Method for constructing double-order-reduced digital twin physical field of numerically controlled machine tool

Abstract

Disclosed in the present invention is a method for constructing a double-order-reduced digital twin physical field of a numerically controlled machine tool. The method comprises: performing preliminary order reduction on finite element simulation sample data sets of a physical field in a working state sampling space to form sparse grid node data by means of an improved KNN algorithm, so that the number of nodes sets is kept within a real-time rendering capability of graphics rendering software; by using a radial basis function (RBF), obtaining a digital twin physical field proxy model by means of training, to implement reconstruction of the physical field; on the basis of a genetic algorithm, iteratively optimizing the digital twin physical field proxy model, to solve the problem of deviation between a proxy physical field model and a real physical model; and finally, deploying the digital twin physical field proxy model to a digital twin system and solving a physical field distribution in real time. According to the present invention, reflecting of the spatial distribution of a related structural field and a temperature field in the digital twin system is implemented, so that simulation of a virtual-real mirror mapped physical field driven by real-time operation data is implemented.

Description

A double-reduced-order method for constructing the physical field of digital twins of CNC machine tools

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on September 6, 2023, with application number 202311144249.5 and invention name “A method for constructing a digital twin physical field of a double-reduced-order CNC machine tool”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present invention relates to a method for constructing a finite element physical field of a CNC machine tool, and in particular to a method for constructing a digital twin physical field of a CNC machine tool with double order reduction. Background Art

[0003] In industrial production, operations, and maintenance, digital twin technology leverages physical models to integrate real-time online data with historical data from test experiments. This technology integrates multidisciplinary, multi-performance simulation processes, maps physical properties in virtual space, and provides feedback on the equipment's operating status. To fully reflect the spatial distribution of multiple physical properties of industrial equipment, the physical properties of the equipment are typically simulated and analyzed using numerical methods such as finite element analysis.

[0004] Due to the complex nature of industrial production environments, only a small amount of data can be obtained from sensors during the production process. For operational status monitoring, computationally intensive finite element analysis methods struggle to meet real-time requirements and cannot simultaneously visualize key physical properties of machine tools during operation. Therefore, there is an urgent need for digital twin systems that can fit the physical field in real time and enable visual monitoring of equipment physical properties.

[0005] The computational speed of a twin system is closely related to the hardware's computing power, algorithm complexity, and model complexity. For solving physical field problems in scenarios involving large datasets, a suitable proxy model can be used to fit and solve the physical field, thereby meeting the digital twin system's requirements for fast and accurate results. As a real-time fitting method for physical field states, the proxy model can present the spatial distribution of a product's key physical properties, driven by time series and environmental data. Using physical parameters as input, the proxy model can solve the three-dimensional field in seconds, replacing time-consuming finite element calculations.

[0006] Model reduction methods based on radial basis functions can, to a certain extent, meet the requirements for solving proxy models. However, for currently common virtual simulation software, the constructed proxy models must consider the real-time rendering capabilities of the twin system. Both the communication interface between the proxy model and the software and the software's real-time rendering capabilities place limitations on the number of model nodes. Low-quality proxy models often produce poor accuracy, resulting in a trade-off between the number of meshes and accuracy in current common proxy models.

[0007] Summary of the Invention

[0008] To address the issues presented in the prior art, this paper proposes a dual-reduction method for constructing a digital twin physical field for CNC machine tools. This method overcomes the shortcomings of the aforementioned existing methods, enabling real-time and stable communication between the digital twin system and the proxy model, virtual-to-real mirror-image triangular mesh rendering, and real-time physical field simulation. It also reduces the deviation between the physical field model and the actual physical model.

