Real-time simulation method for key pressure-bearing component of mechanical equipment structure based on digital twinning

Abstract

The invention provides a mechanical equipment structure key pressure-bearing component real-time simulation method based on digital twinning, which takes a cubic press hinge beam as an example, and combines finite element analysis, Latin hypercube sampling, a K nearest neighbor algorithm, Gaussian interpolation and an RBF (Radial Basis Function) proxy model to realize stress-strain rapid prediction and three-dimensional visualization. According to the method, an efficient prediction model is established through structure database construction, dimension reduction processing, neighbor search and interpolation calculation, a simulation result is presented in real time by utilizing Python and Unity interaction, the design efficiency and accuracy are improved, and the method is suitable for structure optimization analysis under complex working conditions.

Description

Technical Field

[0001] This patent application relates to the field of digital twins, specifically a real-time simulation method for key pressure-bearing components of mechanical equipment structures based on digital twins. Background Art

[0002] In mechanical equipment, critical pressure-bearing components are responsible for transferring loads, supporting, and withstanding mechanical stress. They are the core components of the equipment, determining its operational performance and service life. Their role is not limited to supporting loads; they must also ensure the proper functioning of the entire mechanical system under high-intensity, high-frequency, and complex environmental conditions. Failure or performance degradation of any pressure-bearing component can lead to equipment failure, further impacting the stability, reliability, and safety of the entire system. Therefore, the design, manufacture, and maintenance of these critical pressure-bearing components are crucial and fundamental to ensuring the safe and reliable operation of mechanical equipment.

[0003] Mechanical equipment often operates in complex and changing environments, subject to factors such as high temperature, high pressure, and vibration. Pressure-bearing components, when subjected to varying loads and stress distributions, may experience deformation, fatigue, wear, and even cracks, impacting the proper functioning of the equipment. To ensure the stability and reliability of mechanical equipment in complex environments, accurate performance prediction and monitoring of pressure-bearing components is essential.

[0004] For example, a six-sided diamond press is a key piece of equipment in the diamond production process, responsible for the ultra-high-temperature and high-pressure synthesis process, including pressure feeding, pressure maintenance, ultra-high pressure, and heating. However, under long-term alternating loads, the hinge beam ears of the six-sided press are prone to cracks and fractures, making it unable to meet the demand for increasingly large-scale diamond presses.

[0005] Traditional multi-condition analysis methods, especially in the finite element analysis (FEA) process, are difficult to meet the needs of real-time monitoring and design optimization due to problems such as large computational complexity and long time consumption. In order to improve the efficiency of stress and strain analysis of the hinge beam of the six-sided top press and adapt to the demand for fast stress and strain solution methods in production, the introduction of digital twins in recent years has provided a new approach to solving this problem. Through the digital twin system, the stress and strain data of the hinge beam under different working conditions can be quickly predicted at a lower computational cost. Compared with traditional methods, it not only significantly improves the analysis efficiency, but also combines visualization means to intuitively display the stress state of the hinge beam in a very short time, providing engineers with reliable information and helping to optimize design and decision-making.

[0006] Traditional mechanical equipment detection and analysis methods mainly rely on field testing, manual experience judgment and static simulation models. Although these methods have achieved certain success in some applications, they cannot effectively cope with dynamically changing environments and variable states of equipment under complex working conditions. In addition, with the increasing complexity of mechanical structures, traditional methods often find it difficult to capture and analyze subtle changes in key pressure-bearing components in real time, resulting in poor failure prediction capabilities. At present, the force analysis of the hinge beam of the six-sided top press mainly relies on finite element analysis (FEA) technology. The finite element method can provide more accurate calculation results such as stress, strain, and displacement by discretizing the hinge beam into small units and solving its force state. However, the FEA method has the following defects in practical applications:

