A data-model hybrid driven ball screw thermal error prediction method

Abstract

The present application relates to the technical field of machine tool manufacturing, and discloses a data-model hybrid driving ball screw thermal error prediction method, comprising the following steps: establishing a ball screw thermal error physical model, and acquiring sample data by using a Latin hypercube design LHD method; building a ball screw pair thermal error test platform, analyzing the optimal temperature measuring point by ANSYS Workbench, and collecting state information such as temperature, current and power; processing the data through gray correlation analysis, abnormal value processing and normalization operation; building a data-model hybrid driving convolution long short-term memory network model C-LSTM; and inputting the current collected relevant state information data into the trained model to perform thermal error prediction. The present application ensures the interpretability of data, thereby improving the accuracy of ball screw thermal error prediction.

Description

Technical Field

[0001] This invention relates to the field of machine tool manufacturing technology, and specifically to a data-model hybrid driven method for predicting thermal errors in ball screws. Background Technology

[0002] Errors in CNC machine tools include geometric errors, errors caused by cutting forces, thermal deformation errors, tool wear errors, and CNC monitoring system errors. Among these, thermal errors account for a relatively large proportion, approximately 40%, and in precision machine tools, thermal errors can even reach 40%-70%. Thermal errors are highly nonlinear, influenced by numerous factors, and highly coupled.

[0003] In the field of CNC machine tools, the ball screw feed system is one of the core components for achieving precision machining. It is responsible for converting the rotary motion of the motor into the precise linear motion of the cutting tool or worktable, directly determining the machining accuracy, surface quality, and production efficiency of the CNC machine tool. However, under the conditions of long-term, high-load operation of CNC machine tools, the accuracy of the ball screw feed system inevitably degrades. This is mainly attributed to continuous frictional heat generation; the accumulation of heat causes thermal expansion, affecting the accuracy of the ball screw feed system. Thermal errors increase the pitch error of the screw, reduce the smoothness of motion, and consequently lead to out-of-tolerance dimensional accuracy and increased surface roughness of the machined parts, seriously affecting product quality.

[0004] In existing thermal error prediction techniques, most are based on a single data-driven approach, which has poor interpretability and lacks accurate modeling of the thermal characteristics of ball screws, ignoring some factors that may have an inherent impact. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention aims to provide a data-model hybrid-driven method for predicting the thermal error of ball screws. By establishing a thermal characteristic model of the ball screw and collecting information such as temperature, voltage, and vibration of the CNC machine tool's ball screw, the thermal characteristic model is coupled with state information to construct a data-model hybrid-driven model for predicting the thermal error of the ball screw feed system. This ultimately enables the prediction of thermal errors in the CNC machine tool's ball screw feed system. Compared to single data-driven methods, this invention can utilize the model's prior knowledge to perform more targeted processing and analysis of the data, reducing the impact of noise and outliers on the prediction results. It achieves real-time prediction of the thermal error of the CNC machine tool's ball screw feed system, improving the interpretability and generalization of thermal error prediction, which is of great significance for improving the performance and reliability of CNC machine tools.

[0006] To achieve the above-mentioned objectives and advantages of the present invention, the present invention is implemented through the following technical solutions:

[0007] A data-model hybrid-driven method for predicting thermal errors in ball screws includes the following steps:

[0008] Step 1: Establish a physical model of the thermal error of the ball screw in the CNC machine tool and obtain theoretical data;

[0009] Step 2: Perform steady-state thermal characteristic analysis on the ball screw using ANSYS Workbench to determine the optimal placement of the temperature sensor.

[0010] Step 3: Build a test platform for the ball screw feed system of CNC machine tools and obtain temperature, power, speed, current and thermal error data of the ball screw feed system;

[0011] Step 4: Preprocess the experimental and theoretical data, including grey relational analysis, outlier handling and normalization, and use the processed data as the sample dataset for training the data-model hybrid model.

[0012] Step 5: Construct a data-model hybrid driven model, namely a convolutional long short-term memory network (C-LSTM), and train it using the sample dataset of the data-model hybrid driven model from Step 4.

