Multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers

Abstract

This invention relates to the field of machine tool machining control technology, and discloses a multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers. Temperature sensor arrays are deployed on the bed, column, and spindle box, with sensor nodes acting as graph nodes. A spatial topological adjacency matrix is ​​constructed based on the physical structure and connection relationships of the machine tool. Temperature time-series data and the adjacency matrix are input into a spatiotemporal graph convolutional network model. The graph convolutional layer captures the spatial thermal conduction characteristics of adjacent nodes, and the gated cyclic unit layer captures the temporal temperature change characteristics, outputting thermal deformation prediction vectors for each motion axis. A multi-axis interpolation calculator converts the prediction vectors into reverse displacement compensation values, which are then superimposed on the position commands of each axis for execution. This invention eliminates prediction lag caused by delays in the thermal conduction path, reduces spatial offset errors in multi-axis linkage trajectories, and improves position following stability.

Description

Technical Field

[0001] This invention relates to the field of machine tool processing control technology, and discloses a multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers. Background Technology

[0002] Currently, during long-term operation, horizontal machining centers experience thermal deformation in components such as the spindle, column, and bed due to friction and cutting heat, leading to a misalignment between the tool and workpiece. Existing thermal error compensation methods generally employ independent time-series-based models such as multiple linear regression or support vector machines. These conventional solutions typically deploy multiple temperature sensors at key locations on the machine tool, directly inputting the temperature data collected by each sensor as independent feature variables into the prediction model. The model establishes a mapping relationship between historical temperature data and thermal deformation measured by displacement sensors, outputting the linear offset of each motion axis during CNC system operation. The CNC system's interpolation unit then directly superimposes these offsets into the position commands for post-processing compensation.

[0003] The drawback of the existing technology is that there is a rigid physical connection between the bed, column, and spindle box of a horizontal machining center, and heat has a clear conduction path between adjacent components. Inputting temperature measurement data as independent variables into the model severs the spatial heat conduction topology between the machine tool's physical structures. When a horizontal machining center performs multi-axis high-speed linkage machining, the alternating motion of each axis generates complex heat source abrupt changes, and the spatial gradient of the temperature field changes drastically in a very short time. Existing independent time-series models lack the ability to represent the physical path of spatial heat conduction and cannot respond promptly to temperature fluctuations between non-adjacent components caused by heat conduction delays. This results in lag and abrupt distortion in the model's output thermal deformation predictions, leading to spatial deviations in the multi-axis linkage trajectory and failing to meet the requirements of high-precision coordinated motion. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers, which can effectively solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers includes a temperature sensor array, a data processing module, a spatiotemporal graph convolutional network model, and a multi-axis interpolation calculator. The temperature sensor array is deployed on the bed, column and spindle box of the horizontal machining center. The data processing module uses each temperature sensor node as a graph node, constructs a spatial topological adjacency matrix based on the connection relationship of the machine tool's physical structure, and inputs the temperature time series data collected by the temperature sensor array and the spatial topological adjacency matrix into the spatiotemporal graph convolutional network model. The spatiotemporal graph convolutional network model captures the spatial heat conduction characteristics between adjacent graph nodes through graph convolutional layers, captures the temperature change characteristics over time through gated recurrent unit layers, and outputs thermal deformation prediction vectors for each motion axis relative to the initial coordinate system. The multi-axis interpolation calculator converts the thermal deformation prediction vector into a reverse displacement compensation value, adds the reverse displacement compensation value to the position commands of each axis generated by the multi-axis interpolation calculator, and sends the superimposed position commands to each axis servo driver to execute position closed-loop control.

[0006] Preferably, the data processing module constructs the spatial topological adjacency matrix by extracting the physical mating surfaces of the bed and column and the guide rail mating surfaces of the spindle box and column in the three-dimensional assembly model of the horizontal machining center as edges, setting the initial weight of the adjacency matrix based on the reciprocal of the physical distance of the heat conduction path between each pair of graph nodes, and superimposing convective heat transfer association weights on the initial weight of the adjacency matrix for graph nodes in the same coolant pipe coverage area to generate the spatial topological adjacency matrix that integrates conduction and convection heat transfer paths.

[0007] Preferably, the graph convolutional layer in the spatiotemporal graph convolutional network model is configured with a local convolutional kernel based on the Chebyshev polynomial approximation. The local convolutional kernel calculates the temperature aggregation features of the first-order and second-order neighbor nodes of each graph node according to the spatial topological adjacency matrix. The first-order neighbor nodes correspond to temperature sensor nodes on physically directly connected components, and the second-order neighbor nodes correspond to temperature sensor nodes physically separated by an intermediate component. The graph convolutional layer fuses the temperature aggregation features of the first-order and second-order neighbor nodes with the temperature time series data of the current graph node through the local convolutional kernel to generate a graph node spatial feature matrix containing the local spatial heat conduction gradient.

[0008] Preferably, the gated loop unit layer receives the graph node spatial feature matrix as an input sequence. The gated loop unit layer contains an update gate and a reset gate. The update gate is used to calculate the retention ratio between the hidden state at the previous time and the candidate hidden state at the current time. The reset gate is used to control the proportion of features related to historical temperature change trends in the graph node spatial feature matrix at the current time flowing into the candidate hidden state. The gated loop unit layer dynamically adjusts the bias parameters of the update gate and the reset gate according to the feed speed status of each motion axis of the horizontal machining center, and outputs a spatiotemporal feature tensor with fused time dimension.

[0009] Preferably, the process of converting the thermal deformation prediction vector into the reverse displacement compensation value includes: inputting the spatiotemporal feature tensor into a fully connected mapping layer; the fully connected mapping layer using the geometric axis directions of each motion axis of the horizontal machining center in the initial coordinate system as a reference; decoupling the spatiotemporal feature tensor into linear thermal deformation components of the X-axis, Y-axis, and Z-axis, and angular displacement thermal deformation components around the X-axis, Y-axis, and Z-axis; converting the angular displacement thermal deformation components into equivalent linear compensation components corresponding to the linear drive ends of each axis according to the inverse kinematic transformation formula; and summing the linear thermal deformation components and the equivalent linear compensation components to generate the reverse displacement compensation value.