[0009] To achieve the above object, the technical solution of the present invention is as follows:

[0010] S1: Based on the working state parameters of the CNC machine tool, a finite element analysis mesh model of the CNC machine tool is established, as well as a working state sampling space of the CNC machine tool and a physical field finite element simulation sample data set constructed in the working state sampling space;

[0011] S2: Based on the physical field finite element simulation sample data set, the improved K-nearest neighbor algorithm is used to perform preliminary simulation data reduction on the finite element analysis mesh model to obtain the sparse mesh model and the simulation data corresponding to its mesh nodes;

[0012] S3: Based on the simulation data corresponding to the sparse grid model and its grid nodes, a digital twin physical field proxy model is established using radial basis functions to establish a mapping relationship between the grid nodes and the sampled data collected by the sensors at the key sampling points;

[0013] S4: Verify the virtual-real consistency of the digital twin physical field proxy model and the real sample data of the CNC machine tool. If the verification fails, optimize the digital twin physical field proxy model until a verified digital twin physical field proxy model is obtained and deployed in the digital twin system.

[0014] S5: Real-time sensor data is input into the digital twin system. Combined with the mapping relationship between the sampling data collected by the sensors of the grid nodes and key sampling points, the physical field distribution is obtained in real time through the digital twin physical field proxy model in the digital twin system.

[0015] The present invention adopts a double-reduction physical field proxy model construction method, and preliminarily reduces the sample data of the finite element solution results into relatively sparse grid node data through the KNN algorithm, so that the number of point sets remains within the real-time rendering capability of the graphics rendering software; uses RBF radial basis functions to train the proxy model to achieve physical field reconstruction; uses a genetic algorithm to iteratively optimize the proxy model; for proxy models that still have large deviations after convergence, a solution of reconstructing the proxy model is adopted; and realizes real-time data-driven virtual-to-real mirror mapping physical field simulation.

[0016] Compared with existing technologies and methods, the present invention has the following beneficial effects:

[0017] The present invention adopts the K-nearest neighbor algorithm with integrated boundary conditions to perform preliminary reduction of the physical field model, thus avoiding the center deviation of the physical field boundary fitting result, reducing the dense grid point cloud features to the physical information values ​​of each point of the sparse grid triangle patch, and keeping the number of grid points within the real-time rendering capability of the graphics rendering software.

[0018] After preliminarily reducing the physical field grid model, the present invention establishes a mapping relationship between all grid cells and the sensor sampling data of key sampling points through radial basis functions, thereby inferring the distribution of physical properties of the entire physical field based on different boundary condition information.

[0019] The present invention uses a genetic algorithm to iteratively optimize the proxy model. For proxy models that still have large deviations after convergence, the proxy model is reconstructed. This reduces the deviation between the proxy model results and the real physical model and improves the optimization efficiency of the proxy model.

[0020] In summary, the present invention achieves the construction of a physical field proxy model suitable for the digital twin system, thereby realizing real-time solution and simulation of the physical fields of key components in the industrial production process.

[0021] Figures in the specification

[0022] FIG1 is a schematic diagram of the overall process for the spindle portion of a grinding machine in an embodiment of the present invention;

[0023] FIG2 is a schematic diagram of the process of preliminary reduction of the physical field model using the K-nearest neighbor algorithm with fused boundary conditions in the implementation of the present invention;

[0024] FIG3 is a schematic diagram of the process of judging the virtual-real consistency of the digital twin physical field model during the implementation of the present invention;

[0025] FIG4 is a flowchart of an algorithm for iteratively optimizing a digital twin physical field proxy model using a genetic algorithm during the implementation of the present invention;

[0026] FIG5 is a schematic diagram of the process of optimizing the optimal solution of the digital twin physical field proxy model using a genetic algorithm during the implementation of the present invention. DETAILED DESCRIPTION

[0027] The present invention will be further described below with reference to the accompanying drawings and specific examples:

[0028] As shown in FIG1 , the embodiment of the present invention is described using a surface forming grinder as an example:

[0029] The CNC grinding machine model has a complex geometry, making it difficult to directly construct a complete physical model of the machine. This model also fails to clearly demonstrate the stress and deformation of key components during operation. The grinding head and spindle are the components that directly impact machining accuracy during actual machining. We extracted these spindle components from the CNC grinding machine model for boundary condition analysis and physical model construction.

[0030] From the perspective of physical field analysis, the physical field of the CNC grinding machine spindle is divided into two parts: structure field and temperature field. The main parameter variables include grinding depth a p , Grinding head speed V s and feed speed V w The force acting on the grinding wheel and workpiece during grinding is divided into two components, namely the normal component F of the grinding force n and the tangential component F t Grinding force can be divided into two parts: cutting deformation force and sliding force. Cutting deformation force can be divided into chip forming force and plowing force.

