Machine tool table force response prediction method and device

Abstract

The application provides a machine tool workbench force response prediction method and device, the method comprises the following steps: obtaining the working condition parameters of the machine tool workbench under the cutting load working condition, and the measuring point position and force response data of multiple discrete measuring points, and constructing a physical reference model based on the working condition parameters; determining a physical baseline force response based on the physical reference model, and performing spatial reconstruction on the residual of the measuring point position and force response data of the multiple discrete measuring points relative to the physical baseline force response to obtain a global continuous force response field; dividing the workbench surface area of the machine tool workbench into subfields according to the gradient characteristics output by the physical reference model to obtain a high-frequency force response subfield and a low-frequency force response subfield; predicting the residual of the high-frequency force response subfield based on a geometric-enhanced Fourier neural operator, and predicting the residual of the low-frequency force response subfield based on a non-uniform Fourier neural operator; and obtaining a global force response prediction result according to the residual prediction result of each subfield and the physical baseline force response.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and processing technology, and in particular to a method and apparatus for predicting the force response of a machine tool worktable. Background Technology

[0002] The machine tool table is a crucial component in CNC machine tools, responsible for supporting the workpiece, connecting fixtures, and transmitting cutting loads. During actual machining, the cutting load generated between the tool and workpiece is transmitted to the supporting structure via the workpiece, fixture, and table, resulting in differentiated force responses in different areas of the table. Because the table typically has complex structures such as ribs, guideways, sliders, and connecting interfaces, the transmission of cutting loads within it is influenced by factors including load magnitude, load location, load direction, table geometry, and support constraints. This leads to a spatial distribution characterized by drastic changes in response near the load area and gradual attenuation in the distant load area. This force response distribution is closely related to localized stress concentration on the table, changes in structural stiffness, and machining errors. Therefore, accurately obtaining the full-domain force response of the machine tool table under different cutting load conditions is of great significance for machining condition assessment, structural optimization, and error compensation.

[0003] In existing technologies, the force response of machine tool worktables is typically determined through finite element simulation, experimental measurement point analysis, or data-driven models. While finite element simulation can describe the stress state of the worktable, its modeling, solving, and condition updating costs are high, making it difficult to meet the need for rapid prediction across multiple working conditions. Experimental measurement point analysis is limited by the number and placement of measurement points, usually only reflecting the force response at local locations and failing to directly obtain the global continuous force response distribution on the worktable surface. Although purely data-driven prediction methods offer fast inference speeds, they easily overlook the physical transmission laws of cutting loads within the worktable when there are limited discrete measurement points, complex load transmission paths, and coexisting high and low temperature variations, leading to insufficient physical consistency and local accuracy in the prediction results. Summary of the Invention

[0004] This invention provides a method and apparatus for predicting the force response of a machine tool worktable, which solves the problem in the prior art that, under the cutting load condition of a machine tool worktable, the number and arrangement of discrete measuring points make it difficult to obtain a continuous force response across the entire range by combining the physical transmission law of the cutting load in the worktable, resulting in insufficient accuracy and physical consistency in force response prediction.

[0005] This invention provides a method for predicting the force response of a machine tool table, comprising: acquiring working parameters of the machine tool table under cutting load conditions, as well as the measurement point positions and force response data of multiple discrete measurement points, and constructing a physical reference model based on the working parameters; determining a physical baseline force response based on the physical reference model, and performing spatial reconstruction based on the residuals of the measurement point positions and force response data of the multiple discrete measurement points relative to the physical baseline force response to obtain a global continuous force response field; dividing the table surface region of the machine tool table into subdomains based on the gradient characteristics output by the physical reference model to obtain a high-frequency force response subdomain and a low-frequency force response subdomain; predicting the residuals of the high-frequency force response subdomain based on a geometrically enhanced Fourier neural operator, and predicting the residuals of the low-frequency force response subdomain based on a non-uniform Fourier neural operator; and obtaining a global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response.

[0006] According to the machine tool table force response prediction method provided by the present invention, the operating parameters include cutting load parameters, load application point parameters, and machine tool table geometric parameters; the step of constructing a physical benchmark model based on the operating parameters includes: determining a load intensity term of the cutting load acting on the machine tool table according to the cutting load parameters and the load application point parameters; determining a distance attenuation term of the table surface position relative to the load application point according to the load application point parameters and the machine tool table geometric parameters; determining a direction modulation term of the table surface position relative to the load application point according to the cutting load parameters and the load application point parameters; and constructing a physical benchmark model characterizing the force response distribution law of the machine tool table surface based on the load intensity term, the distance attenuation term, and the direction modulation term.

[0007] According to the machine tool table force response prediction method provided by the present invention, the step of determining the physical baseline force response based on the physical reference model and spatially reconstructing the global continuous force response field based on the residuals of the force response data of the plurality of discrete measuring points relative to the physical baseline force response includes: inputting the measuring point positions of the plurality of discrete measuring points into the physical reference model to obtain the physical baseline force response corresponding to each measuring point position; determining the discrete residuals corresponding to each measuring point position based on the difference between the force response data corresponding to each measuring point position and the physical baseline force response; spatially reconstructing the discrete residuals corresponding to each measuring point position to obtain the global residual field corresponding to the surface area of ​​the machine tool table; and superimposing the global residual field with the physical baseline force response corresponding to the surface area of ​​the machine tool table to obtain the global continuous force response field.

[0008] According to the machine tool table force response prediction method provided by the present invention, the step of dividing the table surface area of ​​the machine tool table into subdomains based on the gradient features output by the physical reference model to obtain high-frequency force response subdomains and low-frequency force response subdomains includes: determining multiple sampling points in the table surface area of ​​the machine tool table, and determining the physical reference force response corresponding to each sampling point based on the physical reference model; determining the gradient feature value corresponding to each sampling point based on the physical reference force response corresponding to each sampling point; recursively dividing the table surface area using a Monte Carlo tree search KD tree with the objective of satisfying a preset condition for the dispersion of gradient feature values ​​within the subdomain, to obtain multiple candidate subdomains; and dividing the multiple candidate subdomains into high-frequency force response subdomains and low-frequency force response subdomains based on the average level of the gradient feature values ​​within each candidate subdomain.

[0009] According to the machine tool table force response prediction method provided by the present invention, the method for predicting the residuals of the high-frequency force response subdomain based on a geometrically enhanced Fourier neural operator and the residuals of the low-frequency force response subdomain based on a non-uniform Fourier neural operator includes: constructing high-frequency subdomain input features based on the coordinates of sampling points in the high-frequency force response subdomain, the operating parameters, and physical prior features determined by the physical benchmark model; inputting the high-frequency subdomain input features into the geometrically enhanced Fourier neural operator to obtain high-frequency residual prediction results; constructing low-frequency subdomain input features based on the coordinates of sampling points in the low-frequency force response subdomain, the operating parameters, and physical prior features determined by the physical benchmark model; and inputting the low-frequency subdomain input features into the non-uniform Fourier neural operator to obtain low-frequency residual prediction results.

[0010] According to the machine tool table force response prediction method provided by the present invention, the step of obtaining the global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response includes: integrating the high-frequency residual prediction results and the low-frequency residual prediction results according to the distribution positions of the high-frequency force response subdomain and the low-frequency force response subdomain in the table surface area of ​​the machine tool table to obtain a global residual prediction field; determining the global physical baseline force response corresponding to the table surface area based on the physical reference model; and superimposing the global residual prediction field with the global physical baseline force response to obtain the global force response prediction result.

[0011] The present invention also provides a machine tool table force response prediction device, comprising: a model building module, used to acquire working parameters of the machine tool table under cutting load conditions and the measurement point positions and force response data of multiple discrete measurement points, and to build a physical reference model based on the working parameters; a spatial reconstruction module, used to determine the physical baseline force response based on the physical reference model, and to perform spatial reconstruction based on the residuals of the measurement point positions and force response data of the multiple discrete measurement points relative to the physical baseline force response, to obtain a global continuous force response field; a partitioning module, used to partition the table surface area of ​​the machine tool table into subdomains based on the gradient characteristics output by the physical reference model, to obtain a high-frequency force response subdomain and a low-frequency force response subdomain; a residual prediction module, used to predict the residuals of the high-frequency force response subdomain based on a geometrically enhanced Fourier neural operator, and to predict the residuals of the low-frequency force response subdomain based on a non-uniform Fourier neural operator; and a response prediction module, used to obtain a global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the machine tool table force response prediction method as described above.