[0010] Preferably, the specific logic of the multi-axis interpolation arithmetic unit superimposing the reverse displacement compensation value onto the position command of each axis is as follows: the multi-axis interpolation arithmetic unit obtains the theoretical position command of each axis in the current interpolation cycle, performs a difference operation on the reverse displacement compensation value of the current cycle and the historical reverse displacement compensation value of the previous interpolation cycle to obtain the single-cycle compensation increment, and performs an algebraic addition on the single-cycle compensation increment and the theoretical position command of each axis to generate the superimposed position command carrying compensation information, ensuring that the slope of the position command output by the multi-axis interpolation arithmetic unit is continuous.

[0011] Preferably, the data processing module dynamically updates the spatial topology adjacency matrix during operation. The data processing module obtains the current rotational speed of the horizontal machining center spindle and the current flow rate of the coolant pump in real time. Based on the current rotational speed, it calculates the intensity of the frictional heat source of the spindle bearing. Based on the current flow rate, it calculates the change in the convective heat transfer coefficient of the area covered by the coolant pipeline. The data processing module increases the initial weight of the adjacency matrix of the corresponding graph node based on the heat source intensity. Based on the change in the convective heat transfer coefficient, it dynamically corrects the convective heat transfer association weight, generating a dynamic spatial topology adjacency matrix that adapts to the machining conditions.

[0012] Preferably, the local convolutional kernel in the graph convolutional layer adopts an adaptive order adjustment mechanism. The graph convolutional layer calculates the variance of the temperature difference between graph nodes in the spatial topological adjacency matrix in real time. When the variance is greater than a preset thermal field mutation threshold, the Chebyshev polynomial order of the local convolutional kernel is increased from second to third order to introduce the temperature aggregation characteristics of third-order neighbor nodes and expand the receptive field of spatial heat conduction characteristics. When the variance is less than the thermal field mutation threshold, the local convolutional kernel is restored to second-order calculation to reduce the computational resource consumption of the graph convolutional layer.

[0013] Preferably, after generating the reverse displacement compensation value, a nonlinear hysteresis correction step is introduced. The nonlinear hysteresis correction step extracts the real-time current feedback value and real-time position feedback value of the servo motor of each axis of the horizontal machining center, calculates the thermal coupling deformation hysteresis of each axis lead screw based on the real-time current feedback value, and inputs the thermal coupling deformation hysteresis as a correction factor into a preset hyperbolic tangent function. The hyperbolic tangent function performs nonlinear marginal reduction correction on the equivalent linear compensation component in the reverse displacement compensation value corresponding to the force axis direction, generating the final reverse displacement compensation value that overcomes mechanical transmission backlash and elastic deformation.

[0014] Preferably, the multi-axis interpolation arithmetic unit introduces a timing alignment anti-jitter filtering mechanism when generating the single-cycle compensation increment. The multi-axis interpolation arithmetic unit is equipped with a sliding window queue, which stores the single-cycle compensation increment of the current interpolation cycle and the previous consecutive interpolation cycles into the sliding window queue. The moving average of all single-cycle compensation increments in the sliding window queue is calculated. When the deviation between the single-cycle compensation increment of the current interpolation cycle and the moving average exceeds the mechanical stiffness sensitivity threshold, the single-cycle compensation increment of the current interpolation cycle is replaced with the moving average to filter out high-frequency calculation jitter in the reverse displacement compensation value.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention treats each temperature sensor node as a graph node and constructs a spatial topological adjacency matrix based on the physical structure and connection relationships of the machine tool. The time-series temperature data and the spatial topological adjacency matrix are then input into a spatiotemporal graph convolutional network model. The graph convolutional layer utilizes Chebyshev polynomial approximation of local convolutional kernels to aggregate the temperature aggregation features of first- and second-order neighbor nodes. The gated recurrent unit layer dynamically adjusts the bias parameters based on the feed rate to calculate the hidden states in the time dimension. This approach directly integrates the physical heat conduction paths between machine tool components into the model's data processing flow, enabling the model to synchronously acquire temperature gradient changes of adjacent and spaced components based on physical connections during high-speed multi-axis linkage and alternating heat sources. The resulting thermal deformation prediction vectors for each motion axis eliminate prediction lag caused by delays in heat conduction paths, reducing the spatial offset error of the multi-axis linkage trajectory.

[0016] 2. In the fully connected mapping stage, this invention decouples the spatiotemporal feature tensor into linear thermal deformation components and angular displacement thermal deformation components. These are then transformed into equivalent linear compensation components using an inverse transformation formula. The single-cycle compensation increment is calculated and superimposed within each interpolation cycle of the multi-axis interpolation operator, ensuring the continuity of the position command slope. By dynamically adjusting the weights of the spatial topological adjacency matrix based on spindle speed and coolant flow rate, and adaptively adjusting the polynomial order of the convolution kernel based on the temperature difference variance, the prediction process can adapt to sudden changes in the thermal field under different processing conditions. Combined with a nonlinear hysteresis correction stage that corrects the compensation components based on motor current feedback, and a timing alignment anti-jitter filtering mechanism that uses a sliding window queue to filter out high-frequency calculation jitter in the single-cycle compensation increment, this overcomes compensation deviations caused by mechanical transmission backlash and elastic deformation, suppresses high-frequency jitter in the interpolation command, and improves the position following stability during multi-axis cooperative motion. Attached Figure Description