[0013] Step 6: Calculate the thermal error of the CNC machine tool ball screw feed system in real time based on the prediction model driven by the data-model hybrid approach in Step 5.

[0014] Furthermore, step 1 establishes a physical model of the thermal error of the ball screw in the CNC machine tool, and the process is as follows:

[0015] According to heat transfer theory, the heat transfer process of a linear feed axis mainly includes heat conduction, heat convection, and radiation heat transfer. According to Fourier's law of thermal conductivity, the expression for the heat flux density of the CNC machine tool ball screw components during the heat conduction process is:

[0016]

[0017] in, It is the heat flux density of thermal conduction; It is the thermal conductivity. It is the temperature of the components. It represents the temperature gradient of the components. The negative sign indicates that the heat transfer direction is opposite to the temperature gradient direction.

[0018] The heat flux density of convective heat transfer in CNC machine tool ball screw components can be calculated using Newton's law of cooling, the expression of which is:

[0019]

[0020] in, It is the heat flux density in the convective heat transfer process. It is the convective heat transfer coefficient. It is the temperature of the air in contact with the surface of the component.

[0021] The heat flux density radiated outward from the ball screw components of a CNC machine tool can be calculated using a modified form of the Stefan-Boltzmann law, the expression of which is:

[0022]

[0023] in, It is the heat flux density in the radiative heat transfer process. It refers to the emissivity of the components, with values ​​between 0 and 1. It is the blackbody radiation coefficient;

[0024] Then, using the formulas for heat conduction, heat convection, and radiation heat transfer, the temperature field of the lead screw under the action of the bearing and the lead screw nut was calculated. .

[0025] Finally, at any given moment, the lead screw... Thermal error:

[0026]

[0027] in, It is the coefficient of thermal expansion of the lead screw. It is the thermal drift correction factor.

[0028] Furthermore, step 2 involves performing a steady-state thermal characteristic analysis of the ball screw using ANSYS Workbench, and the steps are as follows:

[0029] First, the ball screw feed system model was simplified and exported as a .x_t file, then imported into Workbench. Next, the ball screw model was meshed. Then, parameters were set according to the material properties of each component. Finally, the steady-state thermal characteristics of the ball screw were solved. Important temperature measurement points in the ball screw were identified through finite element analysis.

[0030] Furthermore, step 3 involves building a test platform for the CNC machine tool ball screw feed system, the process of which is as follows:

[0031] Temperature sensors are placed at the temperature measurement points in step 3 above to measure the temperature at key points in the ball screw feed system, as well as the room temperature; the axial thermal error of the ball screw is measured using a laser interferometer; and the power and speed of the ball screw feed system are measured using the module built into the ball screw test bench control system. The data matrix of the ball screw can be represented as follows: ,in, express The state data matrix of the ball screw at any given time. express Time of the first The temperature at each temperature measuring point express The current of the motor at all times, express The thermal error is constantly measured using a laser interferometer. express The power of the ball screw feed system at all times. This indicates the rotational speed of the ball screw.

[0032] Furthermore, step 4 preprocesses the experimental and theoretical data, including grey relational analysis, outlier handling, and normalization. The processed data is then used as the sample dataset for training the data-model hybrid model. The process is as follows:

[0033] First, outlier processing was performed on the collected experimental and theoretical data. Based on the physical model and prior data, outlier data was initially screened out.

[0034] Then, through grey relational analysis, the degree of correlation between different factors affecting the thermal error of the ball screw was determined, and the influence factors of different factors were given. ;

[0035] Finally, the theoretical data of ball screw thermal error is normalized using the maximum-minimum normalization method, as follows:

[0036]

[0037] in, The theoretical value is obtained from the physical model of the thermal error of the ball screw. This represents the minimum theoretical value obtained from the physical model of ball screw thermal error. This represents the maximum theoretical value obtained from the physical model of the thermal error of the ball screw.

[0038] Furthermore, step 5 constructs a data-model hybrid driven model, namely a convolutional long short-term memory network (C-LSTM) model, which includes a convolutional neural network (CNN) module and a long short-term memory network (LSTM) module.