[0031] The boundary conditions of the temperature field are mainly the two parts of the grinding wheel spindle with rolling bearings and the grinding wheel. The heating of the rolling bearing is mainly affected by three factors: the rolling bearing model, the lubricant type, and the force of the rolling bearing. The heat flux of the grinding wheel mainly includes the heat flux into the workpiece q w , heat flux q removed by chips ch , heat flow q transferred to the grinding wheel s and the heat flux q transferred to the fluid by convection f .

[0032] As shown in FIG1 , the method includes the following steps:

[0033] S1: In the offline stage, according to the working state parameters of the CNC machine tool, a finite element analysis mesh model of the precision CNC machine tool is established, as well as a working state sampling space of the CNC machine tool and a physical field finite element simulation sample data set constructed under the working state sampling space.

[0034] Among them, in the physical field finite element simulation sample data set, the physical field includes the structural field and the temperature field, and the objects to which the finite element simulation sample data belongs are key components in CNC machine tools.

[0035] First, a working state sampling space of the CNC machine tool is established according to the working state parameters of the CNC machine tool (such as working time, spindle speed, feed rate, vibration and ambient temperature, etc.). Then, the working state of the CNC machine tool is sampled in the working state sampling space to obtain the machine tool sampling points. After parametric simulation analysis of the machine tool under the working state corresponding to each machine tool sampling point, a physical field finite element simulation sample data set is obtained.

[0036] In the specific implementation, the parameters that affect the physical properties of the target in the working state are divided into two aspects: timing parameters and environmental parameters. Based on the above two parameters, the working state parameters are constructed and parametric finite element analysis is performed. Among them, the timing parameters are variables such as execution time and movement speed that can be extracted through timing data; environmental parameters are variables such as temperature and vibration that are sensed by sensors. The working state parameter p can be represented as a vector: p = [a1,…,a m ,c1,…,c n ] T , where a1,…,a m are m timing parameters, c1,…,c n There are n environmental parameters. In addition, it is necessary to determine the value range of each parameter in the working state, so as to determine the sampling space p∈A1×…A m ×C1× …×C n , where A m 、C n They represent the value ranges of timing parameters and environmental parameters in the working state. Each additional parameter is equivalent to adding a dimension to the parameter space. m Indicates parameter a m The value range of C n Indicates parameter c n range of values. Then, according to the determined working state parameters, a parameterized finite element model is established, and the working state parameters are loaded onto the finite element model as boundary conditions. At the same time, the meshing of the finite element model remains consistent under various boundary conditions. Maintaining the uniformity of the finite element meshing provides a constant spatial distribution of unit nodes for the construction of the proxy model, thereby simplifying the selection of key sampling points. Several key values ​​are selected in the sampling space of the working state parameters, and the parameterized finite element model solution under multiple boundary conditions is implemented in the finite element analysis tool. In this embodiment, the force analysis and thermal boundary condition analysis of the spindle system are carried out, and the finite element solution of the temperature field of the spindle system is performed.

[0037] For each triangular patch in the finite element analysis mesh model of a CNC machine tool, each edge of the triangular patch consists of two directed half edges, which are used to represent its planar structure.

[0038] S2: Based on the physical field finite element simulation sample data set, the improved K-nearest neighbor algorithm (i.e., the K-nearest neighbor algorithm that integrates the boundary features of the mesh model) is used to perform preliminary reduction of the simulation data of the finite element analysis mesh model to obtain the simulation data corresponding to the sparse mesh model and its mesh nodes.

[0039] S2 is specifically:

[0040] S21: According to the physical field finite element simulation sample data set, all triangular facets in the finite element analysis mesh model are mapped to three-dimensional space, and then it is determined whether each triangular facet is on the surface of the mesh body or inside the mesh body, so as to determine whether each mesh node is an internal node of the mesh body or a surface node of the mesh body, and obtain a sparse mesh model; in the specific implementation, the triangular facets are used to construct a half-edge face S with vertex data, and the number of times t that the half-edge face S is used in all mesh units E is used to determine whether the triangular facet is on the surface of the mesh body, satisfying t=∑E∩S; when the number of times t is used is equal to 1, the node corresponding to the half-edge face is a surface node of the mesh body, and if the number of times t is used is greater than 1, it is an internal node of the mesh body.

