A five-axis numerical control machine tool precision direct drive rotary table thermal deformation prediction method and system

Abstract

The application discloses a kind of five-axis numerical control machine tool precision direct drive rotary table thermal deformation prediction method and system, comprising: constructing the geometric point cloud model of direct drive rotary table;Temperature field function is constructed on point cloud;Non-uniform fast Fourier transform-based neural operator model is constructed;The heat conduction physical model is used as constraint term, and based on the uncertainty of prediction error, the physical loss weight of adaptive adjustment is constructed, and finally the total loss function is constructed;Based on the total loss function, train neural operator model under multiple time, multiple working condition;After training is completed, using neural operator model, the data collected by sparse temperature sensor is used to complete and high-resolution reconstruction to point cloud thermal deformation field;Output point cloud thermal deformation field and calculate the geometric error parameter of direct drive rotary table, realize thermal deformation compensation.The present application can realize high-resolution, visual and on-line updated thermal deformation prediction under the condition of small amount of sensor data and low-resolution sampling.

Description

Technical Field

[0001] This invention relates to the field of precision control and thermal deformation compensation for five-axis CNC machine tools, and in particular to a method and system for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool. Background Technology

[0002] In five-axis CNC machine tools, the high-precision, high-torque direct-drive rotary table is a crucial functional component for machining complex curved surfaces and achieving high dynamic positioning. Its rotational and positioning accuracy directly affects the overall machining quality. Direct-drive rotary tables generally have advantages such as fast response speed, short transmission chain, and zero mechanical backlash. However, under long-term operation or high-load conditions, factors such as motor losses, bearing friction, and changes in ambient temperature can easily cause significant heat accumulation, leading to thermal deformation.

[0003] Direct-drive rotary tables are characterized by their compact structure, high torque density, and concentrated heat source distribution. Their temperature field and thermal deformation processes typically exhibit significant nonlinearity, time-varying characteristics, and spatial inhomogeneity. Rotary table thermal deformation usually manifests as axial drift of the rotation axis, as well as tilting errors and rotation center offsets. These are easily amplified during five-axis simultaneous machining, severely limiting machining accuracy.

[0004] In existing technologies, one type of method typically models the relationship between temperature sensor data and thermal deformation based on convolutional neural networks, fully connected neural networks, or time-series prediction models. This type of method relies on fitting a large number of samples, usually requiring many sensor measurement points and training data, and the model output is often a single error value or a finite-dimensional result, which cannot directly describe the overall distribution of the thermal field or thermal deformation field under complex structures.

[0005] To improve the physical consistency of the model, some patents introduce Physical Information Neural Networks (PINNs), which assist training by adding control equation constraints to the loss function. For example, Chinese patent document CN121257261A discloses a method for modeling assembly process errors that considers heat, enabling rapid and accurate calculation of the thermal deformation of assembly joint surfaces affected by heat during component assembly. During component assembly, the heat generated is a significant factor affecting assembly accuracy. To achieve rapid calculation of thermal deformation during component assembly, this application utilizes a Physical Information Neural Network to construct a predictive model for the thermal deformation of assembly joint surfaces during component assembly.

[0006] However, PINN still uses traditional neural networks as its basic modeling unit, and its modeling process usually relies on a fixed spatial discretization form and a specific resolution. When the spatial sampling resolution changes or the operating conditions switch, the model often needs to be retrained or significantly adjusted, making it difficult to achieve a unified mapping across resolutions and operating conditions.

[0007] In recent years, operator learning methods such as Fourier neural operators have shown potential in field modeling. However, existing operator methods typically rely on standard regular grids for fast Fourier transform. In the modeling of complex turntable structures, to meet the requirements of regular grids, it is often necessary to introduce a large number of redundant sampling points that are unrelated to actual thermal behavior, resulting in a significant waste of data and computation, thus limiting its efficiency in engineering applications.