[0039] The convolutional neural network (CNN) layer uses two convolutional kernels of different sizes. , Convolution is then performed. The data, after grayscale correlation analysis, outlier handling, and normalization in step 4 above, is passed through the input layer convolution to extract features between variables. Different features are learned using different convolution kernels. The feature vector contains combined information on temperature, current, and power, retaining the variable features most strongly correlated with thermal error, which are then used for subsequent model training.

[0040] The Long Short-Term Memory (LSTM) network consists of an input layer, a hidden layer, and an output layer.

[0041] The input layer consists of the output of the aforementioned convolutional neural network;

[0042] The basic unit of the hidden layer is the storage unit, which consists of self-connected storage units that store time states. These storage units can pass information from previous outputs to the current output. By continuously memorizing and processing past input data, the hidden layer learns the overall variation characteristics of temperature, current, power, and rotational speed. Each storage unit consists of four parts: an input gate, a forget gate, autoregressive neurons, and an output gate. The output expression of the LSTM is:

[0043]

[0044] in, The input matrix includes temperature, power, current, and speed. This represents the output of the fully connected layer, i.e., the thermal error of the ball screw. , This represents the weight matrix of the fully connected layer. This represents the bias vector of the fully connected layer.

[0045] The predictive performance of the algorithm is evaluated using the mean absolute error (MAE), and its mathematical expressions are as follows:

[0046]

[0047] in, For predicted values, For the true value, For the sample size, , This serves as the input to the model. A target mean absolute error is set to determine the iterative training of the network model until the required accuracy is achieved.

[0048] Furthermore, in step 6, based on the data-model hybrid driving prediction model from step 5, the real-time collected temperature, power, current, and rotational speed are input into the prediction model to predict the thermal error of the ball screw at the next moment.

[0049] Design concept of this invention:

[0050] A physical model of the thermal error of the ball screw was established, and sample data was obtained using the Latin Hypercube Design (LHD) method. A thermal error test platform for the ball screw pair was built, and the optimal temperature measurement point was analyzed using ANSYS Workbench to collect state information such as temperature, current, and power. The data was processed through grey relational analysis, outlier handling, and normalization. A data-model hybrid driven convolutional long short-term memory (C-LSTM) network model was built. The currently collected relevant state information data was input into the trained model to predict the thermal error.

[0051] The beneficial effects of this invention are:

[0052] (1) By establishing a physical model to obtain theoretical data and combining it with experimental data obtained from the actual test platform to drive the training model, the correlation between various factors can be comprehensively considered, ensuring the interpretability of the data, thereby improving the accuracy of ball screw thermal error prediction.

[0053] (2) The optimal placement of the temperature sensor was determined by using ANSYS Workbench to perform steady-state thermal characteristic analysis on the ball screw, which reduced unnecessary data and ensured that the collected temperature data was more representative and effective.

[0054] (3) The C-LSTM prediction model can predict the thermal error of the ball screw in the next time step, providing accurate input for subsequent thermal error compensation, thereby improving the accuracy of the ball screw feed system. Attached Figure Description

[0055] Figure 1 A schematic diagram of the data-model hybrid driven ball screw thermal error prediction process;

[0056] Figure 2 A schematic diagram of a 3D model of a ball screw feed system;

[0057] Figure 3 This is a steady-state thermal error cloud map of ANSYS Workbench.

[0058] Figure 4 Test bench for data acquisition of ball screw feed system;

[0059] Figure 5 This is a schematic diagram of a convolutional long short-term memory neural network. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0061] A data-model hybrid driven method for predicting thermal errors in ball screws, the specific flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0062] Step 1: Establish a physical model of the thermal error of the ball screw in the CNC machine tool and obtain theoretical data;

[0063] A schematic diagram of the physical model of the ball screw in a CNC machine tool is shown below. Figure 2 As shown, the machine includes a motor 1, coupling 2, front bearing 3, worktable 4, lead screw nut 5, lead screw 6, rear bearing 7, and bed 8. Step 1 is as follows:

[0064] According to heat transfer theory, the heat transfer process of a linear feed axis mainly includes heat conduction, heat convection, and radiation heat transfer. According to Fourier's law of thermal conductivity, the expression for the heat flux density of the CNC machine tool ball screw components during the heat conduction process is:

[0065]

[0066] in, It is the heat flux density of thermal conduction; It is the thermal conductivity. It is the temperature of the components. It represents the temperature gradient of the components. The negative sign indicates that the heat transfer direction is opposite to the temperature gradient direction.