[0007] 1. High computational cost and difficulty in real-time solution: Due to the geometric complexity and demanding load environment of hinged beams, FEA models typically contain a large number of elements and nodes. Each adjustment to loads or geometric parameters requires recalculation, resulting in long calculation times and failing to meet the real-time feedback requirements of engineering. 2. Difficulty in data storage and management: Traditional FEA simulation results are typically large discrete data files with a lack of efficient organization, making data storage and access difficult and hindering further optimization and application. Summary of the Invention

[0008] To overcome the limitations of traditional FEA methods, this paper proposes a real-time simulation method for key pressure-bearing components of mechanical equipment structures based on digital twins. By leveraging machine learning proxy models and 3D visualization technology, this method achieves efficient simulation and intuitive interaction of hinged beam structures. The method includes the following steps:

[0009] S1: Finite Element Preprocessing

[0010] S2: Extract working condition samples

[0011] S3: simulation sampling points

[0012] S4: Create a database

[0013] S5: Simplify the mesh and perform stress analysis

[0014] S6: Using radial basis function (RBF) to build a proxy model

[0015] S7: Unity model import

[0016] S8: Python and Unity interaction

[0017] S9: Create input boxes in Unity to allow users to enter different loads, boundary conditions and other parameters.

[0018] Furthermore, step S1 is specifically as follows:

[0019] S1.1 3D modeling and file export

[0020] S1.2 Import into Ansys and perform thermal-structural analysis pre-processing

[0021] S1.3 Setting material properties

[0022] S1.4 Create analysis unit type

[0023] S1.5 Grid division

[0024] S1.6 Setting fixed constraints

[0025] S1.7: Apply boundary conditions

[0026] S1.8: Perform coupled thermal-structural analysis

[0027] Furthermore, step S2 is specifically as follows:

[0028] S2.1: Constructing the initial Latin hypercube sampling

[0029] S2.2: Sorting and Optimizing Latin Hypercube Matrices

[0030] Furthermore, step S4 is specifically as follows:

[0031] S4.1: Obtain sample data

[0032] S4.2 Extracting simulation result information

[0033] S5: Simplify the mesh and perform stress analysis

[0034] Furthermore, step S5 is specifically as follows:

[0035] S5.1: Mesh simplification and dimensionality reduction

[0036] S5.2: Mesh Preprocessing

[0037] S5.3: Use K-nearest neighbor (KNN) algorithm for classification or regression analysis

[0038] S5.4: Gaussian function interpolation

[0039] Compared with the prior art, this patent application has the following advantages:

[0040] 1. Improve computational efficiency: By using machine learning proxy models (such as neural networks and XGBoost), a fast prediction model can be trained based on existing FEA data, which can respond to changes in input parameters in a short time and significantly reduce computational costs.

[0041] 2. Intelligent data management: By building a structured database, FEA simulation data can be organized into a unified training data set to facilitate subsequent calls and optimization.

[0042] 3. Interactive visualization improves engineering design efficiency: Using Python-Unity interaction, the prediction results of the proxy model are displayed in a 3D environment in intuitive forms such as stress cloud maps and deformation animations. This allows engineers to adjust parameters in real time and observe their impact, improving the optimization design efficiency of the hinge beam of the six-sided top press.

[0043] Through digital twin modeling, machine learning prediction and three-dimensional interactive visualization, this invention provides a simulation solution that is more efficient and intuitive than the traditional FEA method, which is of great significance to the design optimization of the hinge beam of the six-sided top press. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is the overall flow chart of this method;

[0045] Figure 2 Simple structural framework of radial basis function RBF algorithm;

[0046] Figure 3 Flowchart of radial basis function RBF algorithm;

[0047] Figure 4 Import the model into Unity flowchart;

[0048] Figure 5 Visualizing prediction graphs of hinged beams in Python;

[0049] Figure 6 Visualization of hinge beam predictions in Unity. DETAILED DESCRIPTION

[0050] like Figures 1-6 As shown, the present invention provides a real-time simulation method for key pressure-bearing components of mechanical equipment structures based on digital twins, which can efficiently predict the force response of hinge beams and display deformation and stress cloud maps in real time in a virtual environment. The present invention includes the following steps:

[0051] S1: Finite Element Preprocessing

[0052] S1.1 3D modeling and file export

[0053] Use SolidWorks 3D modeling software to model the hinge beam of a six-sided top press. Ensure the model is complete, including all key structural details such as ear holes, chamfers, and piston travel. Export the completed hinge beam to .xt format for import into Ansys for finite element analysis.