[0013] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the machine tool table force response prediction method as described above.

[0014] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the machine tool table force response prediction method as described above.

[0015] The machine tool table force response prediction method and apparatus provided by this invention acquires the working parameters under cutting load conditions, as well as the measurement point positions and force response data of multiple discrete measurement points. Based on the working parameters, a physical reference model is constructed, enabling the prediction process to incorporate the basic transmission law of cutting load in the machine tool table. Furthermore, the physical baseline force response is determined based on the physical reference model, and spatial reconstruction is performed using the residuals of the discrete measurement point force response data relative to the physical baseline force response. This yields a more consistent global continuous force response field under limited measurement point conditions. Simultaneously, the table surface area is divided into high-frequency and low-frequency sub-domains according to the gradient characteristics output by the physical reference model. Geometrically enhanced Fourier neural operators and non-uniform Fourier neural operators are used to predict the residuals of different sub-domains, allowing for targeted modeling of the drastic changes in the near-load region and the gradual changes in the far-load region. Finally, the residual prediction results of each sub-domain are combined with the physical baseline force response to obtain the global force response prediction result. Therefore, the present invention can solve the problem in the prior art that, under the cutting load condition of a machine tool worktable, the limited number and arrangement of discrete measuring points make it difficult to take into account the physical transmission law of the cutting load and the differences in force response changes in different regions, resulting in insufficient accuracy and physical consistency of the whole-domain force response prediction. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the machine tool worktable force response prediction method of the present invention; Figure 2 This is a flowchart illustrating an example of constructing a physical baseline model based on the aforementioned operating parameters according to the present invention; Figure 3 The flowchart illustrates an example of the present invention of determining the physical baseline force response based on the physical benchmark model, and spatially reconstructing the global continuous force response field based on the residuals of the force response data of the plurality of discrete measuring points relative to the physical baseline force response. Figure 4 The flowchart illustrates an example of the present invention of dividing the worktable surface region of the machine tool worktable into subdomains based on the gradient features output by the physical reference model, thereby obtaining a high-frequency force response subdomain and a low-frequency force response subdomain. Figure 5The flowchart illustrates an example of the present invention for determining the residual prediction results of the high-frequency force response subdomain based on a geometrically enhanced Fourier neural operator and the residual prediction results of the low-frequency force response subdomain based on a non-uniform Fourier neural operator. Figure 6 A flowchart illustrating an example of the present invention is provided, showing how to obtain a global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response. Figure 7 This is a structural block diagram of the machine tool worktable force response prediction device of the present invention; Figure 8 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] An embodiment of the present invention provides a method for predicting the force response of a machine tool worktable.

[0020] Figure 1 This is a flowchart of the machine tool worktable force response prediction method of the present invention.

[0021] like Figure 1 As shown, the method includes operations S110~S150.

[0022] During operation S110, the working parameters of the machine tool table under cutting load conditions, as well as the measurement point positions and force response data of multiple discrete measurement points, are acquired, and a physical reference model is constructed based on the working parameters.

[0023] According to an embodiment of the present invention, the cutting load condition can be the force condition corresponding to the machine tool during cutting. The condition parameters can include parameters characterizing the magnitude of the cutting load, the location of the load application, the direction of the load application, and the geometric state of the machine tool table. Each discrete measuring point can be a measuring point pre-arranged on the surface of the machine tool table or in the force-sensitive area of ​​the machine tool table, and the measuring point position of each discrete measuring point is used to characterize the spatial distribution position of the measuring point on the machine tool table.

[0024] According to an embodiment of the present invention, the worktable surface of a machine tool can be parameterized to form multiple table surface calculation positions. These table surface calculation positions serve as evaluation positions for the physical reference force response output by the physical reference model. They can be determined on the worktable surface according to a preset radial path, a preset angular path, or a preset mesh method. A physical reference model can be established based on these table surface calculation positions and combined with operating parameters.

[0025] For example, coordinate parameterization can be achieved through the following process: The origin of polar coordinates can be set at a preset position on the surface of the machine tool table. Establish a polar coordinate system on the table. .Pick The origin of the coordinate system is... Any sampling point on the workbench surface is denoted as... ,in Number the angular path Numbering the radial sampling points: The sampling points are located in Cartesian coordinates. . Path angle Defined counterclockwise from the +X axis: Along each radial path, the radius interval [0, R] is equidistantly distributed. There are sampling points, where R represents the upper limit of radial sampling (determined by the stage geometry and the region of interest). The radial step size is defined as: The final calculated positions of multiple platforms are obtained.

[0026] It should be noted that the calculated position of the table surface is different from the actual discrete measurement points; the discrete measurement points are the actual measured positions used to collect force response data, while the calculated position of the table surface is the calculated position used to characterize the force response distribution in the workbench surface area.

[0027] In some embodiments, discrete measurement points can be partial locations in the table surface calculation positions; in other embodiments, discrete measurement points may not completely coincide with the table surface calculation positions. In this case, the discrete measurement points can be mapped to adjacent table surface calculation positions based on their positions in the same workbench surface coordinate system, or the discrete measurement point positions can be directly used as input positions for the physical reference model.

[0028] According to embodiments of the present invention, the force response data can be data collected by strain gauges, pressure sensors, force sensors or other mechanical measuring devices under cutting load conditions, or it can be stress response, strain response, support reaction force response, equivalent force response or force response amplitude, etc., converted from the collected data.

[0029] According to an embodiment of the present invention, the physical reference model is not obtained by solving the global force response using finite element methods, but is a physical prior model constructed based on the cutting load conditions and the force flow transmission mechanism of the machine tool table. This model is used to output the physical reference force response at different locations on the machine tool table surface under given operating parameters, to characterize the macroscopic distribution trend of the force response. Furthermore, the scale or parameters output by the physical reference model can be modified by combining force response data from discrete measurement points, so that it forms a physical baseline force response that matches the actual measurement results.

[0030] In operation S120, the physical baseline force response is determined based on the physical reference model, and spatial reconstruction is performed based on the residuals of the force response data of multiple discrete measurement points relative to the physical baseline force response to obtain a global continuous force response field.

[0031] According to an embodiment of the present invention, the physical baseline force response can be understood as the basic distribution of the table surface force response given by the physical reference model under the current cutting load condition.

[0032] In practical engineering testing, due to limitations such as the number of sensors, installation location, wiring space, and testing costs, only a small amount of force response data at discrete measurement points can usually be obtained. Directly performing spatial interpolation based on this discrete force response data can easily lead to interpolation results that overly rely on the measurement point placement, making it difficult to reflect the force flow transmission law of the cutting load on the machine tool table. On the other hand, while physical baseline models can reflect the overall distribution trend of force response on the table surface, they are typically based on simplified mechanical assumptions and operating parameters, making it difficult to fully characterize local response deviations caused by factors such as connection gaps, local structural details, and changes in clamping conditions. Therefore, this invention does not directly use the output of the physical baseline model as the final result, nor does it directly perform global interpolation on the force response data of discrete measurement points. Instead, it uses the physical baseline force response as a benchmark to spatially reconstruct the residuals at discrete measurement points.

[0033] Specifically, the locations of each discrete measuring point can be input into the physical reference model to obtain the physical baseline force response corresponding to each discrete measuring point. Then, the force response data collected at each discrete measuring point is compared with the corresponding physical baseline force response to determine the discrete residual corresponding to each discrete measuring point. This discrete residual is used to characterize the local deviation of the actual measurement result relative to the physical reference distribution. Furthermore, the discrete residual corresponding to each discrete measuring point can be spatially reconstructed to obtain the global residual field corresponding to the workbench surface area. This global residual field is then superimposed with the physical baseline force response corresponding to the workbench surface area to obtain the global continuous force response field.