[0067] The heat flux density of convective heat transfer in CNC machine tool ball screw components can be calculated using Newton's law of cooling, the expression of which is:

[0068]

[0069] in, It is the heat flux density in the convective heat transfer process. It is the convective heat transfer coefficient. It is the air temperature in contact with the surface of the component.

[0070] The heat flux density radiated outward from the ball screw components of CNC machine tools can be calculated using a modified form of the Stefan-Boltzmann law, the expression of which is:

[0071]

[0072] in, It is the heat flux density in the radiative heat transfer process. It refers to the emissivity of the components, with a value between 0 and 1. It is the blackbody radiation coefficient.

[0073] By integrating the above formula, the heat of the lead screw can be obtained, and the temperature field can be determined.

[0074] First, calculate the temperature field of the leadscrew under the friction between the nut and the leadscrew:

[0075] According to the formula ,exist The heat transfer of the ball screw during the time period is as follows:

[0076]

[0077]

[0078] in, The equivalent diameter of the ball screw. for time The temperature gradient at the location is numerical. for time Temperature gradient at the location. During the operation of the ball screw. The heat transfer during the combined heat transfer process of thermal radiation and thermal convection within the time period is:

[0079]

[0080] in, It is the amplification factor of convective heat transfer in ball screws. yes ball screw Temperature at location yes The air temperature that is in constant contact with the surface of the ball screw.

[0081] ball screw micro-end at the location With nut The amount of heat generated by friction during the time period is:

[0082]

[0083] in, It is a nut friction ball screw micro segment The heat generated at one time, It is the interaction between the nut and the ball screw per unit time. The average number of friction cycles per segment.

[0084] exist ball screw micro segment within a time period The heat increment is:

[0085]

[0086] in, It is the specific heat capacity of the ball screw material. It refers to the density of the ball screw material.

[0087] Considering only the friction between the nut and the ball screw, the temperature of the ball screw is .exist Constant ball screw micro segment The heat balance formula is:

[0088]

[0089] The formula ~ Substitution We can obtain:

[0090]

[0091] in, It can be approximated by the ambient temperature near the ball screw. Substitution, that is The temperature field of the lead screw under the friction between the nut and the lead screw is as follows:

[0092]

[0093] Secondly, calculate the temperature field of the lead screw under the action of a single-point heat source at both ends of the bearings:

[0094] According to the principle of conservation of energy The energy equation for the segment is:

[0095]

[0096] Based on the temperature field distribution of the lead screw under the action of a single-point heat source, the lead screw micro-segment The temperature gradients on both sides have the following relationship:

[0097]

[0098] The formula ~ , , Substitution get:

[0099]

[0100] Therefore, the temperature field of the lead screw under the action of single-point heat sources in bearing housing 1 and bearing housing 2 is as follows:

[0101]

[0102] in This represents the available travel length of the leadscrew.

[0103] According to the principle of temperature field superposition, the temperature field of the leadscrew is:

[0104]

[0105] At any time, the lead screw Thermal error:

[0106]

[0107] in, It is the coefficient of thermal expansion of the lead screw. It is the thermal drift correction factor.

[0108] The physical model sample data was obtained using Latin hypercube design (LHD). The LHD first determined the number and value range of variables in the ball screw physical model and then uniformly divided them. portions, then from A value is randomly selected from each interval to form... The data is processed, and the final result is derived based on the physical model of the ball screw. The final sample data is a... A matrix of × (number of variables + 1) dimensions.

[0109] Step 2: Perform steady-state thermal characteristic analysis on the ball screw using ANSYS Workbench to determine the optimal placement of the temperature sensor.