[0041] S22: Use the K-nearest neighbor algorithm to calculate and update the physical property values ​​corresponding to each mesh internal node and each mesh surface node, and obtain simulation data corresponding to each mesh node in the sparse mesh model, where the weights of the mesh internal nodes and the mesh surface nodes are different.

[0042] Specifically:

[0043] For the spindle part of the grinding machine system, the spindle model is sparsely meshed using Ansys software. In order to keep the number of mesh points after division within the real-time rendering capability of the digital twin system, the number of mesh points divided is 6750 and the number of original mesh points is 24964. The vertex set of all surface mesh triangles after deduplication is recorded as D o Assuming that the grid points are evenly distributed, for each sparse grid node Q i For example, the n nodes of its nearest neighbors are calculated by Euclidean distance, denoted as D q .

[0044] For nodes inside the mesh, Then Q i is an internal node. Let the neighbor Q i The physical information value of the n nodes of the physical field is {p1, p2...p n}, in this embodiment, n=15, which is related to node Q i The distance is {d1, d2...d n}, then Q i The calculation of the corresponding point value of the physical field follows the following formula:

[0045] For nodes on the surface of the mesh, if D q ∩D o is not empty, the quantity is recorded as u, then Q i is the edge node in the sparse grid. i Neighbor's D oThe number of points u is used to assign the influence weights of n neighboring points. Then Q i The calculation of the corresponding point value of the physical field follows the following formula:

[0046] Among them, p out Q i The physical information value of the mesh surface node in the neighboring points, d out Q i The mesh surface nodes in the neighboring points of Q i The distance, d k Q i The kth nearest neighbor and Q i The distance, p in Q i The physical information value of the internal nodes of the mesh in the neighboring points, d in Q i The internal nodes of the grid body and Q i distance.

[0047] In the online phase, radial basis functions (RBFs) are used to build a digital twin physical field proxy model based on the simulation data corresponding to the sparse grid model and its grid nodes. Gaussian kernel functions are used as interpolation kernels for the RBFs. Quadratic order reduction of the simulation data is performed, and a mapping relationship is established between the grid nodes and the sampled data collected by sensors at key sampling points. This mapping relationship allows the physical property distribution of the entire physical field to be inferred from the discrete sensor data at key sampling points.

[0048] Specifically, suppose there are N input grid nodes with physical field analysis results in the multidimensional space, and the corresponding physical property value of each grid node at the spatial coordinate is d i , find a mapping function f(x)=d that satisfies the following conditions through RBF interpolation i , i = 1, 2, ... N. The digital twin system drives model updates through sensor data. The input variables in the training sample dataset are usually a subset of the control variables. Using the response values ​​of some nodes in the physical field as input, a mapping relationship f(x) is constructed from these discrete measurement points to all spatial nodes to achieve physical field reconstruction. The interpolation function t(x) based on the radial basis is defined as a linear combination of basis functions following the following formula:

[0049] Among them, w i is the interpolation coefficient, is the kernel function, x is the interpolation point, x i is the interpolation center, ||xx i || is the distance from the interpolation point to the interpolation center.

[0050] Calculate the RBF interpolation coefficient matrix W through the training sample data set, W = Φ -1 y, Φ are the radial basis function matrices, and y is the training sample matrix. The spatial coordinates and physical parameter values ​​of the sparse grid nodes sampled multiple times are used as input to train the physical field proxy model. By inputting variable parameters at different times, the corresponding physical values ​​of each node are output.

[0051] Since the position of the spindle where sensors can be placed directly is limited and the main heat flow comes from the two areas connected to the bearings, the boundary condition update process samples from the outside of the bearings at both ends of the spindle. T The corresponding temperature t=[t(x1),t(x2)] T Input the proxy model, x1 and x2 represent the positions of the bearings at both ends of the spindle, and solve the temperature field of the entire spindle system, as shown in Figure 2.