[0034] During operation S130, based on the gradient characteristics output by the physical reference model, the worktable surface area of ​​the machine tool worktable is divided into subdomains to obtain high-frequency force response subdomains and low-frequency force response subdomains.

[0035] According to embodiments of the present invention, gradient features can be used to characterize the spatial variation of the physical reference force response output by the physical reference model within the worktable surface region. Specifically, multiple worktable surface sampling points can be determined within the worktable surface region of the machine tool worktable, and the physical reference force response corresponding to each worktable surface sampling point can be determined based on the physical reference model; further, the gradient features corresponding to each worktable surface sampling point can be determined based on the variation of the physical reference force response between adjacent sampling points or neighboring sampling points. Gradient features may include gradient magnitude, local rate of change, neighborhood difference value, or other features used to characterize the drastic degree of spatial variation of the force response.

[0036] According to embodiments of the present invention, the high-frequency force response subdomain can be understood as the region where the physical reference force response changes rapidly with the position of the worktable surface, such as the region near the load application location, where the force response gradient is large, or where the local force change is significant. Within this region, the force response distribution typically exhibits strong local variation characteristics, and if a unified model is used for prediction, insufficient capture of local details is likely to occur.

[0037] According to embodiments of the present invention, the low-frequency force response subdomain can be understood as a region where the physical reference force response changes relatively smoothly with the position of the worktable surface, such as a region far from the load application location, with a small force response gradient, or a relatively stable response decay trend. Within this region, the force response distribution typically exhibits an overall decay trend or a smooth change, with relatively weak dependence on local high-gradient details.

[0038] Therefore, by dividing the worktable surface region into subdomains based on the gradient characteristics output by the physical baseline model, different residual prediction methods can be adopted for regions with different spatial variation characteristics during subsequent prediction. For the high-frequency force response subdomain, the focus can be on capturing the effects of rapid local changes and geometric irregularities; for the low-frequency force response subdomain, the focus can be on learning the overall residual variation law within smooth regions. This helps to avoid the problem of decreased prediction accuracy when using a single prediction model to simultaneously handle drastically changing and gently changing regions, and improves the stability and local accuracy of the global force response prediction results.

[0039] In operation S140, the residual prediction results of the high-frequency force response subdomain are determined based on the geometrically enhanced Fourier neural operator, and the residual prediction results of the low-frequency force response subdomain are determined based on the non-uniform Fourier neural operator.

[0040] According to embodiments of the present invention, after obtaining the high-frequency force response subdomain and the low-frequency force response subdomain, the residual distribution within each subdomain can be predicted. Here, the residual can be understood as the deviation of the actual force response from the physical baseline force response, used to compensate for factors such as local structural influences, clamping state influences, connection interface influences, and measurement point errors that are difficult for the physical reference model to fully represent. Since the spatial variation characteristics of the force response in the high-frequency and low-frequency force response subdomains are different, their corresponding residual distributions usually also have different characteristics. Therefore, the present invention employs different neural operators for residual prediction in different subdomains.

[0041] Specifically, the high-frequency force response subdomain typically encompasses regions with drastic stress response changes, large local gradients, or significant geometric influences. Within these regions, the residual distribution often exhibits strong locality and non-smoothness. Directly regularizing it into a uniform grid can weaken local abrupt changes during interpolation or grid transformation, leading to decreased residual prediction accuracy in high-gradient regions. Therefore, a geometrically enhanced Fourier neural operator can be used to predict residuals in the high-frequency force response subdomain. This operator can incorporate the spatial distribution characteristics of sampling points within the subdomain for operator learning, making it more suitable for handling locally rapidly changing residuals in the high-frequency force response subdomain.

[0042] The low-frequency force response subdomain typically represents regions where stress response changes are relatively gradual, gradients are small, or the overall attenuation trend is relatively stable. Within these regions, the residual distribution is generally continuous and smooth, with low sensitivity to local abrupt changes. Therefore, non-uniform Fourier neural operators can be used to predict the residuals in the low-frequency force response subdomain. Non-uniform Fourier neural operators can efficiently learn the overall residual variation patterns in the low-frequency subdomain, reducing computational complexity while maintaining prediction accuracy.

[0043] In this way, instead of using a single neural operator to uniformly predict the residuals of the entire worktable surface area, the present invention selects matching residual prediction operators according to the spatial variation characteristics of different subdomains. This reduces the problems of insufficient detail capture in high-gradient regions and high computational redundancy in flat regions caused by a single prediction model, making the residual prediction results more adaptable to the force response distribution characteristics of different regions of the machine tool worktable surface.

[0044] In operation S150, the global force response prediction result is obtained based on the residual prediction results of each subdomain and the physical baseline force response.

[0045] According to embodiments of the present invention, the physical baseline force response is used to characterize the distribution trend of the basic force response determined by the physical reference model, while the residual prediction results are used to characterize local deviations that the physical reference model fails to fully express. Since the physical reference model can generally describe the macroscopic distribution of cutting loads transmitted along the machine tool table well, but is difficult to completely cover the detailed changes caused by factors such as local structure, connection interfaces, clamping conditions, and measurement environment, the present invention combines the residual prediction results of each subdomain with the corresponding physical baseline force response to obtain prediction results that are closer to the actual force response distribution.

[0046] Specifically, the physical baseline force response at each location on the worktable surface can be determined based on a physical benchmark model. Then, according to the distribution of the high-frequency and low-frequency force response subdomains, the high-frequency residual prediction results and low-frequency residual prediction results are mapped to their respective locations on the worktable surface. Subsequently, the residual prediction result at the same location is superimposed with the physical baseline force response to obtain the predicted force response value at that location. By performing the above processing on multiple locations within the worktable surface, the global force response prediction result can be obtained.

[0047] In some embodiments, for the boundary region between the high-frequency force response subdomain and the low-frequency force response subdomain, the residual prediction results of adjacent subdomains can be made continuous to reduce possible prediction jumps at the subdomain boundaries. For example, the residual prediction values ​​near the boundaries of adjacent subdomains can be smoothed, weighted fused, or constrained to ensure that the obtained global force response prediction results remain continuous at the subdomain boundaries.

[0048] Based on the above setup, a physical baseline model provides macroscopic distribution constraints for the force response of the machine tool table. Spatial reconstruction and domain-specific prediction are performed using the residuals of the force response at discrete measurement points relative to the physical baseline. This avoids the problem of insufficient physical constraints when directly interpolating the force response data at discrete measurement points. Simultaneously, by dividing the data into high-frequency and low-frequency subdomains based on gradient features, and using geometrically enhanced Fourier neural operators and non-uniform Fourier neural operators to predict the residuals, differentiated modeling can be performed for regions with different spatial variation characteristics, improving the prediction accuracy in areas of drastic local change and the prediction efficiency in areas of smooth change. Therefore, this invention can improve the accuracy, stability, and physical consistency of the global force response prediction results of the machine tool table under cutting load conditions.

[0049] In one illustrative embodiment, the operating parameters include cutting load parameters, load application point parameters, and machine tool table geometry parameters.

[0050] Figure 2 This is a flowchart illustrating an example of constructing a physical benchmark model based on operating condition parameters according to the present invention.

[0051] like Figure 2 As shown, operation S110 includes operations S210~S240.

[0052] In operation S210, the load strength of the cutting load acting on the machine tool table is determined based on the cutting load parameters and the load application point parameters.

[0053] According to an embodiment of the present invention, the cutting load parameter can be a cutting force vector; the load application point parameter can include parameters such as the equivalent application height, eccentric distance or equivalent application arm length of the cutting load relative to the surface of the machine tool table, which are used to characterize that the cutting load does not necessarily act directly on the surface of the table, but may be transmitted to the table through the workpiece, fixture or clamping structure.

