and keyboard shortcuts. It identifies collision objects in the animation at the mouse click location. This identification process involves emitting a ray from the 2D coordinates of the mouse click into the 3D virtual scene, detecting the first intersection point between the ray and the 3D geometric model in the scene, and marking the surface or entity of the 3D model at the intersection point as the collision object. The system also parses the modification intent corresponding to the keyboard shortcuts, which may include undoing the previous step, rotating the viewpoint, or adding support structures. The mapping relationship between keyboard shortcuts and modification intents is maintained through a predefined configuration table. When the parsed modification intent is to add support structures, a conical support geometry is generated below the collision object. The center of the bottom surface of the conical support geometry is located at the projection point of the collision object onto the printing platform plane, and the vertices of the conical support geometry connect to the bottom edge or lowest point of the collision object. The conical support geometry is used as a new geometric constraint and incorporated into the boundary constraint conditions of the three-dimensional geometric topology. The incorporation operation is to perform a Boolean union operation on the triangular mesh data of the conical support geometry and the mesh data of the original three-dimensional geometric topology to form a new three-dimensional geometric topology that includes the support structure.

[0039] In some embodiments, the conical support geometry in the boundary constraints is converted into a finite element load boundary. The bottom nodes of the conical support geometry in contact with the printing platform are subject to fixed constraints, restricting all translational and rotational degrees of freedom. A binding contact relationship is established between the top nodes of the conical support geometry in contact with the original model and the corresponding nodes of the original model. The thermal stress distribution of the multiphysics coupled printing process simulation model is re-solved. The solution process uses the updated three-dimensional geometric topology containing the conical support geometry as the computational domain, and the finite element analysis is performed again. The presence of regions exceeding the material yield strength in the thermal stress distribution is detected. The detection process traverses the stress values ​​of all elements or nodes in the finite element analysis results and compares them with the yield strength read from the material physical property database. It can be understood that the judgment condition can be expressed as:

[0040] in: This represents the internal stress value of the material calculated from the thermal stress distribution (e.g., Mises equivalent stress). This indicates the material's yield strength. If any region exceeds the material's yield strength, the system generates revised printing tutorial feedback information including risk warning text and structural optimization suggestions. The risk warning text marks the location of the stress exceeding the limit, and the structural optimization suggestions include increasing the density of the support structure, adjusting the angle of the support structure, or modifying the local geometry of the model. If no region exceeds the material's yield strength, the system generates revised printing tutorial feedback information including printing time estimation and material usage statistics. The printing time estimation is calculated based on the total length of the optimal nozzle movement trajectory and the preset printing speed, and the material usage statistics are obtained by calculating the volume and material density of the new 3D geometric topology including the support structure.

[0041] Optionally, the data comparison can be shown in Table 2 below, which illustrates the changes in thermal stress in key areas of the model before and after adding the tapered support geometry.

[0042] Table 2: Example of thermal stress distribution comparison before and after adding support structure

[0043] In some embodiments, when a region exceeding the material's yield strength is detected, the generated structural optimization suggestion text will explicitly point to the specific high-risk location, such as "The maximum stress value of region A is 45 MPa, exceeding the material's yield strength of 40 MPa. It is recommended to add a support column with a larger diameter or increase the infill density below region A." It is understood that when generating corrected printing tutorial feedback information with estimated printing time and material consumption statistics, specific numerical values ​​will be presented, such as "Estimated total printing time: 2 hours and 15 minutes; Estimated material consumption: 18.5 grams."

[0044] See Figure 4In the path planning stage of the virtual simulation 3D printing interactive teaching method for science popularization education, the convergence process of the printing path using the particle swarm optimization algorithm is intuitively presented through this diagram. Specifically, the algorithm takes the evolution data of a multi-physics coupled printing process simulation model as input and constructs a fitness function that includes path length cost and a heat accumulation penalty term. The heat accumulation penalty term is calculated based on the local temperature history in the evolution data, and each particle represents a candidate nozzle scanning path. As shown in the figure, the fitness function value (path cost) shows a continuous decreasing trend and eventually stabilizes with the increase of the number of optimization iterations: In the early stage of iteration (0-10 iterations), the fitness function value drops rapidly from the initial 115.8 to 106.6. The algorithm quickly explores the path space through global search and greatly optimizes the nozzle motion trajectory; In the middle stage of iteration (10-15 iterations), the fitness function value fluctuates slightly in the range of 106.6-107.8. The algorithm enters the local optimization stage and makes fine adjustments to the path; In the 15th iteration (the algorithm convergence iteration point, marked by the green dashed line), the fitness function value stabilizes at 106.1. Subsequent iterations (15-20 iterations) show only slight fluctuations, indicating that the algorithm has completed convergence. At this time, the particle position information after convergence is extracted and smoothed to obtain the optimal nozzle motion trajectory. The convergence process verified the effectiveness of the particle swarm optimization path planning engine: by iteratively updating the velocity and position of the particle swarm, the algorithm achieved the global optimal solution for the printing path while taking into account both path length and the risk of heat accumulation. This provides a precise trajectory basis for the subsequent virtual rendering engine to drive the real-time printing process animation, and also provides a quantitative basis for the visualization of the 3D printing path optimization principle in popular science education.