[0017] Figure 1 This is an overall flowchart of the multi-axis collaborative intelligent control and thermal error compensation method for horizontal machining centers according to the present invention; Figure 2 This is a flowchart illustrating the spatial topology adjacency matrix construction and dynamic update process of this invention. Figure 3 The figure shows a flowchart of the convolutional layer for extracting spatial heat conduction features and adaptive order adjustment in this invention. Figure 4 This is a flowchart of the time dimension feature processing of the gated loop unit layer in this invention; Figure 5 This is a flowchart of the thermal deformation prediction vector decoupling and nonlinear hysteresis correction process of the present invention; Figure 6 This is a flowchart of the multi-axis interpolation arithmetic unit instruction superposition and timing alignment anti-jitter filtering process of the present invention. Detailed Implementation

[0018] Please refer to the attached document. Figure 1 This embodiment provides a multi-axis collaborative control and thermal error compensation system for horizontal machining centers. The system operates within the CNC system of the horizontal machining center, which includes a bed, column, spindle box, and three linear motion axes: X, Y, and Z. Each motion axis is equipped with a corresponding servo driver and position feedback element. The system includes a temperature sensor array, a data processing module, a spatiotemporal graph convolutional network model, and a multi-axis interpolation calculator. The temperature sensor array is deployed on the bed, column, and spindle box of the horizontal machining center. Each temperature sensor node is positioned at the component mating surface and guide rail mounting reference surface of the bed; the upper and lower end mating surfaces and guide rail mating surfaces of the column; the spindle bearing mounting position and the connection position between the spindle box and the guide rail of the spindle box. Each temperature sensor node collects temperature data at its corresponding location at a fixed sampling period, generating continuous temperature time-series data. The data processing module receives time-series temperature data output from the temperature sensor array. Each temperature sensor node is treated as a graph node, and a spatial topological adjacency matrix is ​​constructed based on the physical structure and connectivity of the horizontal machining center. The dimension of the spatial topological adjacency matrix is ​​the same as the number of temperature sensor nodes, and the elements in the spatial topological adjacency matrix correspond to the heat transfer correlation strength between two graph nodes. The data processing module inputs the preprocessed temperature time-series data and the constructed spatial topological adjacency matrix into the spatiotemporal graph convolutional network model. Preprocessing operations include outlier removal and smoothing filtering of the temperature time-series data. Outlier removal uses the Laida criterion to remove sampled data exceeding a preset deviation range. Specifically, it calculates the arithmetic mean and standard deviation of a preset number of consecutive sampled values, and identifies sampled values ​​exceeding ±3 times the standard deviation of the arithmetic mean as outliers, replacing them with linear interpolation of adjacent valid sampled values. Smoothing filtering uses a moving average filter to smooth the continuous sampled data. The arithmetic mean of the sampled data within a fixed-length sliding window is calculated as the smoothed temperature data for the current moment, eliminating random noise during the temperature sampling process.

[0019] The spatiotemporal graph convolutional network model comprises graph convolutional layers and gated recurrent unit layers. The graph convolutional layers receive a spatial topological adjacency matrix and temporal temperature data, capturing the spatial thermal conduction characteristics between adjacent graph nodes. Specifically, the graph convolutional layers use the temporal temperature data of each graph node as input features, and based on the node connectivity represented by the spatial topological adjacency matrix, aggregate the temperature features of adjacent graph nodes to extract the temperature gradient and thermal conduction correlation features between different graph nodes. The gated recurrent unit layers receive the spatial thermal conduction features output by the graph convolutional layers, capturing the temperature variation characteristics over time. Using the spatial thermal conduction features at consecutive time points as input sequences, the gated recurrent unit layers model the correlation relationships of temperature features at different times, extracting the temporal variation trend and dynamic evolution characteristics of the temperature data. The spatiotemporal graph convolutional network model outputs thermal deformation prediction vectors for each motion axis relative to the initial coordinate system through serial operations of graph convolutional layers and gated recurrent unit layers. The thermal deformation prediction vectors contain the thermal deformation offset of each motion axis in three-dimensional space. The initial coordinate system is the machine tool reference coordinate system of the horizontal machining center, with its origin coinciding with the machine tool mechanical origin, and the coordinate axis directions corresponding to the linear motion directions of each motion axis.

[0020] The multi-axis interpolation calculator receives the thermal deformation prediction vector output by the spatiotemporal graph convolutional network model and converts it into a reverse displacement compensation value. The direction of the reverse displacement compensation value is opposite to the direction of the thermal deformation offset, used to compensate for the relative positional offset between the tool and the workpiece caused by thermal deformation. Based on the trajectory planning data corresponding to the machining code, the multi-axis interpolation calculator generates position commands for each motion axis. These position commands correspond to the theoretical motion positions of each axis in the machining trajectory planning. The multi-axis interpolation calculator superimposes the reverse displacement compensation value into the generated position commands for each axis, generating superimposed position commands, and sends these superimposed position commands to the corresponding servo drivers for each axis. The servo drivers receive the superimposed position commands and execute closed-loop position control for each motion axis. Based on the position commands and the actual position information collected by the position feedback element, they generate a position loop deviation value. The position loop controller and speed loop controller adjust the output torque of the servo motors to drive each motion axis to the target position, achieving real-time compensation for thermal errors and multi-axis coordinated motion control.

[0021] Table 1. Layout and Association Information of Temperature Sensor Nodes in Horizontal Machining Center Node number Deploy the components Deployment location type Physically Directly Associated Components N1 bed frame Column mating surface Column N2 bed frame X-axis guide rail mounting reference surface X-axis drive components N3 bed frame Bed end reference surface Machine tool base N4 Column Bed frame mating surface bed frame N5 Column Spindle box guide rail mating surface Spindle box N6 Column Column middle structural surface Column structure N7 Spindle box Spindle front bearing mounting position spindle components N8 Spindle box Rear bearing mounting position of spindle spindle motor components N9 Spindle box Column guide rail mating surface Column N10 Spindle box spindle box side wall Spindle box structure This table is used to clarify the layout location and physical connection relationship of each temperature sensor node, providing a physical structural basis for the construction of the spatial topological adjacency matrix. The layout location types in the table include locations directly related to the heat transfer path, such as component mating surfaces, guide rail mounting surfaces, and bearing mounting positions. Physically directly associated components correspond to horizontal machining center components that have rigid physical connections with the components to which the current node belongs, and correspond to the first-order neighbor node association relationships of the graph nodes.