[0008] Therefore, there is a need for a technical solution that can reduce redundant calculations under complex structural conditions, maintain stable modeling even with a limited number of sensors and varying spatial resolution, and be applicable to the prediction of thermal deformation of precision direct-drive rotary tables in five-axis CNC machine tools. Summary of the Invention

[0009] To address the problems of existing neural network models based on function fitting in modeling complex structures, such as strong spatial resolution dependence, large redundant computational load, and insufficient adaptability across working conditions, this invention provides a method and system for predicting thermal deformation of a precision direct-drive rotary table for five-axis CNC machine tools. Under conditions of limited sensor data and low-resolution sampling, it achieves high-resolution, visualized, and online-updable thermal deformation prediction.

[0010] A method for predicting thermal deformation of a precision direct-drive rotary table in a five-axis CNC machine tool includes the following steps:

[0011] (1) Construct a geometric point cloud model of the direct drive turntable and use the point cloud as the spatial domain of the neural operator model;

[0012] (2) Construct a temperature field function on the point cloud. Based on several temperature sensors, use the data from each temperature sensor as the temperature field function value at the corresponding point cloud location.

[0013] (3) Construct a neural operator model based on non-uniform fast Fourier transform to learn the mapping relationship between point cloud temperature field function and thermal deformation field function;

[0014] (4) The heat conduction physical model is used as a constraint term, and an adaptively adjusted physical loss weight is constructed based on the uncertainty of the prediction error, and finally the total loss function is constructed;

[0015] (5) Based on the total loss function, train the neural operator model under multiple time points and multiple operating conditions;

[0016] (6) After training, the point cloud thermal deformation field is completed and reconstructed at high resolution using the neural operator model and the data collected by the sparse temperature sensor.

[0017] (7) Output the point cloud thermal deformation field and calculate the geometric error parameters of the direct drive turntable to achieve thermal deformation compensation.

[0018] This invention uses geometric point clouds as a unified spatial representation of the direct-drive turntable structure. By constructing a neural operator model based on non-uniform fast Fourier transform, it directly learns the spatial and temporal mapping relationship of the turntable's thermal field or thermal deformation field. While avoiding the computational waste caused by standard regular grids, it achieves efficient modeling, online updating, and stable compensation of the thermal deformation field of the direct-drive turntable. Thus, under conditions of limited sensor data and low-resolution sampling, it achieves high-resolution, visualized, and online-updable thermal deformation prediction.

[0019] The specific process of step (2) is as follows:

[0020] The temperature field function is constructed on the point cloud, with the following formula:

[0021] ;

[0022] In the formula, Indicates the first Point cloud coordinates, This indicates the position at time [time]. Temperature value, Represents the set of real numbers. This indicates the number of spatial points contained in the point cloud;

[0023] Then, the data from several deployed temperature sensors are used as the temperature field function values ​​for the corresponding point cloud locations to construct the point cloud temperature field function input vector. As input to the neural operator model, it is used to describe the thermal state of the direct-drive rotary table under the current operating conditions.

[0024] In step (3), the neural operator model achieves feature dimensionality enhancement and cross-scale modeling through a multi-layer Fourier transform-inverse transform structure. The Fourier transform part adopts non-uniform fast Fourier transform (NUFFT), which enables the operator to directly act on irregular point cloud sampling data, avoiding a large number of redundant sampling points and invalid calculations introduced by standard regular grids.

[0025] Through layer-by-layer Fourier operator mapping, the model can be naturally generalized to high-resolution point clouds under low-resolution input conditions, thereby achieving high-resolution reconstruction of the thermal deformation field.

[0026] In step (3), the mapping relationship between the point cloud temperature field function and the thermal deformation field function is as follows:

[0027] ;

[0028] In the formula, Represents a neural operator. This represents the thermal deformation field function on the point cloud.

[0029] In step (4), the heat conduction physical model is used as a constraint term, and an adaptively adjusted physical loss weight is constructed based on the uncertainty of the prediction error. The specific process is as follows:

[0030] Using the heat conduction physical model as a constraint in the training process of the neural operator model, the theoretical response of the heat conduction physical model on the point cloud is... for:

[0031] ;

[0032] in, Operators representing physical models based on heat conduction mechanisms;

[0033] Prediction error uncertainty is defined as:

[0034] ;

[0035] in, This represents the expectation operator, which averages the distribution of error data.