[0054] According to an embodiment of the present invention, the magnitude of the resultant force of the cutting load can be determined first based on the cutting force vector, and the equivalent action arm corresponding to the cutting load can be determined based on the load application point parameters. Further, the equivalent torque can be determined based on the cutting force vector and the equivalent action arm. The equivalent torque is used to characterize the additional load effect caused by clamping height, load eccentricity, or deviation of the force application position from the worktable surface.

[0055] When determining the load strength term of the cutting load acting on the machine tool table, the magnitude of the resultant force of the cutting load can be used as the basic strength, and the ratio of the equivalent torque to the resultant force and characteristic length can be used as a correction factor, thus obtaining a load strength term that simultaneously reflects the cutting force and torque. For example, the load strength term can be determined by the following formula:

[0056] in, Indicates the load strength term. Represents the cutting force vector. The magnitude of the cutting force vector. This represents the equivalent torque determined by the cutting force vector and the equivalent action arm. The modulus of the equivalent moment is represented by... Indicates torque weighting. This represents the feature length after dimensionless processing.

[0057] According to embodiments of the present invention, the characteristic length can be determined based on the scale of the calculation area or sampling path on the machine tool table surface. For example, the characteristic length can be determined based on the mean square distance between multiple radial sampling positions on the table surface, so that the equivalent torque term can be compared with the cutting force term under the same strength scale.

[0058] The above processing avoids the problem of ignoring the influence of eccentric load or clamping height when characterizing load intensity by only the magnitude of the resultant cutting force, and enables the physical benchmark model constructed subsequently to more accurately reflect the comprehensive load effect borne by the machine tool table under different cutting conditions.

[0059] In operation S220, the distance attenuation term of the worktable surface position relative to the load application point is determined based on the load application point parameters and the machine tool worktable geometry parameters.

[0060] According to embodiments of the present invention, the load application point parameter can be used to determine the equivalent application position of the cutting load on the machine tool table surface, and the machine tool table geometric parameters can be used to determine the calculation area of ​​the table surface, the radial distance range, and the distance of each table surface position relative to the load application point. For any position on the table surface, the corresponding distance attenuation term can be determined based on the table surface distance between that position and the load application point.

[0061] According to an embodiment of the present invention, the distance attenuation term is used to characterize the law that the force response gradually weakens with increasing distance during the transmission of cutting load along the machine tool table. Specifically, the distance attenuation term can be set as the product of the geometric diffusion attenuation part and the equivalent dissipation attenuation part. The geometric diffusion attenuation part characterizes the attenuation caused by the expansion of the propagation path when the load is transmitted in the table structure; the equivalent dissipation attenuation part characterizes the additional attenuation caused by factors such as material internal friction, interface friction, micro-slippage, and boundary constraints.

[0062]

[0063] in, Represents the distance attenuation term. This indicates the distance of the worktable surface position relative to the point of load application. This represents the geometric diffusion attenuation portion. This represents the equivalent dissipation attenuation portion. Indicates the effective diffusion order. Indicates the comprehensive equivalent dissipation scale. This represents the combined shape parameters.

[0064] By using the aforementioned distance attenuation term, the physical baseline model can not only consider the basic transmission trend of "the farther away from the load application point, the weaker the response" when characterizing the force response distribution, but also incorporate the energy dissipation caused by factors such as the workbench material, connection interface, and support boundary into the model, thereby improving the ability of the physical baseline force response to express the actual force flow transmission law of the workbench.

[0065] During operation S230, the direction modulation term of the worktable surface position relative to the load application point is determined based on the cutting load parameters and the load application point parameters.

[0066] According to embodiments of the present invention, a direction modulation term is used to characterize the difference in the effect of cutting load on different transmission directions on the machine tool table surface. Since the cutting load is directional, when the table surface is located in or near the main direction of the cutting load, the force response at that location is generally more susceptible to load transmission; conversely, when the table surface is located in a direction significantly different from the main direction of the cutting load, the force response at that location is relatively weaker. Therefore, when constructing the physical reference model, a direction modulation term can be introduced to reflect the modulation effect of the load direction on different table transmission paths.

[0067] For example, the directional component of the resultant cutting force in the table surface coordinate system can be determined based on the cutting load parameters, and the table path direction from the load application point to the table surface can be determined based on the load application point parameters. Furthermore, a direction modulation term can be determined based on the degree of directional consistency between the table direction component of the resultant cutting force and the table path direction.

[0068] For example, let the direction cosine vector of the resultant cutting force within the worktable surface be:

[0069] in ， .

[0070] and These represent the components of the cutting force in two directions within the coordinate system of the worktable surface. For any path direction along the worktable surface from the point of application of the load to the position of the worktable surface, its unit direction vector can be expressed as:

[0071] in, This represents the direction angle of the path on the worktable relative to the worktable's coordinate system. The direction projection modulation function can be determined using the dot product of the direction cosine vector and the unit direction vector.

[0072] Furthermore, to avoid unreasonable negative amplification of the physical reference response by the path direction opposite to the main transmission direction of the cutting load, the direction projection modulation function can be non-negatively processed to obtain the direction modulation term:

[0073] in, This indicates the direction modulation term. When the direction of the table path is consistent with or nearly consistent with the main direction of the cutting force within the table surface, the direction modulation term has a larger value, indicating that the force response transmission efficiency on this transmission path is higher; when the direction of the table path is approximately orthogonal to or opposite to the main direction of action, the direction modulation term has a smaller value, indicating that the force response on this transmission path is relatively weakened.

[0074] In operation S240, a physical benchmark model is constructed based on the load strength term, distance attenuation term, and direction modulation term to characterize the force response distribution law on the surface of the machine tool table.

[0075] For example, the physical baseline model can be obtained by the following formula:

[0076] in, This represents the equivalent force response at the calculated position of the j-th table surface along the i-th path on the worktable surface.

[0077] Figure 3 The flowchart illustrates an example of the present invention of determining the physical baseline force response based on a physical benchmark model, and spatially reconstructing the global continuous force response field based on the residuals of the force response data of multiple discrete measuring points relative to the physical baseline force response.

[0078] like Figure 3 As shown, operation S120 includes operations S310~S340.

[0079] In operation S310, the positions of multiple discrete measuring points are input into the physical reference model to obtain the physical baseline force response corresponding to each measuring point position.

[0080] According to an embodiment of the present invention, after obtaining the physical reference model, the measurement positions of each discrete measurement point can be input into the physical reference model to obtain the output value of the physical reference model at each measurement point location. Since the original physical reference model is mainly used to characterize the macroscopic distribution law of the force response on the machine tool worktable surface, its output is more inclined to reflect the relative distribution trend of the force response strength at different locations, and usually cannot be directly used as the true force response result with the same dimensions and scale as the measured force response data. Therefore, the output value of the physical reference model can be further converted into the physical baseline force response based on a preset calibration mapping.

[0081] For example, the physical baseline force response can be expressed as:

[0082] in, Indicates position Physical baseline force response at that point Indicates the physical reference model at location The output value at that location, This represents the undetermined mechanistic parameters in the physical baseline model. Indicates calibration mapping, Indicates the calibration mapping parameters. This is the scaling factor. This is the offset.

[0083] In operation S320, the discrete residual corresponding to each measuring point is determined based on the difference between the force response data corresponding to each measuring point location and the force response of the physical baseline.

[0084] According to an embodiment of the present invention, after determining the physical baseline force response corresponding to each discrete measuring point, the force response data collected at each measuring point can be compared with the physical baseline force response at that measuring point to obtain the discrete residual corresponding to each discrete measuring point.

[0085] For example, the discrete residual can be expressed as:

[0086] in, Indicates the first The location of each discrete measuring point. This represents the measured force response data at the location of the measuring point. This indicates the physical baseline force response at the measurement point location. This represents the discrete residual at the location of the measuring point.

[0087] By operating S330, the discrete residuals corresponding to each measuring point are spatially reconstructed to obtain the global residual field corresponding to the surface area of ​​the machine tool table.

[0088] According to an embodiment of the present invention, since the discrete residuals exist only at a finite number of measurement points, they cannot directly characterize the residual distribution across the entire machine tool table surface area. Therefore, spatial reconstruction can be performed on the discrete residuals corresponding to each measurement point location to obtain a global residual field covering the entire table surface area.