[0054] S1.2 Import into Ansys and perform thermal-structural analysis pre-processing

[0055] Import the hinge beam model in xt format into Ansys Workbench, select the static structural analysis module to simulate the stress conditions of the hinge beam in the working state, and set the pre-processing settings such as analysis unit type, mesh division rules, and boundary conditions.

[0056] S1.3 Setting material properties

[0057] The six hydraulic cylinders must withstand pressures up to 96 MPa. 42CrMo alloy structural steel was selected as the material for the hinge beams, and its mass density, elastic modulus, Poisson's ratio, shear modulus, and thermal expansion coefficient were assigned. The accuracy of these material parameters ensured the reliability of the simulation results.

[0058] S1.4 Create analysis unit type

[0059] The mesh is generated using the tetrahedral Solid187 element, which is suitable for complex geometries and can well adapt to the irregular shapes of hinge beams. It has high computational accuracy and is suitable for static analysis.

[0060] S1.5 Grid division

[0061] Due to the complex structure of the hinge beam, meshing was performed using a coarse mesh overall with refinement in key areas. A 30mm mesh was used throughout the hinge beam to ensure computational efficiency. Critical stress-bearing areas (high stress concentration zones) were refined to a 10mm mesh. The bottom and chamfered areas were refined to improve stress analysis accuracy. The piston travel was refined to accurately capture stress variations. Areas prone to deformation or fracture (the ear holes and the sides of the ears) were refined to a 10mm mesh to improve the accuracy of fracture and fatigue predictions.

[0062] S1.6 Setting fixed constraints

[0063] Degrees of freedom were restricted at the hinge beam axis holes to ensure that the simulation matched actual operating conditions. For the double-ear holes, their y-axis rotation was restricted to prevent lateral deviation, and their x-axis movement was restricted to ensure stable position under load. For the triple-ear holes, their x-axis rotation was restricted to prevent excessive distortion under load, and their y-axis movement was restricted to prevent structural deformation and failure.

[0064] S1.7: Apply boundary conditions

[0065] In Ansys, the temperature T is simulated and analyzed first, and then the results are imported into the static structure module to continue the simulation of the pressure P. The pressurization process of diamond usually includes the following stages: pressure feeding, pressure holding, ultra-high pressure, pressure holding, secondary pressurization, and pressure holding. The temperature range is 0 to 200 ° C. Two boundary conditions are set in the simulation: temperature T and pressure P. In order to fully analyze the behavior of the system, n different temperature boundary conditions Ti (i = 1 ... n) and m different pressure boundary conditions Fj (j = 1 ... m) are applied respectively, and the stress distribution ε under each temperature Ti and pressure Fj is analyzed. ij And the strain σ under the corresponding working condition ij .

[0066] S1.8: Perform coupled thermal-structural analysis

[0067] Thermal-structural coupling analysis is a key step in analyzing the stress and deformation of a structure in a thermal environment. The main process includes temperature field analysis, thermal stress analysis, and structural stress analysis.

[0068] S1.8.1: Temperature field analysis:

[0069] Thermodynamic finite element analysis follows the basic principles of the finite element method, dividing the structure into several units and calculating the temperature distribution within the entire structure by solving the temperature of each unit. In ANSYS Workbench, there are two thermal analysis methods to choose from: steady-state thermal analysis and transient thermal analysis.

[0070] Perform thermal steady-state analysis, the formula is as follows:

[0071] [K]{I}={Q}

[0072] Where [K] is the conduction matrix, {I} is the temperature vector of the node, and {Q} is the heat flow vector of the node.