[0036] Based on time Prediction error uncertainty Constructed physical loss weights for:

[0037] ;

[0038] In the formula, As the initial physical loss weights, For adjustment coefficients, To prevent numerically unstable constants.

[0039] In step (4), the total loss function is constructed, and the formula is:

[0040] ;

[0041] In the formula, This represents thermal deformation data obtained from prediction or calibration. The loss weight constant for the data item.

[0042] The specific process of step (7) is as follows:

[0043] Based on the point cloud thermal deformation field output by the neural operator model, the geometric error parameters of the direct drive rotary table are further calculated, and the geometric error parameters are converted into compensation quantities and output to the control system of the five-axis CNC machine tool to realize real-time or near-real-time compensation of thermal deformation.

[0044] The geometric error parameters mentioned are rotation axis drift, tilt error, or rotation center offset.

[0045] A thermal deformation prediction system for a precision direct-drive rotary table of a five-axis CNC machine tool includes a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the aforementioned thermal deformation prediction method for a precision direct-drive rotary table of a five-axis CNC machine tool.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1. This invention achieves overall learning of the thermal deformation field of a direct-drive turntable through a point cloud-based neural operator modeling method, which is different from the traditional neural network method based on function fitting.

[0048] 2. This invention employs non-uniform fast Fourier transform, which avoids a large number of redundant sampling points and invalid calculations caused by standard regular grids, and significantly reduces the amount of computation.

[0049] 3. This invention has the ability to generalize across spatial resolutions and working conditions, and can achieve high-resolution thermal deformation prediction under low-resolution sampling conditions.

[0050] 4. This invention supports online updates and result visualization, and is applicable to digital twins and long-term operation compensation of the thermal behavior of direct drive turntables.

[0051] 5. This invention can maintain stable prediction performance even when the number of sensors is limited or there are local anomalies, and it has strong engineering applicability. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart of a method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool, according to an embodiment of the present invention.

[0054] Figure 2 This is a prediction result diagram using a turntable rotary shaft as an example in an embodiment of the present invention.

[0055] Figure 3 This is a prediction error diagram using the rotary axis of a turntable as an example in an embodiment of the present invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0058] like Figure 1 As shown, a method for predicting thermal deformation of a precision direct-drive rotary table in a five-axis CNC machine tool includes the following steps:

[0059] S01, Construct the geometric point cloud model of the direct-drive turntable.

[0060] First, a three-dimensional geometric model of the direct-drive turntable is obtained, and then the three-dimensional geometric model is spatially discretized to represent the solid structure of the direct-drive turntable as a geometric point cloud model composed of several discrete spatial points.

[0061] The geometric point cloud serves as the spatial domain for subsequent neural operator modeling, representing the temperature and thermal deformation field functions. By employing a geometric point cloud for spatial representation, the construction of standard regular meshes can be avoided, thereby reducing unnecessary computations caused by redundant sampling points.

[0062] S02, construct the temperature field function on the point cloud.

[0063] The thermal state of the direct-drive turntable is represented as a function defined on a point cloud space. Assuming the point cloud contains N spatial points, the temperature field function can be expressed as:

[0064] ;

[0065] In the formula, Indicates the first Point cloud coordinates, This indicates the position at time [time]. Temperature value.

[0066] For point cloud locations with temperature sensors, the function value is given by the measurement data; for locations without sensors, the function value is to be inferred. Thus, the point cloud temperature function input vector is constructed:

[0067] ;

[0068] This point cloud function serves as the input to the neural operator, used to describe the thermal state of the direct-drive turntable under current operating conditions.

[0069] S03, Construct a Fourier neural operator model based on non-uniform fast Fourier transform to learn the mapping relationship between point cloud thermal field function and thermal deformation field function:

[0070] ;

[0071] In the formula, Represents a neural operator. This represents the thermal deformation field function on the point cloud.

[0072] The neural operator model achieves feature dimensionality enhancement and cross-scale modeling through a multi-layer Fourier transform-inverse transform structure. The Fourier transform part adopts non-uniform fast Fourier transform (NUFFT), which enables the operator to directly operate on irregular point cloud sampling data, avoiding a large number of redundant sampling points and invalid calculations introduced by standard regular grids.