[0089] For example, a Gaussian process regression model can be used to learn the spatial distribution of discrete residuals. Specifically, the location of each discrete measuring point can be used as the input to the Gaussian process regression model, and the corresponding discrete residuals can be used as the output labels of the Gaussian process regression model. A kernel function is used to describe the spatial correlation between residuals at different locations. After model training, residuals at other locations within the workbench surface area can be predicted to obtain the global residual field.

[0090] When operating S340, the global residual field is superimposed with the physical baseline force response corresponding to the surface area of ​​the machine tool table to obtain the global continuous force response field.

[0091] According to an embodiment of the present invention, after obtaining the global residual field, the physical baseline force response corresponding to each position within the worktable surface area can be further determined, and the physical baseline force response at the same position can be superimposed with the residual reconstruction result to obtain the continuous force response value at that position. After performing the above processing on multiple positions within the worktable surface area, the global continuous force response field can be obtained.

[0092] For example, the global continuous force response field can be represented as:

[0093] in, Indicates position Continuous force response at the point, Indicates position Physical baseline force response at that point Indicates position The residual at the location.

[0094] Through the above processing, the final global continuous force response field retains the macroscopic force transmission trend characterized by the physical baseline force response, while also compensating for local deviations that are difficult to express by the physical reference model using measured data from discrete measurement points. Compared with directly interpolating the force response data from discrete measurement points, this method does not directly reconstruct the absolute force response value. Instead, it first locks the overall distribution trend using the physical baseline and then spatially reconstructs the local residuals. Therefore, it can reduce the uncertainty of global reconstruction under limited measurement point conditions, making the obtained continuous force response field more consistent with the force transmission law in the machine tool table.

[0095] Figure 4 The flowchart illustrates an example of the present invention of dividing the worktable surface region of a machine tool worktable into subdomains based on gradient features output by a physical benchmark model, thereby obtaining a high-frequency force response subdomain and a low-frequency force response subdomain.

[0096] like Figure 4 As shown, operation S130 includes operations S410~S440.

[0097] In operation S410, multiple sampling points are determined on the surface area of ​​the machine tool worktable, and the physical reference force response corresponding to each sampling point is determined based on the physical reference model.

[0098] According to an embodiment of the present invention, multiple sampling points can be determined first within the surface area of ​​the machine tool worktable. These sampling points can be determined according to a preset grid, a preset radial path, a preset angular path, or other surface discretization methods, and are used to characterize the force response changes at different locations within the worktable surface area.

[0099] It should be noted that different partitioning criteria can be used for domain decomposition depending on the application stage. During model training, for sample cutting load conditions in the training or validation set, since the global continuous force response field can be reconstructed based on discrete force response data and the physical baseline force response, the partitioning criterion can be determined based on the gradient characteristics of the global continuous force response field. During model prediction, for the test set or the cutting load condition to be predicted, typically only the corresponding condition parameters are available, and the global continuous force response field under that condition cannot be obtained in advance. Therefore, the gradient characteristics output by the physical baseline model can be used as a priori partitioning criterion.

[0100] In this embodiment, taking the subdomain partitioning under the cutting load condition to be predicted as an example, the positions of each sampling point can be input into the physical reference model to obtain the physical reference force response corresponding to each sampling point. The physical reference force response is used to characterize the distribution of the basic force response on the worktable surface predicted by the physical reference model under the current cutting load condition, and serves as the basis for subsequent calculation of gradient feature values.

[0101] Operate S420 to determine the gradient characteristic value corresponding to each sampling point based on the physical reference force response corresponding to each sampling point.

[0102] According to an embodiment of the present invention, the gradient characteristic value corresponding to each sampling point can be determined based on the spatial variation of the physical reference force response within the worktable surface area corresponding to each sampling point. The gradient characteristic value is used to characterize the degree of drastic change of the physical reference force response near the corresponding sampling point.

[0103] Under the cutting load condition to be predicted, the spatial gradient magnitude output by the physical benchmark model can be used as a priori partitioning index, which can be exemplarily expressed as:

[0104] in, Indicates sampling point The corresponding gradient feature values, This indicates the physical baseline model at the sampling points. The physical reference force response output at the point, The spatial gradient magnitude represents the physical reference force response.

[0105] Under the sample cutting load conditions in the training or validation set, if the global continuous force response field has been obtained, the partition index can also be determined based on the gradient magnitude of the global continuous force response field, which can be exemplarily expressed as:

[0106] in, This represents the global continuous force response field reconstructed based on the physical baseline force response and the global residual field. This method allows the subdomain partitioning during the training phase to match the actual force response variation characteristics under sample conditions; while during the testing phase, subdomain partitioning is achieved without the need for measured global responses, using the prior gradient features provided by the physical benchmark model.

[0107] In operation S430, based on gradient feature values, with the goal of satisfying the preset conditions for the degree of dispersion of gradient feature values ​​within a subdomain, the KD tree of Monte Carlo tree search is used to recursively divide the worktable surface area to obtain multiple candidate subdomains.

[0108] According to an embodiment of the present invention, after obtaining the gradient feature values ​​corresponding to each sampling point, the workbench surface area can be used as the initial region, and the initial region can be recursively binary divided using a KD tree to obtain multiple non-overlapping candidate subdomains.

[0109] To ensure that the force response variation characteristics within each candidate subdomain are as consistent as possible, the subdomain can be divided based on the goal of satisfying a preset condition regarding the dispersion of its gradient feature values. For example, for the i-th candidate subdomain, the sum of squared deviations of the features of that candidate subdomain can be determined based on the difference between the gradient feature values ​​at each sampling point in that candidate subdomain and the average gradient feature value of that candidate subdomain:

[0110] in, Indicates the first Sum of squared feature deviations of each candidate subdomain This indicates the number of sampling points in the candidate subdomain. Indicates the first candidate subdomain. Gradient feature values ​​of each sampling point This represents the average value of the gradient eigenvalues ​​in the candidate subdomain.

[0111] The goal of region partitioning can be to minimize the sum of the squared deviations of features from multiple candidate subdomains, i.e.:

[0112] In other words, the gradient feature values ​​within each candidate subdomain should be as close as possible after partitioning, so that the same candidate subdomain is mainly composed of sampling points with similar degrees of change.

[0113] According to an embodiment of the present invention, the aforementioned region partitioning problem is a combinatorial optimization problem. Directly enumerating all possible partitioning methods results in high computational costs. Therefore, Monte Carlo tree search can be used to optimize the recursive partitioning path of the KD tree. Specifically, each node in the Monte Carlo tree search can represent a KD tree partitioning state, and each action corresponds to a recursive KD tree partition. A partitioning action can include: selecting the molecular domain to be partitioned, determining the partitioning dimension, and determining the partitioning position. Through multiple searches and evaluations, a better recursive partitioning result can be obtained.

[0114] For example, the reward value of the segmentation scheme can be determined based on the sum of the squared deviations of the overall features of the initial region and the sum of the squared deviations of the features of each candidate subdomain after segmentation:

[0115] in, This represents the sum of squared deviations of the overall characteristics of the initial region. This represents the sum of the squared deviations of the features of each candidate subdomain after the segmentation. A larger reward value indicates that the segmentation scheme can reduce the dispersion of gradient feature values ​​within the subdomains.

[0116] It should be noted that the above-described KD-tree recursive splitting and Monte Carlo tree search optimization process can be applied regardless of whether the gradient feature values ​​originate from the global continuous force response field in the training or validation set, or from the output of the physical benchmark model in the test set or the condition to be predicted. The only difference lies in the source of the gradient feature values.

[0117] In operation S440, multiple candidate subdomains are divided into high-frequency force response subdomains and low-frequency force response subdomains based on the average level of gradient eigenvalues ​​within each candidate subdomain.