[0073] Heat transfer methods include heat conduction, heat convection, and heat radiation. In the heat transfer of the top hammer, heat conduction is the main method. In the steady-state heat transfer process, the applied temperature load remains unchanged, and the expression is:

[0074]

[0075] Where Φ is the heat flow, A is the area of ​​the anvil surface, λ is the thermal conductivity of the anvil material, T is the temperature, and x is the coordinate axis perpendicular to the action surface.

[0076] For any point P(x,y,z) in the rectangular coordinate system, the heat conduction differential equation can be established based on energy conservation and Fourier's law:

[0077]

[0078] Where ρ is the density of the material, c is the specific heat capacity, t is the time, and λ x ,λ y ,λ z is the thermal conductivity of the material in the x, y, and z directions. Φ0 is the density of the heat source.

[0079] In thermal analysis, the temperature load is applied to each element node using the interpolation method, thereby determining the temperature function of the element, which is expressed as:

[0080]

[0081] Since the temperature load remains unchanged during steady-state heat transfer, the unit heat transfer matrix equation can be obtained by combining the unit temperature field function with the boundary conditions of steady-state heat transfer.

[0082]

[0083] Where, is the unit heat transfer matrix, is the unit node temperature matrix, is the equivalent temperature load matrix of the unit node.

[0084] S1.8.2: Thermal Stress Analysis

[0085] The finite element analysis is performed using the indirect one-way coupling method of thermal force, the physical equation based on temperature analysis, and the principle of virtual work. Due to the temperature difference ΔT(x,y,z) inside the top hammer structure, it will cause the corresponding thermal expansion α T ·ΔT(x,y,z)(α T is the thermal expansion coefficient of the material). Substituting the thermal expansion into the physical equation of the structure:

[0086]

[0087] S1.8.3: Structural Stress Analysis:

[0088] Stress field analysis is essential for analyzing the mechanical properties of a structure under specific loading conditions, such as the stress and deformation at a specific location. The hinged beam structure in this paper is susceptible to cyclical loading, which can lead to structural failure. Therefore, stress field analysis of the hinged beam structure not only analyzes the stress and strain distribution at various locations, identifying stress concentrations and vulnerable areas, but also provides a reference for subsequent structural optimization.

[0089] In the finite element analysis of Workbench, the displacement and stress of the entire model are obtained by solving the displacement and stress of each unit. The expression is:

[0090] {f}=[K]{δ}

[0091] Where {f} is the load matrix of the entire structure, [K] is the stiffness matrix of the entire structure, and {δ} is the displacement matrix of the entire structure.

[0092] The following formula is then used to determine whether the structure will fail. This formula assumes that material yield is caused by the distortion energy density. Assuming that the shape-change energy density is the cause of material yield, plastic yield will occur under any stress conditions if the shape-change energy density at any point in the structure exceeds the material's yield threshold.

[0093]

[0094] Where, σ eq is the equivalent stress, σ1σ2σ3 are the first, second and third principal stress values ​​respectively, [σ] is the allowable stress value. The formula is: when the stress value applied to the structure is less than the allowable stress value, the strength of the structure meets the design requirements and static failure will not occur.

[0095] S2: Extract working condition samples

[0096] Because the pressure and temperature ramps in the diamond hexagonal press synthesis process take a long time, a joint simulation of n pressure points and m temperature points to obtain the corresponding stress and strain data would result in n × m scenarios, resulting in excessive simulation times and time. To avoid this, a Latin hypercube sampling method was employed to sample the various temperature and pressure stages of the hexagonal press hinge beam during pressure delivery, pressure holding, pressurization, and ultrahigh pressure. By selecting a limited number of key points to replace the entire simulation process, sample optimization was achieved with minimal computational effort.

[0097] Sampling is performed using the improved Latin Hypercube method (LHS):

[0098] Assume that the input variable of the problem is n-dimensional, the input variable can be continuous or discrete, and each input variable X i The distribution of is specified as the interval [a i ,b i ] or probability distribution function P i (x). The distribution of each input variable can be uniform distribution, normal distribution, etc.