[0022] This embodiment fully implements the core architecture and data processing flow of the system. It transforms the physical structural connection relationship of the horizontal machining center into a spatial topological adjacency matrix and integrates it into the thermal deformation prediction process. By extracting thermal conduction features in the spatial dimension and temperature change features in the time dimension, a thermal deformation prediction vector is generated. The compensation value and position command are superimposed and closed-loop control are achieved through a multi-axis interpolation arithmetic unit, eliminating the spatial offset of the multi-axis linkage trajectory caused by thermal deformation.

[0023] In one preferred embodiment, please refer to the appendix. Figure 2 During the construction of the spatial topological adjacency matrix by the data processing module, the physical mating surfaces of the bed and column, and the guide rail mating surfaces of the spindle box and column in the 3D assembly model of the horizontal machining center are extracted as connecting edges between drawing nodes. The physical mating surfaces include the positioning mating surface and the fixed connection surface between the bed and column. The guide rail mating surfaces include the rolling guide rail contact surface and the slider mounting mating surface between the column and the spindle box. The existence of connecting edges corresponds to a direct heat transfer path between two drawing nodes; two drawing nodes without connecting edges do not have a direct rigid heat conduction path. The data processing module sets the initial weight of the adjacency matrix based on the reciprocal of the physical distance of the heat conduction path between each pair of drawing nodes. The physical distance of the heat conduction path is the shortest heat conduction path length along the horizontal machining center component entity between the positions of the two drawing nodes. The initial weight of the adjacency matrix is ​​negatively correlated with the physical distance of the heat conduction path; the shorter the physical distance, the larger the initial weight, and the stronger the heat conduction association between the two drawing nodes. For graph nodes within the same coolant piping coverage area, the data processing module superimposes convective heat transfer association weights onto the initial weights of the adjacency matrix. The same coolant piping coverage area includes the front and rear bearing nodes corresponding to the spindle bearing cooling sleeve and the guide rail mounting surface nodes corresponding to the guide rail cooling piping. The convective heat transfer association weights are set based on the coverage area of ​​the coolant piping and the node's position within the piping. Nodes located at the inlet and outlet ends of the same coolant piping correspond to higher convective heat transfer association weights, while nodes without any coolant piping coverage have a convective heat transfer association weight of 0. The data processing module generates a spatial topology adjacency matrix that integrates both conduction and convection heat transfer paths through the superposition of the initial weights and the convective heat transfer association weights.

[0024] The formula for calculating the initial weights of the adjacency matrix is:

[0025] in, Let be the initial weight corresponding to the element in the i-th row and j-th column of the spatial topological adjacency matrix. Let be the physical distance along the shortest heat conduction path between the i-th graph node and the j-th graph node, within the component entity. It is a non-zero regularization constant used to avoid the case where the denominator is zero, and its value is a fixed minimum positive value.

[0026] The final weight calculation formula for the adjacency matrix of the fused convection heat transfer is as follows:

[0027] in, Let be the final weight value in the i-th row and j-th column of the spatial topological adjacency matrix. Let be the convective heat transfer association weight between the i-th graph node and the j-th graph node, when the two nodes are located in the same coolant piping coverage area. Take the preset positive value, otherwise take 0. This is the convective heat transfer weighting coefficient, used to adjust the proportion of the convective heat transfer term in the adjacency matrix weights. Its value is a fixed value between 0 and 1.

[0028] The data processing module dynamically updates the spatial topology adjacency matrix during operation. It acquires the current spindle speed and coolant pump flow rate of the horizontal machining center in real time. Based on the current spindle speed, it calculates the spindle bearing frictional heat source intensity, which is positively correlated with the square of the current spindle speed. A preset normalization mapping transforms the spindle speed into a normalized heat source intensity value between 0 and 1. The module also calculates the change in convective heat transfer coefficient over the coolant piping coverage area based on the current coolant pump flow rate. This change is positively correlated with the increment of the current coolant pump flow rate, and a preset normalization mapping transforms the flow rate increment into a normalized change in the convective heat transfer coefficient between 0 and 1. The data processing module increases the initial weight of the adjacency matrix of the corresponding graph node based on the calculated heat source intensity. The higher the heat source intensity, the greater the adjustment of the initial weight between the corresponding graph node and its adjacent nodes. The module also dynamically corrects the convective heat transfer association weights based on the change in the convective heat transfer coefficient. The greater the change in the convective heat transfer coefficient, the greater the correction of the convective heat transfer association weights. This generates a dynamic spatial topology adjacency matrix that adapts to the processing conditions.

[0029] The formula for calculating the weight correction of the dynamic space topological adjacency matrix is ​​as follows:

[0030] in, The weight value of the i-th row and j-th column in the dynamic spatial topological adjacency matrix at time t, and Q(t) is the normalized value of the frictional heat source intensity of the spindle bearing at time t. This is the weighting correction factor for heat source intensity. Let be the normalized change in the convective heat transfer coefficient of the coolant at time t. This is the weighting correction factor for the convective heat transfer coefficient.

[0031] Table 2 Spatial Topological Adjacency Matrix Weight Parameter Configuration Table Node pair type Initial weight range Preset value of convection heat transfer correlation weight Heat source intensity correction factor α Convection heat transfer correction factor β Adjacent nodes of the same component 0.5-1.0 0 0.3 0 Cross-component direct connection nodes 0.2-0.5 0 0.2 0 Same coolant piping node 0.1-0.3 0.4 0.1 0.5 Non-directly connected nodes 0-0.1 0 0 0 This table clarifies the adjacency matrix weight parameter configurations for different types of node pairs, providing a parameter basis for the construction and dynamic updating of the spatial topology adjacency matrix. The node pair types are classified according to the physical connection relationship between graph nodes and the coolant pipeline coverage relationship. Different types of node pairs correspond to different weight configurations and correction coefficients to match different heat transfer path characteristics.