[0073] Through layer-by-layer Fourier operator mapping, the model can be naturally generalized to high-resolution point clouds under low-resolution input conditions, thereby achieving high-resolution reconstruction of the thermal deformation field.

[0074] S04 uses the heat conduction physical model as a constraint term and constructs an adaptively adjusted physical loss weight based on the uncertainty of prediction error, and finally constructs the total loss function.

[0075] To improve the stability and physical consistency of neural operators under complex working conditions, the Physical Information Neural Operator (PINO) framework is introduced, which uses the heat conduction physical model as a constraint in the operator training process.

[0076] Let the theoretical response of the heat conduction physical model on the point cloud be... for:

[0077] ;

[0078] in, This represents a physical model operator based on the heat conduction mechanism.

[0079] To avoid the unreasonable impact of physical constraints on model training under different operating conditions and stages, an adaptive adjustment mechanism for physical loss weights is constructed based on the uncertainty of prediction error. The uncertainty of prediction error is defined as:

[0080] ;

[0081] Based on this uncertainty, the physical loss weight is defined as:

[0082] ;

[0083] In the formula, As the initial physical loss weights, For adjustment coefficients, To prevent numerically unstable constants.

[0084] The total loss function for training the neural operator is:

[0085] ;

[0086] In the formula, This represents thermal deformation data obtained from prediction or calibration. The loss weight constant is used for the data items. For adaptive physical loss weights.

[0087] S05, based on the total loss function, trains the neural operator model under multiple time points and operating conditions.

[0088] By introducing point cloud temperature field function inputs at different operating times and under different working conditions, the neural operator can learn the evolution law of thermal deformation with time and working conditions, thereby improving the model's applicability to different working conditions.

[0089] S06, after training is completed, uses a neural operator model to complete and reconstruct the thermal deformation field on the point cloud under the condition of only a small number of temperature measurement points.

[0090] Through the cross-scale modeling capability of neural operators, the model can output a high-resolution point cloud thermal deformation field under low-resolution input conditions, thereby achieving a fine description of the overall thermal deformation distribution of the direct-drive turntable.

[0091] S07 outputs the point cloud thermal deformation field and calculates the geometric error parameters of the direct-drive turntable to achieve thermal deformation compensation.

[0092] Based on the point cloud thermal deformation field output by the neural operator model, geometric error parameters such as the rotation axis drift, tilt error, or rotation center offset of the direct drive rotary table are further calculated and converted into compensation quantities and output to the five-axis CNC machine tool control system to realize real-time or near-real-time compensation of thermal deformation.

[0093] Based on the same inventive principle, this embodiment also provides a thermal deformation prediction system for a five-axis CNC machine tool precision direct drive rotary table, including a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the thermal deformation prediction method for a five-axis CNC machine tool precision direct drive rotary table mentioned in the above embodiment.

[0094] To verify the effectiveness of the present invention, in this embodiment, the temperature field and thermal deformation field of the direct-drive turntable are predicted when it has been running for approximately 1000 s. In this example, only eight PT100 sensors on one side are used as sensor measurement points, and constant-temperature heat sources are symmetrically arranged on both sides of the turntable axis. Considering normal air heat dissipation, the point cloud is directly generated after importing the 3D model.

[0095] The predicted point cloud temperature field results are output in the form of a three-dimensional point cloud. The prediction results and errors are as follows: Figure 2 and Figure 3 As shown, its spatial distribution characteristics can reflect the temperature differences in different shaft sections and step transition areas of the turntable. The areas with higher temperatures are mainly distributed at the ends of the turntable and at locations of local structural changes, while the areas with lower temperatures are distributed in the main shaft section area, and the overall temperature distribution is continuous.

[0096] Simultaneously, the difference between the predicted results and the reference temperature field was analyzed to obtain the corresponding absolute error distribution. The absolute error exhibits a non-uniform distribution in space, with the error mainly concentrated in the local area in direct contact with the heat source, while maintaining a smaller amplitude within the main body of the turntable. The overall error distribution is continuous and without significant abrupt changes.