[0110] First, the ball screw feed system model was simplified and exported as a .x_t file, then imported into Workbench. Next, the ball screw model was meshed. Then, parameters were set according to the material properties of each component. Finally, the steady-state thermal characteristics of the ball screw were solved, and the results are as follows: Figure 3 As shown, the important temperature measurement points in the ball screw were determined through finite element analysis.

[0111] Step 3: Build a test platform for the ball screw feed system of CNC machine tools and obtain temperature, power, speed, current and thermal error data of the ball screw feed system;

[0112] Step 3 Experimental Platform Diagram as shown below Figure 4 As shown, the process is as follows:

[0113] By placing temperature sensors at the temperature measurement points in step 3 above, the temperatures at key temperature points in the ball screw feed system, as well as the room temperature, are measured.

[0114] The axial thermal error of the ball screw was measured using a laser interferometer.

[0115] The power and speed of the ball screw feed system are measured using a module built into the control system of the ball screw test bench.

[0116] The data matrix of a ball screw can be represented as follows: ,in, express The state data matrix of the ball screw at any given time. express Time of the first The temperature at each temperature measuring point express The current of the motor at all times, express The thermal error is constantly measured using a laser interferometer. express The power of the ball screw feed system at all times. This indicates the rotational speed of the ball screw.

[0117] Step 4: Preprocess the experimental and theoretical data, including grey relational analysis, outlier handling and normalization, and use the processed data as the sample dataset for training the data-model hybrid model.

[0118] First, outlier processing was performed on the collected experimental and theoretical data. Based on the physical model and prior data, outlier data was initially screened out.

[0119] Then, through grey relational analysis, the degree of correlation between different factors affecting the thermal error of the ball screw was determined, and the influence factors of different factors were given. ;

[0120] Finally, the theoretical data of ball screw thermal error is normalized using the maximum-minimum normalization method, as follows:

[0121]

[0122] in, The theoretical value is obtained from the physical model of the thermal error of the ball screw. This represents the minimum theoretical value obtained from the physical model of ball screw thermal error. This represents the maximum theoretical value obtained from the physical model of the thermal error of the ball screw.

[0123] Step 5: Construct a data-model hybrid driven model, namely a convolutional long short-term memory network (C-LSTM), and train it using the sample dataset of the data-model hybrid driven model from Step 4.

[0124] The Convolutional Long Short-Term Memory (C-LSTM) model includes a Convolutional Neural Network (CNN) module and a Long Short-Term Memory (LSTM) module, such as... Figure 5 As shown.

[0125] Convolutional Neural Network (CNN) layers use two convolutional kernels of different sizes. , Convolution is then performed. The data, after grayscale correlation analysis, outlier handling, and normalization in step 4 above, is passed through the input layer convolution to extract features between variables. Different features are learned using different convolution kernels. The feature vector contains combined information on temperature, current, and power, retaining the variable features most strongly correlated with thermal error, which are then used for subsequent model training.

[0126] Long Short-Term Memory (LSTM) networks consist of an input layer, hidden layers, and an output layer.

[0127] The input layer consists of the output of the aforementioned convolutional neural network;

[0128] The basic unit of the hidden layer is the storage unit, which consists of self-connected storage units that store time states. These storage units can pass information from previous outputs to the current output. By continuously memorizing and processing past input data, this layer learns the overall variation characteristics of temperature, current, power, and rotational speed. Each storage unit consists of four parts: an input gate, a forget gate, autoregressive neurons, and an output gate. The output expression of LSTM is:

[0129]

[0130] in, The input matrix includes temperature, power, current, and speed. This represents the output of the fully connected layer, i.e., the thermal error of the ball screw. , This represents the weight matrix of the fully connected layer. This represents the bias vector of the fully connected layer.

[0131] The predictive performance of the algorithm is evaluated using the mean absolute error (MAE), and its mathematical expressions are as follows:

[0132]

[0133] in, For predicted values, For the true value, For the sample size, , This serves as the input to the model. A target mean absolute error is set to determine the iterative training of the network model until the required accuracy is achieved.

[0134] Step 6: Based on the data-model hybrid prediction model from Step 5, input the real-time collected temperature, power, current, and rotational speed into the prediction model to predict the thermal error of the ball screw at the next moment.