[0052] S4: Verify the virtual-reality consistency of the digital twin physical field proxy model and the real sample data of the CNC machine tool (signal data collected by the sensor corresponding to the real parts). If the verification fails, optimize the digital twin physical field proxy model until a verified digital twin physical field proxy model is obtained and deployed in the digital twin system.

[0053] S4 is specifically:

[0054] S41: Simulation data of physical quantities collected in the digital twin physical field agent model s and the real model of the CNC machine tool (i.e. the signal data collected by the sensor corresponding to the real part e ) performs virtual-real consistency verification. The smaller the deviation, the stronger the consistency between the virtual and real images of the physical field, and the more accurate the proxy model results, as shown in Figure 3. If the verification passes, the current digital twin physical field proxy model is used as the final digital twin physical field proxy model. Otherwise, execute S42.

[0055] S42: As shown in Figures 4 and 5, where part (a) in Figure 5 is the actual contour line, part (b) in Figure 5 is the RBF proxy model contour line, and part (c) in Figure 5 is the dynamic optimization proxy model contour line, a genetic algorithm with global optimization capability is used to iteratively optimize the digital twin physical field proxy model, where the population size is set to 50, the algorithm's termination evolution generation is 100, and the crossover probability is 0.5; the optimized digital twin physical field proxy model is obtained, where the relative error between the true objective function value corresponding to the possible optimal solution of the kth iteration and the k-1th iteration in the iterative optimization process is used to determine whether it has converged. The optimized digital twin physical field proxy model is verified for virtual-real consistency. If the verification passes, the current digital twin physical field proxy model is used as the final digital twin physical field proxy model. If the verification fails, S43 is executed. In specific implementation, when the relative error between the objective function value of the true model and the proxy model corresponding to the possible optimal solution in the kth iteration exceeds a preset threshold, the verification is considered to have failed.

[0056] S43: Use the Latin hypersquare sampling method to resample the working state of the CNC machine tool in the working state sampling space to obtain the machine tool sampling points, and then obtain the physical field finite element simulation sample data set. Repeat S2, S3 and S41 until the final digital twin physical field agent model is obtained and deployed in the digital twin system.

[0057] S5: Real-time sensor data is input into the digital twin system through socket communication. Combined with the mapping relationship between the sampling data collected by the sensors of the grid nodes and key sampling points, the physical field distribution is obtained in real time through the digital twin physical field proxy model in the digital twin system. The spatial coordinates of each node of the grid model are recorded in the digital twin system. The physical field is fitted in real time according to the solved physical field distribution and the spatial coordinates of the corresponding nodes to achieve visual output.

[0058] In this embodiment, during the offline phase, boundary condition analysis is performed on the spindle system of a CNC grinding machine. Sample points are collected using the Latin hypersquare sampling method, and physical analysis is performed in finite element simulation software to derive node data. Subsequently, the K-nearest neighbor algorithm is used to perform a preliminary reduction of the physical field sample data to a mesh with a specified number of nodes. A radial basis function is used to solve the physical field proxy model using the preliminarily reduced data. After obtaining the physical field proxy model, the parameter values ​​of the test nodes are input into the proxy model and transmitted to the digital twin platform via socket communication. The twin software then performs physical field fitting on the received mesh node parameters. During the online phase, sensor data at specified locations is input into the proxy model, and the entire physical field data of the spindle section is inferred. The proxy model solution values ​​at the sampling point locations are compared with the actual values ​​measured by the actual sensors. The proxy model is iteratively optimized using a genetic algorithm, thereby reducing the deviation between the physical property values ​​solved by the twin system proxy model and the actual values. Compared to existing methods, the proxy model solution method of the present invention can meet the different rendering capabilities of digital twin systems while ensuring the accuracy of physical field solution, achieving real-time simulation of physical fields with virtual-real mirror mapping, and providing a model for digital twin physical field data information.

[0059] Finally, it should be noted that the above embodiments and explanations are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. It should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of the present invention may be made without departing from the spirit and scope of the technical solutions disclosed herein, and all such modifications or equivalent substitutions shall be encompassed within the scope of protection of the claims of the present invention.