[0099] For each variable X i , we can use the following normalization transformation to map it to a standard interval [0,1]:

[0100] X′ i ∈[0,1]

[0101] S2.1: Constructing the initial Latin hypercube sampling

[0102] The input space is divided in each dimension. Let the number of samples be N, and each input variable X i Divided into N equal-length intervals:

[0103] [a i ,b i ] is divided into N intervals

[0104] For each dimension X i , select a sample point X in each interval ij (where j = 1, 2, ..., N.) A point is randomly selected in each interval and the points in all dimensions are combined into an N × n matrix.

[0105] S2.1: Sorting and Optimizing Latin Hypercube Matrices

[0106] Create a new N×n Latin hypercube matrix, sort the sample points on each dimension, and calculate the distance d between all random representative "numbers" through some optimization algorithm ij , and for d ij Sort and get the distance list {d1, d2…d s} and the index list {j1,j2…j s}. Ensure that the distance between each sample point is as large as possible. The new objective function is to minimize the average distance between sample points:

[0107]

[0108] Among them, d i Represents different distance values, j i Represents the distance d i The number of points; d ij is the sample point X i and X j The distance between them is usually defined using the Euclidean distance:

[0109]

[0110] By calculating φ p , to select the most sampled.

[0111]

[0112] Wherein, P is a positive integer;

[0113] If the Latin hypercube sampling φ p If the value is the smallest, then the sample set is selected as the optimal sampling, otherwise recalculate from the first step.

[0114] S3: simulation sampling points

[0115] Through S2, the sampling points of temperature and pressure are obtained after solution. The working condition of the local key point replaces the overall working condition of the hinge beam of the six-sided top press. S1.7 is called to apply boundary conditions for simulation and solve the corresponding stress σ ij , strain ε ij wait.

[0116] S4: Create a database

[0117] S4.1: Obtain sample data

[0118] In the finite element solution - equivalent stress / equivalent strain - export the text file and save the file type as .xls

[0119] S4.2 Extracting simulation result information

[0120] Obtain sample data, in the finite element solution - equivalent stress / equivalent strain - export text file, and save the file type as .xls, extract the mesh node number (ID), the value of the node coordinates X, Y, Z, and the stress and strain corresponding to the node.

[0121] S5: Simplify the mesh and perform stress analysis

[0122] S5.1: Mesh simplification and dimensionality reduction

[0123] Construct a new static structural mesh for the hinge beam. This mesh is not used for any finite element calculations and is only used as a geometric basis for mesh simplification. The specific steps are as follows:

[0124] S5.1.1: Mesh

[0125] The structure is divided into a simplified mesh using standard mesh generation tools. This mesh is not used for any stress calculation and is only used as the basis for the subsequent interpolation process.

[0126] S5.1.2: Export triangular patch format

[0127] Export the geometric information of the simplified mesh as triangular facets and obtain the coordinate position of each mesh node.

[0128] S5.1.3: Dimensionality reduction

[0129] The simplified grid data is processed for dimensionality reduction to reduce the dimension of grid node data and remove redundant information, thereby further reducing the computational burden.

[0130] S5.2: Mesh Preprocessing

[0131] In the simplified mesh model, a total of 22,328 nodes were generated, represented by triangular facets. However, because multiple triangular facets may share the same vertices, this leads to a significant amount of redundancy in the node data. Therefore, the mesh nodes were deduplicated to eliminate duplicate data. After deduplication optimization, 11,486 independent nodes were retained, which were used as 3D coordinate input for subsequent calculations and analysis.

[0132] S5.3: Use K-nearest neighbor (KNN) algorithm for classification or regression analysis

[0133] The K-Nearest Neighbors (KNN) algorithm is used to solve regression and classification problems. For regression problems, the K nearest neighbors of a test sample are found and predictions are made based on the target values ​​of these neighbors. In the KNN algorithm, Euclidean distance is the most commonly used similarity measure, and its calculation formula is:

[0134]

[0135] The KNN algorithm was used for data classification and regression analysis. After simplifying the data points, 11,486 nodes were obtained, which were distributed among the 72,814 nodes in the fine grid. For each simplified node, its 15 nearest neighbors (i.e., K = 15) were found and their location information was used for further calculations. The Euclidean distance between each simplified node and the fine grid node was calculated, and the K nodes with the smallest distance were selected as the node's nearest neighbors.