Claims

1. A data-model hybrid driven method for predicting the thermal error of a ball screw, characterized in that, Includes the following steps: Step 1: Establish a physical model of the thermal error of the ball screw of the CNC machine tool and obtain theoretical data; wherein, the physical model of the thermal error is based on the calculation of the temperature field of the screw under the action of the bearing and the screw nut based on heat conduction, heat convection and radiation heat transfer, and calculates the theoretical thermal error of the screw at any time according to the thermal expansion coefficient and thermal drift correction coefficient of the screw, and obtains theoretical sample data by using the Latin hypercube design (LHD) method. Step 2: Perform steady-state thermal characteristic analysis on the ball screw using ANSYS Workbench to determine the optimal placement of the temperature sensor, i.e., the temperature measurement point. Step 3: Build a test platform for the ball screw feed system of CNC machine tool. Measure the temperature at the temperature measurement point and the room temperature using temperature sensors placed at the temperature measurement point. Measure the axial thermal error of the ball screw using a laser interferometer. Measure the power and speed of the ball screw feed system using the module built into the ball screw test bench control system, and obtain the motor current to obtain experimental data including temperature, power, speed, current, and thermal error. Step 4: Preprocess the experimental and theoretical data; specifically, outlier processing is performed on the experimental and theoretical data based on the thermal error physical model and prior data to initially screen out abnormal data; grey relational analysis is used to determine the correlation between temperature, power, current, and rotational speed and the thermal error of the ball screw, and the influence factors of different factors are given; the theoretical thermal error is normalized using max-min normalization; the experimental and theoretical data after outlier processing, grey relational analysis, and normalization are used as the sample dataset for training the data-model hybrid driving model. Step 5: Construct a data-model hybrid driven model, namely a Convolutional Long Short-Term Memory (C-LSTM) model. The C-LSTM model includes a Convolutional Neural Network (CNN) module and a Long Short-Term Memory (LSTM) module. The CNN module includes a single convolutional layer and convolves the data processed in Step 4 with two convolutional kernels of different sizes to extract features between variables and form a feature vector containing combined information on temperature, current, and power. The LSTM module uses the output of the CNN module as input to learn the overall variation features of temperature, current, power, and rotational speed, and iterates through the Mean Absolute Error (MAE) until the target MAE is reached, thus obtaining the trained data-model hybrid driven prediction model. Step 6: Input the real-time collected temperature, power, current and speed into the prediction model to predict the thermal error of the ball screw at the next moment.

2. The data-model hybrid driven method for predicting thermal errors in ball screws according to claim 1, characterized in that, The process of establishing the physical model of thermal error of the ball screw of the CNC machine tool in step 1 is as follows: First, according to heat transfer theory, the heat transfer process includes: heat conduction, heat convection, and radiation heat transfer; according to Fourier's law of thermal conductivity, the expression for the heat flux density of CNC machine tool ball screw components during the heat conduction process is: ； in, It is the heat flux density of thermal conduction; It is the thermal conductivity. It is the temperature of the components. It represents the temperature gradient of the components; the negative sign indicates that the heat transfer direction is opposite to the temperature gradient direction. The heat flux density of convective heat transfer in CNC machine tool ball screw components is calculated using Newton's law of cooling, and its expression is: ； in, It is the heat flux density in the convective heat transfer process. It is the convective heat transfer coefficient. It is the temperature of the air in contact with the surface of the component; The heat flux density radiated outward from the ball screw components of CNC machine tools is calculated using a modified form of the Stefan-Boltzmann law, and its expression is: ； in, It is the heat flux density in the radiative heat transfer process. It refers to the emissivity of the components, with a value between 0 and 1. It is the blackbody radiation coefficient; Then, using the formulas for heat conduction, heat convection, and radiation heat transfer, the temperature field of the lead screw under the action of the bearing and the lead screw nut was calculated. ; Finally, at any given moment, the lead screw... The thermal error is: ； in, It is the coefficient of thermal expansion of the lead screw. It is the thermal drift correction factor.