Claims

1. A double-reduced-order digital twin physical field construction method for CNC machine tools, characterized in that: The following steps are involved: S1: According to the working state parameters of the CNC machine tool, a finite element analysis mesh model of the CNC machine tool is established, as well as a working state sampling space of the CNC machine tool and a physical field finite element simulation sample data set constructed under the working state sampling space; S2: Based on the physical field finite element simulation sample data set, the improved K nearest neighbor algorithm is used to perform preliminary order reduction on the finite element analysis mesh model to obtain the sparse mesh model and the simulation data corresponding to its mesh nodes; S3: Based on the simulation data corresponding to the sparse grid model and its grid nodes, a digital twin physical field proxy model is established using radial basis functions to establish a mapping relationship between the grid nodes and the sampling data collected by the sensors at the key sampling points; S4: Verify the virtual-real consistency of the digital twin physical field proxy model and the real sample data of the CNC machine tool. If the verification fails, optimize the digital twin physical field proxy model until a verified digital twin physical field proxy model is obtained and deployed in the digital twin system. S5: The real-time sensor data is input into the digital twin system. Combined with the mapping relationship between the sampling data collected by the sensors of the grid nodes and key sampling points, the physical field distribution is obtained in real time through the digital twin physical field proxy model in the digital twin system.

2. According to claim 1, a method for constructing a double-reduced-order digital twin physical field of a CNC machine tool is characterized in that: In S1, first, a working state sampling space of the CNC machine tool is established according to the working state parameters of the CNC machine tool, then the working state of the CNC machine tool is sampled in the working state sampling space to obtain machine tool sampling points, and then a parametric simulation analysis is performed on the machine tool under the working state corresponding to each machine tool sampling point to obtain a physical field finite element simulation sample data set.

3. The method for constructing a digital twin physical field of a CNC machine tool with double reduced order according to claim 1, characterized in that: In S1, for each triangular facet of the finite element analysis mesh model of the numerical control machine tool, each edge of the triangular facet consists of two directed half edges.

4. The method for constructing a digital twin physical field of a CNC machine tool with double reduced order according to claim 1, characterized in that: The S2 is specifically: S21: According to the physical field finite element simulation sample data set, all triangular facets in the finite element analysis mesh model are mapped to three-dimensional space, and then it is determined whether each triangular facet is on the surface of the mesh body or inside the mesh body, so as to determine whether each mesh node is a mesh body internal node or a mesh body surface node, and obtain a sparse mesh model; S22: Use the K nearest neighbor algorithm to calculate and update the physical property values ​​corresponding to each mesh internal node and each mesh surface node, and obtain simulation data corresponding to each mesh node in the sparse mesh model, wherein the weights of the mesh internal nodes and the mesh surface nodes are different.

5. The method for constructing a digital twin physical field of a CNC machine tool with double reduced order according to claim 1, characterized in that: The S4 is specifically: S41: Perform virtual-real consistency verification on the digital twin physical field proxy model and the real model of the CNC machine tool. If the verification passes, the current digital twin physical field proxy model is used as the final digital twin physical field proxy model. Otherwise, execute S42; S42: Iteratively optimize the digital twin physical field proxy model using a genetic algorithm to obtain an optimized digital twin physical field proxy model, and verify the virtual-real consistency of the optimized digital twin physical field proxy model. If the verification passes, the current digital twin physical field proxy model is used as the final digital twin physical field proxy model. If the verification fails, execute S43; S43: The Latin hypersquare sampling method is used to resample the working state of the CNC machine tool in the working state sampling space to obtain the machine tool sampling points, and then obtain the physical field finite element simulation sample data set. S2, S3 and S41 are repeated until the final digital twin physical field proxy model is obtained and deployed in the digital twin system.

6. The method for constructing a double-reduced-order digital twin physical field of a CNC machine tool according to claim 1, characterized in that: In S1, the physical field finite element simulation sample data set is concentrated, the physical field includes a structural field and a temperature field, and the object to which the finite element simulation sample data belongs is a key component in a CNC machine tool.

7. The method for constructing a double-reduced-order digital twin physical field of a CNC machine tool according to claim 1, characterized in that: The interpolation kernel function of the radial basis function adopts a Gaussian kernel function.

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