[0032] This embodiment refines the construction logic of the spatial topology adjacency matrix, incorporates both heat conduction and convection heat transfer paths into the weight setting of the adjacency matrix, and introduces a dynamic update mechanism for the adjacency matrix based on the processing conditions. This enables the adjacency matrix to match the changes in heat transfer characteristics caused by changes in spindle speed and coolant flow rate in real time, improving the accuracy of spatial heat conduction characteristic characterization and adapting to changes in the thermal field under different processing conditions.

[0033] For further implementation details, please refer to the appendix. Figure 3 In the spatiotemporal graph convolutional network model, the graph convolutional layer is configured with local convolutional kernels based on the Chebyshev polynomial approximation. These local convolutional kernels calculate the temperature aggregation features of the first-order and second-order neighbors of each graph node based on the spatial topological adjacency matrix. First-order neighbors correspond to temperature sensor nodes on components physically directly connected to the current graph node, while second-order neighbors correspond to temperature sensor nodes physically separated from the current graph node by one intermediate component. The graph convolutional layer performs convolution operations on the input temperature time-series data through these local convolutional kernels, fusing the temperature aggregation features of the first-order and second-order neighbors with the temperature time-series data of the current graph node to generate a graph node spatial feature matrix containing local spatial heat conduction gradients.

[0034] The formula for graph convolution based on Chebyshev polynomial approximation is:

[0035] in, The output features of graph convolution operation, Graph convolution operator, The spectral domain filter corresponding to the convolution kernel. Let K be the coefficients of the Chebyshev polynomial, and K be the order of the Chebyshev polynomial. It is a k-th order Chebyshev polynomial. is the normalized graph Laplacian matrix, and x is the input graph node temperature feature vector.

[0036] The formula for calculating the normalized graph Laplacian matrix is:

[0037] Where L is the unnormalized graph Laplacian matrix, L=DA, D is the degree matrix of the graph, and A is the spatial topological adjacency matrix. Let L be the largest eigenvalue of the graph Laplacian matrix. A is an identity matrix with the same dimension as the number of graph nodes. The degree matrix D is a diagonal matrix, and the element D(i,i) on its diagonal is equal to the sum of all elements in the i-th row of the spatial topological adjacency matrix A, corresponding to the degree of the i-th graph node.

[0038] During computation, the graph convolutional layer determines the first-order and second-order neighbor nodes for each graph node based on the spatial topological adjacency matrix. Temperature features from these neighbor nodes are extracted, and a weighted aggregation operation is performed to generate a corresponding order of temperature aggregated features. The weights of the aggregation operation are consistent with the weights of the corresponding node pairs in the adjacency matrix. The graph convolutional layer then concatenates and fuses the original temperature features of the current graph node, the aggregated temperature features of the first-order and second-order neighbor nodes along the channel dimension to generate a spatial feature vector for each graph node. All spatial feature vectors from the graph nodes are combined to form the graph node spatial feature matrix.

[0039] The formula for calculating the temperature aggregation characteristics of graph nodes is:

[0040] in, Let be the aggregated spatial features of the i-th graph node. Let be the original input temperature feature of the i-th graph node. Let i be the set of first-order neighbor nodes of the i-th graph node. Let A be the set of second-order neighbor nodes of the i-th graph node, and let A(i,j) be the weight value in the i-th row and j-th column of the spatial topological adjacency matrix. is the weight value of the i-th row and j-th column after squaring the adjacency matrix, corresponding to the association strength of the second-order neighbor nodes.

[0041] Please refer to the attached document. Figure 4The gated recurrent unit layer receives the graph node spatial feature matrix output by the graph convolutional layer as the input sequence. Each time step of the input sequence corresponds to the graph node spatial feature matrix at a given moment, and the length of the time step is consistent with the number of temperature sampling periods. The gated recurrent unit layer contains update gates and reset gates. The update gate calculates the retention ratio between the hidden state at the previous moment and the candidate hidden state at the current moment. The reset gate controls the proportion of features related to historical temperature change trends in the graph node spatial feature matrix at the current moment flowing into the candidate hidden state. The gated recurrent unit layer dynamically adjusts the bias parameters of the update gate and reset gate based on the feed rate of each motion axis of the horizontal machining center. The feed rate corresponds to the current feed rate and acceleration of each motion axis. The higher the feed rate, the faster the frictional heat source of the corresponding component changes; the bias parameter of the update gate is increased accordingly to improve the retention ratio of features at the current moment, while the bias parameter of the reset gate is decreased to reduce the inflow ratio of historical features, adapting to the rapidly changing thermal field. Through the gating operations of the update gate and reset gate, the gated recurrent unit layer outputs a spatiotemporal feature tensor that fuses time-dimensional features.

[0042] The formula for calculating the update door is:

[0043] in, Update the gate's output value at time t. It is the sigmoid activation function. To update the gate weight matrix, for The hidden state of the time-gated loop unit layer Let be the feature matrix of the graph node space input at time t. To update the gate's bias parameters, their values ​​vary with the current feed rate. Dynamic adjustment is achieved by linking the feed rate and the offset parameter through a preset linear mapping relationship.

[0044] The formula for resetting the door is:

[0045] in, The output value of the gate is reset at time t. To reset the weight matrix of the gate, To reset the door's offset parameters, their value varies with the current feed rate. Dynamic adjustment.

[0046] The formulas for calculating the candidate hidden state and the final hidden state are as follows:

[0047]

[0048] in, Let be the candidate hidden state at time t. The hyperbolic tangent activation function is used. Let be the weight matrix of the candidate hidden states. These are fixed bias parameters for the candidate hidden states. This is the Hadamard product operator. The final hidden state of the gated recurrent unit layer output at time t corresponds to the spatiotemporal feature tensor fused with the time dimension.