[0118] According to an embodiment of the present invention, after obtaining multiple candidate subdomains, the candidate subdomains can be classified into high-frequency and low-frequency categories based on the average level of gradient feature values ​​within each candidate subdomain. Specifically, the average gradient feature value of all sampling points within the initial workbench surface area can be calculated first, and this average value can be used as the classification threshold.

[0119] in, This represents the average gradient characteristic of all sampling points within the initial worktable surface area. This represents the total number of sampling points in the initial region. Represents the first region in the initial region The gradient feature value of each sampling point.

[0120] Furthermore, the average value of the gradient eigenvalues ​​within each candidate subdomain can be calculated. When the average gradient characteristic of a candidate subdomain is greater than the average gradient characteristic of the initial region, the candidate subdomain can be classified as a high-frequency force response subdomain; when the average gradient characteristic of a candidate subdomain is less than or equal to the average gradient characteristic of the initial region, the candidate subdomain can be classified as a low-frequency force response subdomain.

[0121] In other words, when ＞ At that time, candidate subdomains Classified as a high-frequency subdomain; when ≤ At that time, it was classified as a low-frequency subdomain.

[0122] Based on the above division, the high-frequency force response subdomain mainly deals with regions where stress response changes drastically and the gradient is large; the low-frequency force response subdomain mainly deals with regions where stress response changes are gradual and the gradient is small. In the training or validation sets, this classification result can be used to enable the neural operator to learn the residual distribution of different variation regions. In the test set or the condition to be predicted, this classification result can be used to guide the trained geometrically enhanced Fourier neural operator and the non-uniform Fourier neural operator to perform residual prediction for different subdomains respectively. This maintains consistency in the subdomain division logic between the training and prediction phases and makes the subsequent residual prediction process more adaptable to the force response variation characteristics of different regions on the workbench surface.

[0123] Figure 5 The flowchart illustrates an example of the present invention for determining the residual prediction results of the high-frequency force response subdomain based on a geometrically enhanced Fourier neural operator, and determining the residual prediction results of the low-frequency force response subdomain based on a non-uniform Fourier neural operator.

[0124] like Figure 5 As shown, operation S140 includes operations S510~S540.

[0125] When operating S510, high-frequency subdomain input features are constructed based on the coordinates of sampling points in the high-frequency force response subdomain, operating parameters, and physical prior features determined by the physical benchmark model.

[0126] According to an embodiment of the present invention, after determining the high-frequency force response subdomain, the coordinate information of each sampling point in the high-frequency force response subdomain can be obtained, and the high-frequency subdomain input features can be constructed by combining the working parameters corresponding to the current cutting load condition and the physical prior features determined by the physical reference model.

[0127] According to embodiments of the present invention, the physical prior features can be features output by a physical baseline model or further calculated based on the physical baseline model, such as at least one of physical baseline force response, distance attenuation features, direction modulation features, and gradient features.

[0128] For example, for sampling points within the high-frequency force response subdomain The following input features can be constructed:

[0129] in, Represents the input features of the high-frequency subdomain. Indicates the coordinates of the sampling point. Indicates operating parameters, This represents the physical prior features determined by the physical benchmark model.

[0130] Furthermore, high-frequency subdomain input features can be uplifted to the hidden feature space through fully connected mapping, for example:

[0131] in, This represents the feature enhancement mapping used for high-frequency subdomains. Represents sampling points in the high-frequency subdomain The corresponding initial hidden features.

[0132] Since the high-frequency force response subdomain is typically a region with a large stress response gradient and drastic local changes, introducing physical prior features when constructing the input features of the high-frequency subdomain can enable the subsequent geometrically enhanced Fourier neural operator to not only rely on the data distribution when predicting the residuals, but also be guided by the force flow transmission law represented by the physical benchmark model.

[0133] In the S520 operation, the high-frequency subdomain input features are input into the geometrically enhanced Fourier neural operator to obtain the high-frequency residual prediction results.

[0134] In some embodiments, the high-frequency force response subdomain can be first mapped from the physical space to an adaptive computational domain, and then Fourier operator learning can be performed in the adaptive computational domain. This is because the residual changes in the high-frequency force response subdomain are often quite drastic; directly regularizing this region into a uniform mesh could weaken local high-gradient information during interpolation or mesh transformation. Geometrically enhanced Fourier neural operators can use geometric mapping to express the high-frequency subdomain in a computational domain more suitable for operator learning, thereby reducing the loss of locally rapidly changing information.

[0135] For example, suppose the first The high-frequency subdomain hiding features of the layer are The propagation process of the geometrically enhanced Fourier neural operator can be represented as:

[0136] in, This represents the geometric Fourier integral operator. Represents a linear mapping. Indicates the first High-frequency subdomains of the layer conceal features.

[0137] After propagation through multiple operators, the hidden features can be mapped to residual prediction results in the high-frequency force response subdomain, for example:

[0138] in, Represents the sampling points in the high-frequency force response subdomain The corresponding high-frequency residual prediction results, This represents the projection mapping used to output the residual prediction results. This represents the hidden features of the high-frequency subdomain after multiple propagations.

[0139] Through the above processing, the geometrically enhanced Fourier neural operator can more effectively learn the residual characteristics of drastically changing local areas in the high-frequency force response subdomain, thereby improving the accuracy of residual prediction in high-gradient regions.

[0140] When operating the S530, the low-frequency subdomain input features are constructed based on the coordinates of the sampling points in the low-frequency force response subdomain, the operating parameters, and the physical prior features determined by the physical benchmark model.

[0141] According to an embodiment of the present invention, after determining the low-frequency force response subdomain, the coordinate information of each sampling point in the low-frequency force response subdomain can be obtained, and the low-frequency subdomain input features can be constructed by combining the working parameters corresponding to the current cutting load condition and the physical prior features determined by the physical reference model. The specific process can be referred to operation S510.

[0142] In the S540 operation, the low-frequency subdomain input features are input into the non-uniform Fourier neural operator to obtain the low-frequency residual prediction results.

[0143] In some embodiments, for the low-frequency force response subdomain, its continuous field or sampling point features can be transformed into a regular grid region before being learned using a non-uniform Fourier neural operator. Since the residual changes in the low-frequency force response subdomain are relatively gradual, the impact of regularization or interpolation on local information is relatively small, while Fourier transform-based operator propagation can learn the overall change pattern more efficiently.

[0144] For example, suppose the first The low-frequency subdomain hiding features of the layer are The propagation process of a non-uniform Fourier neural operator can be represented as:

[0145] in, This represents the non-uniform Fourier integral operator. Represents a linear mapping. Indicates the first Hidden features of low-frequency subdomains in the layer.

[0146] After propagation through multiple operators, the hidden features can be mapped to residual prediction results in the low-frequency force response subdomain, for example:

[0147] in, Represents the sampling points in the low-frequency force response subdomain The corresponding low-frequency residual prediction results, This represents the projection mapping used to output the residual prediction results. This represents the hidden features of the low-frequency subdomain after multiple propagations.

[0148] Through the above processing, the non-uniform Fourier neural operator can learn a smoother overall residual variation law in the low-frequency force response subdomain, reducing the dependence on local complex geometric transformations while ensuring prediction accuracy, and improving the efficiency and stability of residual prediction in the low-frequency region.

[0149] Figure 6 The flowchart illustrates an example of the present invention of obtaining the global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response.

[0150] like Figure 6 As shown, operation S150 includes operations S610 to S630.

[0151] In operation S610, based on the distribution of the high-frequency force response subdomain and the low-frequency force response subdomain on the worktable surface area of ​​the machine tool worktable, the high-frequency residual prediction results and the low-frequency residual prediction results are integrated to obtain the global residual prediction field.

[0152] According to an embodiment of the present invention, after obtaining the high-frequency residual prediction results and the low-frequency residual prediction results respectively, the residual prediction results corresponding to each subdomain can be restored to their corresponding positions in the worktable surface area based on the spatial distribution positions of the high-frequency force response subdomain and the low-frequency force response subdomain in the worktable surface area.