[0045] In one embodiment of the present invention, the knowledge graph association step first extracts feature keywords from the three-dimensional geometric topology. These keywords originate from descriptions of geometric shapes and material names. The extracted feature keywords are input into the retrieval interface of the science knowledge graph, which returns physical principle descriptions and engineering application case introductions related to the feature keywords. The system overlays the returned physical principle descriptions and engineering application case texts in the narration area of ​​the real-time printing process animation. During the retrieval process, the feature keywords are expanded using synonyms to generate a more comprehensive set of expanded query terms. This set of expanded query terms is traversed, and node names are matched in the science knowledge graph. The semantic relevance score between all matched graph nodes and the current virtual simulation teaching scenario is calculated, and nodes with relevance scores higher than a preset threshold and their adjacent nodes in the graph are selected. Text content is extracted from the selected nodes and their adjacent relationships and encapsulated into structured physical principle descriptions and engineering application case data for display.

[0046] In practical implementation, the knowledge graph association step extracts feature keywords from the 3D geometric topology. These feature keywords are derived from the analysis of textual information such as geometric shape descriptions, material names, and Boolean operation types of the 3D geometric topology. The extraction process utilizes natural language processing technology to identify core noun phrases from the attribute tags of the 3D geometric topology and user input commands. The extracted feature keywords are input into the retrieval interface of the science popularization knowledge graph. This retrieval interface is a query service based on a graph database, receiving text keywords and returning related node and edge information from the graph. The science popularization knowledge graph retrieval interface returns physical principle descriptions and engineering application case introductions related to the feature keywords. The physical principle descriptions explain scientific laws related to the 3D geometric topology or material properties, while the engineering application case introductions showcase actual products and application scenarios with similar geometric features or material properties. The returned physical principle descriptions and engineering application case texts are overlaid and displayed in the narration area of ​​the real-time printing process animation. The narration area is a fixed or collapsible text display panel next to the rendered screen, and the physical principle descriptions and engineering application case texts are presented in a segmented, highlighted, or interactively linked format.

[0047] In some embodiments, the feature keywords are expanded using synonyms to generate an expanded query term set. Synonym expansion is achieved by querying a pre-built thesaurus or calculating semantic similarity using a word vector model. The expanded query term set contains the original feature keywords and semantically similar words. The expanded query term set is traversed, and node names are matched in the science knowledge graph. The matching process is either exact string matching or fuzzy matching based on semantic similarity. The matched nodes are graphical nodes representing concepts, entities, or attributes in the knowledge graph. The relevance score between the matched nodes and the current teaching scenario is calculated. The relevance score comprehensively considers the semantic relevance between the node and the feature keywords, the contextual importance of the node in the current simulation teaching step, and the topological centrality of the node in the knowledge graph. One possible calculation method for the relevance score is as follows:

[0048] in: Indicates the relevance score; This represents the semantic similarity score between the node name and the feature keywords; This represents the relevance score of a node to the current teaching context. For example, when explaining support structures, nodes related to "stress concentration" would receive a higher score. value; This represents a measure of the centrality of nodes in a science knowledge graph. , and This is a preset coefficient used for weighted summation. It filters nodes and their adjacency relationships whose relevance scores are higher than a preset threshold. The preset threshold is a configurable value used to filter knowledge nodes with low relevance. Adjacency relationships are edges in the graph connecting the filtered node to its directly adjacent nodes, and the edges themselves have relationship type labels. It extracts the text content from the nodes and their adjacency relationships, encapsulating it into physical principle descriptions and engineering application cases. The text content comes from the attribute fields of the knowledge graph nodes.