[0049] The local convolutional kernels in the graph convolutional layer employ an adaptive order adjustment mechanism. The graph convolutional layer calculates the variance of temperature differences between graph nodes in the spatial topological adjacency matrix in real time. This variance characterizes the uniformity of the current machine tool temperature field; a larger variance indicates a more drastic change in the spatial gradient of the temperature field, suggesting a thermal field abrupt change. When the calculated variance exceeds a preset thermal field abrupt change threshold, the Chebyshev polynomial order of the local convolutional kernel is increased from second to third order. This introduces the temperature aggregation characteristics of third-order neighbor nodes, expanding the receptive field of spatial heat conduction features to capture large-scale temperature gradient changes during thermal field abrupt changes. When the variance is less than the thermal field abrupt change threshold, the local convolutional kernel reverts to second-order calculation, reducing the computational resource consumption of the graph convolutional layer and improving the model's real-time performance. The thermal field abrupt change threshold is set based on the temperature difference variance during steady-state machine tool operation and is a preset multiple of the steady-state variance.

[0050] The formula for calculating the variance of temperature differences between nodes in the graph is as follows:

[0051] in, Let N be the variance of the temperature difference between nodes in the graph, and N be the total number of temperature sensor nodes. Let i be the temperature sample value of the i-th graph node at the current time. This represents the temperature sample value of the j-th graph node at the current moment.

[0052] Table 3. Layer Structure and Operational Parameters of the Spatiotemporal Graph Convolutional Network Model Network layer name Input feature dimension Output feature dimension Core operation parameters Activation function Operation trigger cycle Input layer N×1 N×1 Number of nodes N none Temperature sampling period Convolutional layer N×1 N×C1 Chebyshev order 2-3, output channel C1 ReLU Temperature sampling period Gated loop unit layer T×N×C1 T×C2 Hidden layer dimension C2, time step T tanh Temperature sampling period Fully connected mapping layer C2 6×1 Output dimension 6 none Temperature sampling period This table is used to clarify the structural parameters and computational configuration of each layer of the spatiotemporal graph convolutional network model, providing a complete parameter basis for the model implementation. The core computational parameters include the Chebyshev polynomial order range, the number of gate units, the dimension of the weight matrix, etc. The computation triggering period is consistent with the sampling period of the temperature sensor to ensure the timing synchronization between model computation and temperature data acquisition.

[0053] This embodiment refines the internal computational logic and parameter configuration of the spatiotemporal graph convolutional network model, clarifies the graph convolution operation process based on Chebyshev polynomial approximation and the temporal feature extraction process of the gated recurrent unit layer, and introduces an adaptive adjustment mechanism for the convolution kernel order and a linkage adjustment mechanism for the feed rate of the gated bias parameters. This enables the model to balance the ability to capture a wide range of features during thermal field abrupt changes with computational efficiency under normal operating conditions, thereby improving the real-time performance and accuracy of thermal deformation prediction.

[0054] In one preferred embodiment, please refer to the appendix. Figure 5 In the process of transforming the thermal deformation prediction vector into reverse displacement compensation values, the multi-axis interpolation operator inputs the spatiotemporal feature tensor output by the spatiotemporal graph convolutional network model into the fully connected mapping layer. The fully connected mapping layer uses the geometric axis directions of each motion axis of the horizontal machining center in the initial coordinate system as a reference, decoupling the spatiotemporal feature tensor into linear thermal deformation components along the X, Y, and Z axes, and angular displacement thermal deformation components around the X, Y, and Z axes. The initial coordinate system is the machine tool coordinate system of the horizontal machining center, with its origin located at the machine tool reference point. The geometric axis directions of the X, Y, and Z axes are consistent with the linear motion directions of each motion axis. The fully connected mapping layer uses a preset inverse kinematic transformation formula to transform the angular displacement thermal deformation components into equivalent linear compensation components corresponding to the linear drive ends of each axis. The equivalent linear compensation components correspond to the positional offsets generated by the angular displacement thermal deformation in the linear directions of each motion axis. The fully connected mapping layer sums the linear thermal deformation component and the equivalent linear compensation component to generate the reverse displacement compensation value corresponding to each motion axis. The value of the reverse displacement compensation value is equal in magnitude and opposite in direction to the position offset caused by thermal deformation.

[0055] The formulas for calculating the inverse kinematic transformation and the equivalent linear compensation component are as follows:

[0056] in, This represents the equivalent linear compensation component vector corresponding to the linear drive end of each axis, containing the equivalent linear compensation values ​​in the X, Y, and Z directions. Let be the inverse of the Jacobian matrix of the kinematics of the horizontal machining center. This is the angular displacement thermal deformation component vector, containing the angular displacement thermal deformation values ​​around the X, Y, and Z axes. The kinematic Jacobian matrix is ​​constructed based on the structural topology of the horizontal machining center, representing the linear mapping relationship between the pose change of the tool center point and the displacement changes of each motion axis.

[0057] In the process of superimposing the reverse displacement compensation value onto the position commands of each axis, the multi-axis interpolation calculator obtains the theoretical position command of each axis in each interpolation cycle. The theoretical position command is generated based on the interpolation calculation of the machining trajectory, corresponding to the target theoretical position of each motion axis in the current interpolation cycle. The multi-axis interpolation calculator performs a differential operation between the reverse displacement compensation value of the current cycle and the historical reverse displacement compensation value of the previous interpolation cycle to obtain the single-cycle compensation increment. The single-cycle compensation increment corresponds to the change in compensation value that needs to be superimposed in the current interpolation cycle. The multi-axis interpolation calculator algebraically adds the single-cycle compensation increment to the theoretical position command of each axis to generate a superimposed position command carrying compensation information. By using incremental superposition, the slope of the position command output by the multi-axis interpolation calculator is ensured to be continuous, avoiding position command jumps caused by abrupt changes in compensation values. The interpolation cycle and the temperature sampling cycle are kept in an integer multiple synchronization relationship to ensure the timing alignment of compensation value updates and position command generation.