3. The data-model hybrid driven method for predicting thermal errors in ball screws according to claim 1, characterized in that, The steps for step 2, which involves performing steady-state thermal characteristic analysis of the ball screw using ANSYS Workbench, are as follows: First, the 3D model of the ball screw feed system is simplified and exported as a .x_t file, which is then imported into Workbench. Next, the 3D model of the ball screw feed system is meshed. Then, the parameters are set according to the material properties of each part. Finally, the steady-state thermal characteristics of the ball screw are solved. The temperature measurement points in the ball screw are determined through finite element analysis.

4. The data-model hybrid driven method for predicting thermal errors in ball screws according to claim 1, characterized in that, The process of building the test platform for the CNC machine tool ball screw feed system in step 3 is as follows: By placing temperature sensors at the temperature measurement points in step 2 above, the temperature at the measurement points in the ball screw feed system and the room temperature are measured; the axial thermal error of the ball screw is measured; and the power and speed of the ball screw feed system are measured; the data matrix of the ball screw is obtained, represented as follows: ； in, express The state data matrix of the ball screw at any given time. express Time of the first The temperature at each temperature measuring point express The current of the motor at all times, express The thermal error is constantly measured using a laser interferometer. express The power of the ball screw feed system at all times. This indicates the rotational speed of the ball screw.

5. The data-model hybrid driven method for predicting thermal errors in ball screws according to claim 1, characterized in that, The process of step 4 is as follows: First, outlier processing was performed on the collected experimental and theoretical data. Based on the physical model and prior data, outlier data was initially screened out. Then, through grey relational analysis, the degree of correlation between different factors affecting the thermal error of the ball screw was determined, and the influence factors of different factors were given. ; Finally, the theoretical data of ball screw thermal error is normalized using the maximum-minimum normalization method, as follows: ； in, The theoretical value is obtained from the physical model of the thermal error of the ball screw. This represents the minimum theoretical value obtained from the physical model of ball screw thermal error. This represents the maximum theoretical value obtained from the physical model of the thermal error of the ball screw.

6. The data-model hybrid driven method for predicting thermal errors in ball screws according to claim 1, characterized in that, The convolutional long short-term memory network (C-LSTM) model in step 5 includes a convolutional neural network (CNN) module and a long short-term memory network (LSTM) module. The Convolutional Neural Network (CNN) module includes a single convolutional layer, i.e., data input-convolution-output; the CNN module uses two convolutional kernels of different sizes. , Convolution is performed. The data that has undergone grayscale correlation analysis, outlier processing and normalization in step 4 above is convolved in the input layer to extract the features between variables. Different features are learned through different convolution kernels. The feature vector contains combined information on temperature, current, and power, retaining the variable features most strongly correlated with thermal error for subsequent model training. The Long Short-Term Memory (LSTM) network module consists of an input layer, hidden layers, and an output layer. The input layer is the output of the aforementioned Convolutional Neural Network (CNN) module. The basic unit of the hidden layer is a storage unit, which is composed of self-connected storage units that store time states. The storage unit passes information from previous outputs to the current output. By continuously memorizing and processing past input data, the hidden layer learns the overall variation characteristics of temperature, current, power, and rotational speed. Each storage unit consists of four parts: an input gate, a forget gate, autoregressive neurons, and an output gate. The output expression of the LSTM is: ； in, The input matrix includes temperature, power, current, and speed. This represents the output of the fully connected layer, i.e., the thermal error of the ball screw. , This represents the weight matrix of the fully connected layer. This represents the bias vector of the fully connected layer; The predictive performance of the algorithm is evaluated using the mean absolute error (MAE), and its mathematical expressions are as follows: ； in, For predicted values, For the true value, For the sample size, , The input to the model is used; the iterative training of the network model is determined by setting a target mean absolute error until the accuracy requirement is met.

7. The data-model hybrid driven method for predicting thermal errors in ball screws according to claim 1, characterized in that, Step 6, based on the data-model hybrid driving prediction model from step 5, inputs the real-time collected temperature, power, current, and rotational speed into the prediction model to predict the thermal error of the ball screw at the next moment.

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