[0049] Optionally, data comparison reflects the differences in the content of physical principle descriptions and engineering application cases returned when using different feature keywords for retrieval. For example, when the feature keyword includes "cantilever beam," the retrieval interface may return the physical principle description of "lever principle" and the engineering application case of "crane boom"; when the feature keyword includes "porous structure," the retrieval interface may return the physical principle description of "topology optimization" and the engineering application case of "lightweight aerospace components." In some embodiments, the retrieval interface of the popular science knowledge graph supports multi-hop queries. When querying for "polylactic acid" material, the interface not only returns the direct attributes of the material node but also its adjacent "biodegradable" principle node and "degradable medical device" application case node. It can be understood that when the encapsulated physical principle description and engineering application case text are displayed in the sidebar area, they will be dynamically sorted and updated according to their real-time relevance to the current simulation step. For example, when the printing process reaches the cantilever structure area, the principle description related to "necessity of support structure" or "material thermal deformation" is highlighted.

[0050] See Figure 5In the interactive teaching method of virtual simulation 3D printing for popular science education, the implementation of the nozzle optimal motion path planning module based on particle swarm optimization relies on intelligent optimization technology driven by multi-physics coupled simulation data. Specifically, the dashed line represents the contour boundary of the section to be printed. Its geometry is obtained by slicing the 3D geometric topology generated from the user-input solid modeling command through semantic parsing, and it serves as the constraint space for path planning. The solid line represents the optimal nozzle motion trajectory obtained after iterative convergence by the particle swarm optimization algorithm. This trajectory achieves multi-objective optimization of path length and thermal accumulation effect while satisfying the section contour boundary constraints. Triangular markers indicate the printing start point, and circular markers indicate the printing end point. The trajectory starts from the start point, continuously and smoothly scans back and forth across the printing area, and finally reaches the end point, completing the full printing plan for the section. The core logic of path planning involves deriving the contour curve of the cross-section to be printed from a multi-physics coupled printing process simulation model, using this as the feasible region for path planning; initializing a particle swarm, with each particle corresponding to a candidate nozzle scanning path; constructing a fitness function that integrates path length cost and heat accumulation penalty, where the heat accumulation penalty is calculated based on the local temperature history in the simulation model's evolution data to avoid the risk of local overheating during printing; iteratively updating the velocity and position of the particle swarm to drive the fitness function to continuously optimize until convergence; extracting the converged particle position information and smoothing it to finally generate the optimal nozzle motion trajectory shown in the figure. This trajectory minimizes the total length of the printing path while ensuring the integrity of the printed coverage, suppresses local thermal stress concentration, and provides accurate motion-driven data for the virtual rendering engine, supporting the generation of real-time printing process animations and visualization for popular science education.

[0051] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A virtual simulation 3D printing interactive teaching method for science popularization education, characterized in that: include: Obtain the solid modeling instructions and material selection parameters input by the user; The entity modeling instructions are semantically parsed to generate a three-dimensional geometric topology. The material selection parameters are mapped to a material physical property database to extract thermodynamic property parameters. By integrating the three-dimensional geometric topology and the thermodynamic property parameters, a multi-physics coupled printing process simulation model is constructed. The evolution data of the multiphysics coupled printing process simulation model is input into a path planning engine based on particle swarm optimization to generate the optimal nozzle motion trajectory. The virtual rendering engine is driven by the optimal nozzle motion trajectory to output a real-time printing process animation; Collect learners' interactive behavior in response to the real-time printing process animation, and update the boundary constraints of the three-dimensional geometric topology. Based on the changes in the boundary constraints, the multiphysics coupled printing process simulation model is iterated again to generate corrected printing teaching feedback information.

2. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 1, characterized in that, The entity modeling instructions are semantically parsed to generate a three-dimensional geometric topology, specifically including: The solid modeling instructions input by the user include sketch drawing trajectory, extrusion height value, and Boolean operation type; Identify the feature line segments in the sketch drawing trajectory and extract the endpoint coordinates and curvature extreme points; Based on the stretching height value, the feature line segment is vector-translated to construct an initial three-dimensional mesh framework; The Boolean operation types are parsed, including union, intersection, and difference operations. The initial three-dimensional mesh framework is geometrically merged or trimmed according to the Boolean operation type to form a closed three-dimensional geometric topology; Verify the manifold integrity of the three-dimensional geometric topology and remove overhanging edges and overlapping surfaces.

3. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 2, characterized in that, The material selection parameters are mapped to a material physical property database, and thermodynamic property parameters are extracted, specifically including: The material selection parameters include a material name identifier and a filler density percentage; Retrieve entries from the material physical property database that match the material name identifier; Read the pre-stored melting point temperature, thermal conductivity coefficient, and shrinkage rate values ​​from the entry; The thermal conductivity coefficient is linearly interpolated and corrected based on the fill density percentage to generate an effective thermal conductivity coefficient. The combination of the melting point temperature, the shrinkage rate, and the effective thermal conductivity is defined as the thermodynamic characteristic parameter.

4. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 3, characterized in that, By integrating the aforementioned three-dimensional geometric topology and thermodynamic property parameters, a multi-physics coupled printing process simulation model is constructed, specifically including: The three-dimensional geometric topology is divided into tetrahedral meshes to generate a finite element analysis mesh; The thermodynamic property parameters are assigned to each element node of the finite element analysis mesh; Define a heat source term that simulates the laser heating process of a printhead; A thermal stress constitutive equation is established, which relates temperature change to structural deformation displacement. The heat source term is coupled with the thermal stress constitutive equation to form the multi-physics coupled printing process simulation model.

5. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 4, characterized in that, The evolution data of the multiphysics-coupled printing process simulation model is input into a particle swarm optimization-based path planning engine to generate the optimal nozzle motion trajectory, specifically including: The contour curve of the cross section to be printed is derived from the multiphysics coupled printing process simulation model. Initialize the particle swarm, with each particle representing a candidate nozzle scanning path; Define a fitness function that includes path length cost and heat accumulation penalty term; The heat accumulation penalty term is calculated based on the local temperature history in the evolution data; The velocity and position of the particle swarm are iteratively updated until the fitness function converges. The converged particle position information is extracted and smoothed to obtain the optimal nozzle motion trajectory.

6. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 5, characterized in that, Based on the optimal nozzle motion trajectory, the virtual rendering engine is driven to output a real-time printing process animation, specifically including: Analyze the discrete points and timestamps in the optimal nozzle motion trajectory; Generate a nozzle movement pose matrix based on the discrete points; The shader program is invoked to gradually accumulate material textures on the surface of the three-dimensional geometric topology according to the nozzle movement pose matrix. The color gradient rate of the simulated cooling and curing visual effect is determined by the thermal conductivity coefficient in the thermodynamic property parameters. The rendered frame sequence is encoded into the real-time printing process animation.

7. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 6, characterized in that, Collect learners' interactive behaviors in response to the real-time printing process animation, and update the boundary constraints of the three-dimensional geometric topology, specifically including: Monitor learners’ input device operations, including mouse click locations and keyboard shortcut commands; Identify the collision object at the mouse click location in the real-time printing process animation; The modification intent corresponding to the keyboard shortcut command is analyzed, and the modification intent includes undoing the previous step, rotating the viewing angle, or adding a support structure; When the modification is intended to add a support structure, a tapered support geometry is generated below the collision object; The conical support geometry is used as a new geometric constraint and incorporated into the boundary constraint conditions of the three-dimensional geometric topology.

8. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 7, characterized in that, Based on the changes in the boundary constraints, the multiphysics coupled printing process simulation model is iterated again to generate revised printing teaching feedback information, specifically including: The tapered support geometry in the boundary constraint conditions is converted into a finite element load boundary. The thermal stress distribution of the multiphysics coupled printing process simulation model was re-solved; Detect whether there are regions in the thermal stress distribution that exceed the material's yield strength; If there is a region exceeding the material's yield strength, generate the corrected printed teaching feedback information, which includes risk warning text and structural optimization suggestions; If there is no region exceeding the material yield limit, the corrected printing instruction feedback information, including printing time estimates and material usage statistics, is generated.

9. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 8, characterized in that, It also includes knowledge graph association steps, specifically including: Extract the feature keywords of the three-dimensional geometric topology; Input the aforementioned key features into the science popularization knowledge graph retrieval interface; The popular science knowledge graph retrieval interface returns physical principle descriptions and engineering application cases related to the feature keywords; The description of the physical principles and the engineering application examples are overlaid and displayed in the narration area of ​​the real-time printing process animation.

10. The virtual simulation 3D printing interactive teaching method for science popularization education as described in claim 9, characterized in that, Inputting the aforementioned feature keywords into the science popularization knowledge graph retrieval interface specifically includes: The feature keywords are expanded using synonyms to generate an expanded query term set; Traverse the extended query term set and match node names in the popular science knowledge graph; Calculate the relevance score between the matched nodes and the current teaching scenario; Filter nodes whose correlation scores are higher than a preset threshold and their adjacent relationships; Extract the text content from the nodes and their adjacency relationships, and encapsulate it into the physical principle description and the engineering application case.

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