[0136] S5.4: Gaussian function interpolation

[0137] For the 15 neighbors found, Gaussian interpolation is used to fill in the missing stress data. Gaussian interpolation is used as a weighted average interpolation method, where the weight of each neighbor is calculated based on its distance to the interpolation point. The closer the neighbor, the greater its weight and the greater its contribution. The interpolation formula is:

[0138]

[0139] in,

[0140] w i is the weight of the ith neighbor, usually calculated by the distance.

[0141] f(x i ) is the target value of the i-th neighbor.

[0142] S6: Using radial basis function (RBF) to build a proxy model

[0143] The core idea of ​​RBF networks is to approximate complex nonlinear relationships using a set of radial basis functions. These basis functions transform the input data into a high-dimensional space, making the relationships between the data easier to model using linear methods. The training process involves determining the center and width of the basis functions (usually through clustering methods such as k-means) and learning the weights connecting the hidden layer to the output layer using methods such as least squares or gradient descent.

[0144] Construct the input layer: This layer is responsible for receiving input data and passing the data to the hidden layer. The input layer itself does not perform any calculations, but only passes information.

[0145] Constructing the hidden layer: This layer consists of multiple RBF nodes, each of which uses a basis function (usually a Gaussian function) to process the input data. Each node calculates the distance between the input data and the center point and generates a response based on this distance. The response generally decreases as the distance from the center point increases. Basis function selection: RBF usually uses a Gaussian function, whose formula is as follows:

[0146]

[0147] in,

[0148] x is the input data,

[0149] c is the center of the basis function,

[0150] σ is the width parameter.

[0151] Construct the output layer: The output layer performs a weighted summation on the output of the hidden layer to generate the final prediction result. The nodes in the output layer are usually linear nodes, and the output of the model is calculated by weighted summation. The calculation formula of the output layer is:

[0152]

[0153] in,

[0154] w i is the learned weight,

[0155] φ i (x) is the response of the hidden layer node

[0156] S7: Unity model import

[0157] Import the saved xt format model into 3DMax, convert it to FBX format, and then import it into Unity.

[0158] S8: Python and Unity interaction

[0159] The user input parameters are passed to the Python agent model and the prediction results are obtained through Python-Unity communication (WebSocket). In Unity, a TCP client is created using C# scripts. A connection to the Python server is established, and data is sent and received. In Python, a TCP server is created to communicate with Unity. Through the socket module, a server that listens to a specified IP address and port is created, and connections from Unity are accepted. Once a connection is established, communication with Unity is achieved by sending and receiving data.

[0160] S9: Input boxes are created in Unity to allow users to input different load, boundary conditions, and other parameters.

[0161] The prediction results include stress distribution, deformation data, etc., which are converted to a format suitable for Unity by Python. Unity calls the data returned by Python and renders stress cloud charts in real time in the 3D scene, achieving interactive visualization. Techniques such as Shader are used to render stress distribution charts in Unity. Users can dynamically adjust input parameters and observe the deformation of the beam in real time, supporting interactive operations such as rotation, scaling, and switching between different views.

[0162] The above is only the preferred embodiment of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make a number of improvements and refinements, these improvements and refinements should also be considered within the scope of the present application. The components not explicitly described in the embodiments can be implemented using existing technology.

Claims

1. A real-time simulation method for key pressure-bearing components of mechanical equipment structures based on digital twins, characterized in that: The steps include: S1: finite element pre-processing; S2: Extract working condition samples; S3: simulation sampling point; S4: Establish database; S5: Perform stress analysis after mesh simplification; S6: constructing a proxy model using radial basis function; S7: Unity model import; S8: Python and Unity interaction; S9: Create input boxes in Unity to allow users to enter different loads, boundary conditions and other parameters.

Images