[0097] Under the conditions of this embodiment, when the prediction results are quantitatively evaluated, the average absolute error, root mean square error, and maximum error of the temperature prediction error can be obtained. The numerical range of these values ​​is only a reference result under this embodiment, used to illustrate the feasibility of the method of the present invention in reconstructing the temperature field and thermal deformation field of the direct drive turntable under sparse measurement point conditions.

[0098] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting thermal deformation of a precision direct-drive rotary table in a five-axis CNC machine tool, characterized in that, Includes the following steps: (1) Construct a geometric point cloud model of the direct drive turntable and use the point cloud as the spatial domain of the neural operator model; (2) Construct a temperature field function on the point cloud. Based on several temperature sensors, use the data from each temperature sensor as the temperature field function value at the corresponding point cloud location. (3) Construct a neural operator model based on non-uniform fast Fourier transform to learn the mapping relationship between point cloud temperature field function and thermal deformation field function; (4) The heat conduction physical model is used as a constraint term, and an adaptively adjusted physical loss weight is constructed based on the uncertainty of the prediction error, and finally the total loss function is constructed; (5) Based on the total loss function, train the neural operator model under multiple time points and multiple operating conditions; (6) After training, the point cloud thermal deformation field is completed and reconstructed at high resolution using the neural operator model and the data collected by the sparse temperature sensor. (7) Output the point cloud thermal deformation field and calculate the geometric error parameters of the direct drive turntable to achieve thermal deformation compensation.

2. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 1, characterized in that, The specific process of step (2) is as follows: The temperature field function is constructed on the point cloud, with the following formula: ； In the formula, Indicates the first Point cloud coordinates, express At any moment Temperature value, Represents the set of real numbers. This indicates the number of spatial points contained in the point cloud; Then, the data from several deployed temperature sensors are used as the temperature field function values ​​for the corresponding point cloud locations to construct the point cloud temperature field function input vector. , as input to the neural operator model.

3. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 1, characterized in that, In step (3), the neural operator model achieves feature dimensionality enhancement and cross-scale modeling through a multi-layer Fourier transform-inverse transform structure, wherein the Fourier transform part adopts non-uniform fast Fourier transform.

4. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 2, characterized in that, In step (3), the mapping relationship between the point cloud temperature field function and the thermal deformation field function is as follows: ； In the formula, Represents a neural operator. This represents the thermal deformation field function on the point cloud.

5. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 4, characterized in that, In step (4), the heat conduction physical model is used as a constraint term, and an adaptively adjusted physical loss weight is constructed based on the uncertainty of the prediction error. The specific process is as follows: Using the heat conduction physical model as a constraint in the training process of the neural operator model, the theoretical response of the heat conduction physical model on the point cloud is... for: ； in, Operators representing physical models based on heat conduction mechanisms; Prediction error uncertainty is defined as: ； in, This represents the expectation operator, which averages the distribution of error data. Based on time Prediction error uncertainty Constructed physical loss weights for: ； In the formula, As the initial physical loss weights, For adjustment coefficients, To prevent numerically unstable constants.

6. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 5, characterized in that, In step (4), the total loss function is constructed, and the formula is: ； In the formula, This represents thermal deformation data obtained from prediction or calibration. The loss weight constant for the data item.

7. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 1, characterized in that, The specific process of step (7) is as follows: Based on the point cloud thermal deformation field output by the neural operator model, the geometric error parameters of the direct drive rotary table are further calculated, and the geometric error parameters are converted into compensation quantities and output to the control system of the five-axis CNC machine tool to realize real-time or near-real-time compensation of thermal deformation.

8. The method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool according to claim 7, characterized in that, The geometric error parameters mentioned are rotation axis drift, tilt error, or rotation center offset.

9. A thermal deformation prediction system for a precision direct-drive rotary table of a five-axis CNC machine tool, characterized in that, The method includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the method for predicting thermal deformation of a precision direct-drive rotary table for a five-axis CNC machine tool as described in any one of claims 1-8.

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