[0153] Specifically, for the high-frequency force response subdomain, since the geometrically enhanced Fourier neural operator can perform residual prediction in the adaptive computation domain, the high-frequency residual prediction results in the adaptive computation domain can be remapped back to the physical space location of the corresponding high-frequency force response subdomain. For the low-frequency force response subdomain, since the non-uniform Fourier neural operator can perform residual prediction in the regular grid or the interpolated computation region, the low-frequency residual prediction results on the regular grid can be restored to the physical space location of the corresponding low-frequency force response subdomain.

[0154] For example, the high-frequency residual prediction results and the low-frequency residual prediction results, after being restored to the physical space, can be expressed as follows:

[0155]

[0156] in, This represents the high-frequency residual prediction results after mapping back to physical space. This represents the high-frequency residual prediction results obtained by the geometrically enhanced Fourier neural operator in the computational domain. This represents the reverse mapping from the computational domain to the physical space; This represents the low-frequency residual prediction result after being restored to the physical space. This represents the low-frequency residual prediction result obtained by the non-uniform Fourier neural operator. This represents the reconstruction or interpolation mapping from a regular mesh to the physical coordinates of a low-frequency force response subdomain.

[0157] Furthermore, based on the distribution of the high-frequency force response subdomain and the low-frequency force response subdomain on the worktable surface, the two can be integrated into a global residual prediction field:

[0158] in, Indicates the position of the worktable surface Global residual prediction value at the location, Represents the high-frequency force response subdomain. This represents the low-frequency force response subdomain.

[0159] When operating the S620, the global physical baseline force response corresponding to the worktable surface area is determined based on the physical reference model.

[0160] According to an embodiment of the present invention, the physical baseline force response corresponding to each position in the worktable surface area can be determined by a physical reference model based on the working parameters corresponding to the current cutting load condition, thereby obtaining the global physical baseline force response.

[0161] In operation S630, the global residual prediction field is superimposed with the global physical baseline force response to obtain the global force response prediction result.

[0162] According to an embodiment of the present invention, after obtaining the global residual prediction field and the global physical baseline force response, the residual prediction value at the same workbench surface location can be superimposed with the physical baseline force response to obtain the force response prediction value at that location. After performing the above processing on each location within the workbench surface area, the global force response prediction result is obtained.

[0163] For example, the global force response prediction result can be expressed as:

[0164] in, Indicates position Global force response prediction results at the location, Indicates position Physical baseline force response at that point Indicates position The predicted value of the global residual at the location.

[0165] The final global force response prediction result obtained through the above method consists of two parts: one part is the physical baseline force response, which characterizes the macroscopic transmission law of cutting load in the machine tool table; the other part is the global residual prediction field, which is used to compensate for local deviations that are difficult to accurately represent by the physical reference model. Therefore, while preserving the interpretability of the physical reference model, neural operators can be used to correct the residuals in regions of different complexities, thereby improving the accuracy of the global force response prediction result.

[0166] In some embodiments, since the high-frequency force response subdomain and the low-frequency force response subdomain are predicted by different neural operators, discontinuities in the predicted residual values ​​may occur at the boundary between the subdomains. Therefore, boundary continuity constraints can be introduced during model training or post-processing to ensure that the residual prediction results of the high-frequency and low-frequency force response subdomains remain consistent or smoothly transition in the boundary region. Physical consistency constraints can also be introduced to prevent unreasonable high-frequency oscillations in the residual prediction results far from the load application area, thereby ensuring that the final global force response prediction result maintains a macroscopic attenuation trend consistent with the physical baseline force response.

[0167] In one illustrative embodiment, during the training of geometrically enhanced Fourier neural operators and non-uniform Fourier neural operators, a joint loss function can be constructed based on residual fitting loss, boundary continuity loss, and physical consistency loss to improve the accuracy of residual prediction results in different subdomains and the continuity after global splicing.

[0168] Specifically, since the high-frequency force response subdomain and the low-frequency force response subdomain use different neural operators for residual prediction, inconsistencies in prediction scale, prediction trend, or local errors may exist at the boundary between different subdomains. If the residual prediction results of each subdomain are directly concatenated, residual jumps may occur at the subdomain boundaries, leading to discontinuities in the final global force response prediction result at the boundary location. Therefore, a boundary continuity loss can be introduced to constrain the residual prediction results of the high-frequency and low-frequency force response subdomains in the boundary region, ensuring that adjacent subdomains have similar residual prediction values ​​near the boundary.

[0169] Therefore, a joint loss function can be introduced, which can be expressed as:

[0170] in, This represents the residual fitting loss. Indicates continuous loss at the boundary. Indicates the loss of physical consistency. and These represent the weight coefficients corresponding to boundary continuity loss and physical consistency loss, respectively.

[0171] For example, the residual fitting loss can be expressed as:

[0172] in, Indicates the sampling points used for training. This indicates that the neural operator is at the sampling point. The output residual prediction value, Indicates sampling point Reference residual label at the location, This indicates the number of sampling points involved in the loss calculation.

[0173] Boundary continuity loss can be expressed as:

[0174] in, This represents the set of boundary sampling points between the high-frequency force response subdomain and the low-frequency force response subdomain. This represents the predicted high-frequency residual value after mapping back to physical space. This represents the low-frequency residual prediction value after being restored to the physical space. By minimizing the boundary continuity loss, the prediction jumps at the subdomain boundaries can be reduced, improving the continuity of the global residual prediction field.

[0175] The physical consistency loss can be expressed as:

[0176] in, This represents the set of far-field regions far from the location where the load is applied. Indicates position The residual prediction value at the physical consistency loss can help maintain a smaller amplitude in the residual prediction results in the far field region, thereby avoiding the final global force response prediction results from deviating from the macroscopic decay trend described by the physical baseline force response.

[0177] Furthermore, corresponding optimization objectives can be constructed for the high-frequency force response subdomain and the low-frequency force response subdomain, respectively. For example, the optimization objective for the high-frequency force response subdomain may include residual fitting loss, boundary continuity loss, and physical consistency loss in the high-frequency region; the optimization objective for the low-frequency force response subdomain may include residual fitting loss, boundary continuity loss, and physical consistency loss in the low-frequency region. Through the above joint optimization method, different neural operators can learn the residual distribution in their respective adapted subdomains, while ensuring the continuity at the subdomain boundaries and the physical rationality of the overall prediction results.

[0178] To demonstrate the accuracy of the machine tool table force response prediction method provided by this invention, the following embodiments are given: Table 1 shows a comparison of the prediction accuracy of the machine tool table force response prediction method provided in this embodiment of the invention with that of existing technologies.

[0179] Table 1 Comparison of Prediction Accuracy

[0180] Where MAE is the mean absolute error; RMSE is the root mean square error; and R² is the coefficient of determination.

[0181] Furthermore, robustness experiments were conducted from two dimensions: sparse measurement points and small sample size, to verify its applicability. Based on the original measurement points, observation subsets with proportions of 90%, 80%, and 70% were constructed. Stratified uniform sampling was used to ensure that the measurement points covered different areas, and the machine tool table force response prediction method of this invention was used for prediction.

[0182] This embodiment uses 53 training scenarios as a baseline to construct 42, 32, and 24 sub-training sets. The sample size adopts the same stratified sampling principle to cover different scenarios, and R² is always kept above 0.986.

[0183] In addition, ablation experiments were conducted to compare the prediction method of this embodiment with the prediction method after removing the physical baseline model and the prediction method after removing the boundary loss. The experimental results show that after removing the physical baseline model, the coefficient of determination decreased from 0.990 to 0.814, and the central peak recovery rate was only 56.9%. This indicates that the physical baseline model can provide macroscopic force flow distribution constraints for force response prediction. Without this constraint, when relying solely on data-driven methods for residual or force response prediction, it is difficult to stably recover the peak response near the load application area, resulting in a decrease in overall fitting ability and local peak prediction ability.

[0184] After removing the boundary loss, the mean absolute error increased by 8.447 MPa and the coefficient of determination decreased by 0.338. This indicates that in the process of performing residual predictions in the high-frequency force response subdomain and the low-frequency force response subdomain and integrating them into the global residual prediction field, if there is a lack of constraint on the continuity of the prediction results at the subdomain boundary, prediction jumps or splicing errors are likely to occur at the subdomain boundary, thus affecting the continuity and accuracy of the global force response prediction results.