[0058] The formula for calculating the single-cycle compensation increment is:

[0059] in, This represents the single-cycle compensation increment for the k-th interpolation cycle. This is the reverse displacement compensation value for the kth interpolation cycle. This is the historical reverse displacement compensation value for the (k-1)th interpolation cycle.

[0060] After generating the reverse displacement compensation value, a nonlinear hysteresis correction stage is introduced. This stage extracts the real-time current feedback value and real-time position feedback value of the servo motors of each axis of the horizontal machining center. The real-time current feedback value corresponds to the output torque of the servo motor and is used to characterize the axial force state of the lead screw of each axis. The real-time position feedback value corresponds to the actual position of each motion axis. The nonlinear hysteresis correction stage calculates the thermo-coupling deformation hysteresis of the lead screw of each axis based on the real-time current feedback value. The thermo-coupling deformation hysteresis is positively correlated with the axial force and temperature change of the lead screw, corresponding to the elastic deformation hysteresis and transmission backlash generated by the lead screw under the combined action of force and thermal deformation. The nonlinear hysteresis correction stage inputs the thermo-coupling deformation hysteresis as a correction factor into a preset hyperbolic tangent function. The hyperbolic tangent function performs nonlinear marginal reduction correction on the equivalent linear compensation component in the direction of the force axis in the reverse displacement compensation value, generating the final reverse displacement compensation value that overcomes the mechanical transmission backlash and elastic deformation.

[0061] The formula for calculating nonlinear hysteresis correction is as follows:

[0062] in, This is the final reverse displacement compensation value. The value is the reverse displacement compensation value before correction. This is the hysteresis correction amplitude coefficient. This is the sensitivity coefficient of the correction factor. The normalized thermo-coupling deformation hysteresis has a value range of [0,1].

[0063] Please refer to the attached document. Figure 5 The multi-axis interpolation processor incorporates a timing alignment anti-jitter filtering mechanism when generating single-cycle compensation increments. The processor uses a fixed-length sliding window queue to store the single-cycle compensation increments of the current interpolation cycle and several consecutive previous interpolation cycles. The sliding window queue employs a first-in, first-out (FIFO) update mechanism; each time a new interpolation cycle begins, the earliest stored compensation increment data is removed from the queue, and the current cycle's compensation increment data is stored at the end of the queue. The multi-axis interpolation processor calculates the moving average of all single-cycle compensation increments in the sliding window queue. When the deviation between the current interpolation cycle's single-cycle compensation increment and the moving average exceeds a preset mechanical stiffness sensitivity threshold, the current interpolation cycle's single-cycle compensation increment is replaced with the calculated moving average, filtering out high-frequency calculation jitter in the reverse displacement compensation value and preventing servo system oscillations caused by high-frequency jitter. The mechanical stiffness sensitivity threshold is set based on the mechanical stiffness of each motion axis of the machine tool and the position loop bandwidth of the servo system, representing a preset proportion of the maximum allowable position command change within a single interpolation cycle of the machine tool.

[0064] The formula for calculating the moving average of the sliding window is:

[0065] in, Let M be the moving average of the sliding window corresponding to the kth interpolation period, and M be the length of the sliding window. This represents the single-cycle compensation increment for the km-th interpolation cycle.

[0066] Table 4. Parameter Configuration Table for Interpolation Period Compensation Increment Processing Parameter name Parameter value range Parameter Function interpolation period 0.5ms-2ms Set the time period for position command generation and compensation superposition. Sliding window length M 3-10 Set the sliding window data length for anti-shake filtering Mechanical stiffness threshold 0.1μm-1μm Set the filter threshold for compensating for incremental deviation Hysteresis correction amplitude coefficient γ 0-0.5 Set the maximum magnitude of the nonlinear hysteresis correction Correction factor sensitivity coefficient δ 1-5 Set the response sensitivity of the hysteresis correction factor Compensation Increment Limit 0.5μm-2μm Set the maximum allowable value of single interpolation period compensation increment This table is used to clarify the parameter configurations for the compensation increment processing within the interpolation cycle, providing a parameter basis for the superposition, correction, and filtering of compensation values. The values ​​of each parameter are determined based on the mechanical rigidity characteristics of the horizontal machining center, the response characteristics of the servo system, and the interpolation calculation cycle, ensuring the smoothness and stability of the compensation process.

[0067] This embodiment refines the complete transformation process from thermal deformation prediction vector to reverse displacement compensation value, clarifies the inverse kinematic transformation logic of angular displacement thermal deformation component and the interpolation period increment superposition logic of compensation value, introduces nonlinear hysteresis correction link and timing alignment anti-jitter filtering mechanism, ensures the continuity and smoothness of position command, overcomes nonlinear deviation of mechanical transmission link, suppresses high frequency jitter in interpolation command, and improves position following accuracy and stability in multi-axis cooperative motion process.

Claims

1. A multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers, characterized in that, It includes a temperature sensor array, a data processing module, a spatiotemporal graph convolutional network model, and a multi-axis interpolation operator; The temperature sensor array is deployed on the bed, column and spindle box of the horizontal machining center. The data processing module uses each temperature sensor node as a graph node, constructs a spatial topological adjacency matrix based on the connection relationship of the machine tool's physical structure, and inputs the temperature time series data collected by the temperature sensor array and the spatial topological adjacency matrix into the spatiotemporal graph convolutional network model. The spatiotemporal graph convolutional network model captures the spatial heat conduction characteristics between adjacent graph nodes through graph convolutional layers, captures the temperature change characteristics over time through gated recurrent unit layers, and outputs thermal deformation prediction vectors for each motion axis relative to the initial coordinate system. The multi-axis interpolation calculator converts the thermal deformation prediction vector into a reverse displacement compensation value, adds the reverse displacement compensation value to the position commands of each axis generated by the multi-axis interpolation calculator, and sends the superimposed position commands to each axis servo driver to execute position closed-loop control.

2. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining center of claim 1, wherein, The data processing module constructs the spatial topological adjacency matrix by extracting the physical mating surfaces of the bed and column and the guide rail mating surfaces of the spindle box and column in the three-dimensional assembly model of the horizontal machining center as edges. The initial weights of the adjacency matrix are set based on the reciprocal of the physical distance of the heat conduction path between any two graph nodes. For graph nodes located in the same coolant pipe coverage area, convective heat transfer association weights are superimposed on the initial weights of the adjacency matrix to generate the spatial topological adjacency matrix that integrates both conduction and convection heat transfer paths.

3. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining center of claim 1, wherein, The graph convolutional layer in the spatiotemporal graph convolutional network model is configured with a local convolutional kernel based on the Chebyshev polynomial approximation. The local convolutional kernel calculates the temperature aggregation features of the first-order and second-order neighbor nodes of each graph node according to the spatial topological adjacency matrix. The first-order neighbor nodes correspond to temperature sensor nodes on physically directly connected components, and the second-order neighbor nodes correspond to temperature sensor nodes physically separated by an intermediate component. The graph convolutional layer fuses the temperature aggregation features of the first-order and second-order neighbor nodes with the temperature time series data of the current graph node through the local convolutional kernel to generate a graph node spatial feature matrix containing the local spatial heat conduction gradient.

4. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers according to claim 1, characterized in that, The gated loop unit layer receives the graph node spatial feature matrix as an input sequence. The gated loop unit layer contains an update gate and a reset gate. The update gate is used to calculate the retention ratio between the hidden state at the previous time and the candidate hidden state at the current time. The reset gate is used to control the proportion of features related to historical temperature change trends in the graph node spatial feature matrix at the current time flowing into the candidate hidden state. The gated loop unit layer dynamically adjusts the bias parameters of the update gate and the reset gate according to the feed speed status of each motion axis of the horizontal machining center, and outputs a spatiotemporal feature tensor with fused time dimension.

5. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers according to claim 1, characterized in that, The process of converting the thermal deformation prediction vector into the reverse displacement compensation value includes: inputting the spatiotemporal feature tensor into a fully connected mapping layer; the fully connected mapping layer using the geometric axis directions of each motion axis of the horizontal machining center in the initial coordinate system as a reference; decoupling the spatiotemporal feature tensor into linear thermal deformation components of the X-axis, Y-axis, and Z-axis, and angular displacement thermal deformation components around the X-axis, Y-axis, and Z-axis; converting the angular displacement thermal deformation components into equivalent linear compensation components corresponding to the linear drive ends of each axis according to the inverse kinematic transformation formula; and summing the linear thermal deformation components and the equivalent linear compensation components to generate the reverse displacement compensation value.

6. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers according to claim 1, characterized in that, The specific logic of the multi-axis interpolation arithmetic unit superimposing the reverse displacement compensation value onto the position command of each axis is as follows: the multi-axis interpolation arithmetic unit obtains the theoretical position command of each axis in the current cycle in each interpolation cycle, performs a difference operation on the reverse displacement compensation value of the current cycle and the historical reverse displacement compensation value of the previous interpolation cycle to obtain the single-cycle compensation increment, and performs an algebraic addition on the single-cycle compensation increment and the theoretical position command of each axis to generate the superimposed position command carrying compensation information.

7. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining center of claim 2, wherein, During operation, the data processing module dynamically updates the spatial topology adjacency matrix. The data processing module acquires the current spindle speed and the current flow rate of the coolant pump of the horizontal machining center in real time. Based on the current spindle speed, it calculates the intensity of the frictional heat source of the spindle bearing. Based on the current flow rate, it calculates the change in the convective heat transfer coefficient of the area covered by the coolant pipeline. The data processing module increases the initial weight of the adjacency matrix of the corresponding graph node based on the heat source intensity. Based on the change in the convective heat transfer coefficient, it dynamically corrects the convective heat transfer association weight, generating a dynamic spatial topology adjacency matrix that adapts to the machining conditions.

8. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining center of claim 3, wherein, The local convolutional kernel in the graph convolutional layer employs an adaptive order adjustment mechanism. The graph convolutional layer calculates the variance of the temperature difference between graph nodes in the spatial topological adjacency matrix in real time. When the variance is greater than a preset thermal field abrupt change threshold, the Chebyshev polynomial order of the local convolutional kernel is increased from second to third order to introduce the temperature aggregation characteristics of third-order neighbor nodes and expand the receptive field of spatial heat conduction characteristics. When the variance is less than the thermal field abrupt change threshold, the local convolutional kernel reverts to second-order calculation to reduce the computational resource consumption of the graph convolutional layer.

9. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers according to claim 5, characterized in that, After generating the reverse displacement compensation value, a nonlinear hysteresis correction step is introduced. The nonlinear hysteresis correction step extracts the real-time current feedback value and real-time position feedback value of the servo motor of each axis of the horizontal machining center. Based on the real-time current feedback value, the thermal coupling deformation hysteresis of each axis lead screw is calculated. The thermal coupling deformation hysteresis is used as a correction factor input to a preset hyperbolic tangent function. The hyperbolic tangent function performs nonlinear marginal reduction correction on the equivalent linear compensation component in the direction of the force axis in the reverse displacement compensation value, generating the final reverse displacement compensation value that overcomes mechanical transmission backlash and elastic deformation.

10. The multi-axis collaborative intelligent control and thermal error compensation system for horizontal machining centers according to claim 6, characterized in that, The multi-axis interpolation arithmetic unit introduces a timing alignment anti-jitter filtering mechanism when generating the single-cycle compensation increment. The multi-axis interpolation arithmetic unit is equipped with a sliding window queue, which stores the single-cycle compensation increment of the current interpolation cycle and the previous consecutive interpolation cycles into the sliding window queue. The moving average of all single-cycle compensation increments in the sliding window queue is calculated. When the deviation between the single-cycle compensation increment of the current interpolation cycle and the moving average exceeds the mechanical stiffness sensitivity threshold, the single-cycle compensation increment of the current interpolation cycle is replaced with the moving average.

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