[0185] The machine tool table force response prediction device provided by the present invention is described below. The machine tool table force response prediction device described below and the machine tool table force response prediction method described above can be referred to in correspondence.

[0186] Figure 7 This is a structural block diagram of the machine tool worktable force response prediction device of the present invention.

[0187] like Figure 7 As shown, the machine tool worktable force response prediction device 700 includes a model building module 710, a space reconstruction module 720, a partitioning module 730, a residual prediction module 740, and a response prediction module 750.

[0188] The model building module 710 is used to acquire the working parameters of the machine tool table under cutting load conditions, as well as the measurement point positions and force response data of multiple discrete measurement points, and to build a physical benchmark model based on the working parameters.

[0189] The spatial reconstruction module 720 is used to determine the physical baseline force response based on the physical benchmark model, and to perform spatial reconstruction based on the residuals of the force response data of multiple discrete measuring points relative to the physical baseline force response, so as to obtain a global continuous force response field.

[0190] The partitioning module 730 is used to partition the worktable surface area of ​​the machine tool worktable into subdomains based on the gradient characteristics output by the physical reference model, thereby obtaining a high-frequency force response subdomain and a low-frequency force response subdomain.

[0191] The residual prediction module 740 is used to predict the residuals of the high-frequency force response subdomain based on the geometrically enhanced Fourier neural operator and to predict the residuals of the low-frequency force response subdomain based on the non-uniform Fourier neural operator.

[0192] The response prediction module 750 is used to obtain the global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response.

[0193] Figure 8 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 8As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840. The processor 810, communications interface 820, and memory 830 communicate with each other via the communication bus 840. The processor 810 can call logical instructions from the memory 830 to execute a machine tool table force response prediction method.

[0194] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0195] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the machine tool table force response prediction method provided by the above methods.

[0196] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the machine tool table force response prediction method provided by the methods described above.

[0197] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0198] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0199] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the force response of a machine tool worktable, characterized in that, include: The working parameters of the machine tool table under cutting load conditions, as well as the measurement point positions and force response data of multiple discrete measurement points, are obtained, and a physical benchmark model is constructed based on the working parameters. The physical baseline force response is determined based on the physical benchmark model, and spatial reconstruction is performed based on the residuals of the force response data of the multiple discrete measuring points relative to the physical baseline force response to obtain a global continuous force response field. Based on the gradient characteristics output by the physical benchmark model, the worktable surface area of ​​the machine tool worktable is divided into subdomains to obtain a high-frequency force response subdomain and a low-frequency force response subdomain. The residual prediction results of the high-frequency force response subdomain are determined based on the geometrically enhanced Fourier neural operator, and the residual prediction results of the low-frequency force response subdomain are determined based on the non-uniform Fourier neural operator. Based on the residual prediction results of each subdomain and the physical baseline force response, the global force response prediction results are obtained.

2. The machine tool table force response prediction method according to claim 1, characterized in that, The operating parameters include cutting load parameters, load application point parameters, and machine tool table geometric parameters; The construction of the physical benchmark model based on the operating condition parameters includes: Based on the cutting load parameters and the load application point parameters, determine the load strength term of the cutting load acting on the machine tool table; Based on the load application point parameters and the machine tool table geometry parameters, determine the distance attenuation term of the table surface position relative to the load application point; Based on the cutting load parameters and the load application point parameters, determine the orientation modulation term of the worktable surface position relative to the load application point; Based on the load strength term, the distance attenuation term, and the direction modulation term, a physical benchmark model is constructed to characterize the force response distribution law on the worktable surface of the machine tool worktable.

3. The machine tool table force response prediction method according to claim 1, characterized in that, The process involves determining the physical baseline force response based on the physical benchmark model, and then spatially reconstructing the force response field globally by using the residuals of the force response data from the multiple discrete measurement points relative to the physical baseline force response. This includes: Input the positions of the multiple discrete measuring points into the physical reference model to obtain the physical baseline force response corresponding to each measuring point position; The discrete residual corresponding to each measurement point location is determined based on the difference between the force response data corresponding to each measurement point location and the force response of the physical baseline. Spatial reconstruction is performed on the discrete residuals corresponding to the locations of each measurement point to obtain the global residual field corresponding to the surface area of ​​the machine tool table. The global residual field is superimposed with the physical baseline force response corresponding to the surface area of ​​the machine tool table to obtain the global continuous force response field.

4. The machine tool table force response prediction method according to claim 1, characterized in that, The process of dividing the surface region of the machine tool worktable into subdomains based on the gradient features output by the physical benchmark model to obtain a high-frequency force response subdomain and a low-frequency force response subdomain includes: Multiple sampling points are determined on the surface area of ​​the machine tool worktable, and the physical reference force response corresponding to each sampling point is determined based on the physical reference model. Based on the physical reference force response corresponding to each sampling point, determine the gradient feature value corresponding to each sampling point; Based on the gradient feature values, with the goal of satisfying the preset conditions for the degree of dispersion of the gradient feature values ​​within the subdomain, the KD tree of Monte Carlo tree search is used to recursively divide the worktable surface area to obtain multiple candidate subdomains. Based on the average level of gradient feature values ​​within each candidate subdomain, the multiple candidate subdomains are divided into high-frequency force response subdomains and low-frequency force response subdomains.

5. The machine tool table force response prediction method according to claim 1, characterized in that, The determination of the residual prediction results for the high-frequency force response subdomain based on the geometrically enhanced Fourier neural operator, and the determination of the residual prediction results for the low-frequency force response subdomain based on the non-uniform Fourier neural operator, includes: Based on the coordinates of the sampling points in the high-frequency force response subdomain, the operating parameters, and the physical prior features determined by the physical benchmark model, the high-frequency subdomain input features are constructed. The high-frequency subdomain input features are input into the geometrically enhanced Fourier neural operator to obtain high-frequency residual prediction results; Based on the coordinates of the sampling points in the low-frequency force response subdomain, the operating parameters, and the physical prior features determined by the physical benchmark model, the low-frequency subdomain input features are constructed. The low-frequency subdomain input features are input into the non-uniform Fourier neural operator to obtain the low-frequency residual prediction results.

6. The machine tool table force response prediction method according to claim 1, characterized in that, The process of obtaining the global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response includes: Based on the distribution positions of the high-frequency force response subdomain and the low-frequency force response subdomain in the worktable surface area of ​​the machine tool worktable, the high-frequency residual prediction results and the low-frequency residual prediction results are integrated to obtain the global residual prediction field; The global physical baseline force response corresponding to the surface region of the worktable is determined based on the physical benchmark model. The global residual prediction field is superimposed with the global physical baseline force response to obtain the global force response prediction result.

7. A machine tool worktable force response prediction device, characterized in that, include: The model building module is used to acquire the working parameters of the machine tool table under cutting load conditions, as well as the measurement point positions and force response data of multiple discrete measurement points, and to build a physical benchmark model based on the working parameters. The spatial reconstruction module is used to determine the physical baseline force response based on the physical benchmark model, and to perform spatial reconstruction based on the residuals of the measurement point positions and force response data of the multiple discrete measurement points relative to the physical baseline force response, so as to obtain a global continuous force response field. The partitioning module is used to divide the worktable surface area of ​​the machine tool worktable into subdomains based on the gradient features output by the physical reference model, thereby obtaining a high-frequency force response subdomain and a low-frequency force response subdomain. The residual prediction module is used to predict the residuals of the high-frequency force response subdomain based on the geometrically enhanced Fourier neural operator, and to predict the residuals of the low-frequency force response subdomain based on the non-uniform Fourier neural operator. The response prediction module is used to obtain the global force response prediction result based on the residual prediction results of each subdomain and the physical baseline force response.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the machine tool table force response prediction method as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the machine tool table force response prediction method as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the machine tool table force response prediction method as described in any one of claims 1 to 6.

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