Cross-working-condition migration machine tool thermal error step-by-step prediction method and system

Abstract

The invention belongs to the field of machine tool linear feed shaft thermal error prediction, and provides a cross-working-condition migration machine tool thermal error step-by-step prediction method and a cross-working-condition migration machine tool thermal error step-by-step prediction system. According to the technical scheme, the method comprises the following steps: acquiring thermal error data of the linear feed shaft of the machine tool under two working conditions of natural cooling and forced cooling and time-temperature distribution data of each temperature measurement point of the linear feed shaft; decoupling the thermal error data under each working condition into a linear component and a nonlinear deviation component; according to a heat conduction and convective heat transfer coupling mechanism, the inhibition effect of low-temperature water on the temperature rise of the lead screw is quantified, and a temperature rise inhibition coefficient is calculated; based on the inhibition coefficient, mapping the original temperature rise data and the nonlinear deviation component under the natural cooling working condition to an equivalent temperature rise characteristic space under the forced cooling working condition; and predicting a cross-working-condition linear component and a non-linear deviation component according to the equivalent temperature rise characteristic space, and performing superposition to obtain a thermal error prediction value of the linear feed shaft. And high-precision prediction of the thermal error of the linear feed shaft under different cooling working conditions is realized.

Description

Technical Field

[0001] The present invention belongs to the field of thermal error prediction of a linear feed axis of a machine tool, and in particular relates to a step-by-step prediction method and system for thermal errors of a machine tool that migrates across working conditions. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Existing thermal error prediction methods for machine tool linear feed axes mainly include two research paths: mechanism-driven and data-driven. The mechanism-driven method constructs a temperature-deformation mapping model based on heat conduction theory. By establishing a heat source distribution equation and a structural thermal resistance network, it derives the physical relationship between the temperature rise and thermal error of the linear feed axis. This method has the advantage of interpretability under steady-state temperature field conditions, but it is difficult to accurately describe the local temperature gradient mutation caused by forced convection in the low-temperature water circulation system when facing the unsteady-state heat transfer process when cooling conditions are switched. The data-driven method uses machine learning algorithms to directly establish a correlation model between temperature data and error values. Although it can capture nonlinear relationships under complex working conditions, it lacks mechanistic constraints on the differentiated thermal response characteristics of key components such as screws and guide rails under natural cooling and forced cooling modes, resulting in a decrease in model generalization ability when predicting across working conditions.

[0004] In summary, the common limitations of current technologies are as follows: First, the essential differences in heat exchange patterns between natural cooling and forced cooling conditions lead to significantly different temperature field evolution patterns in linear feed axes. Mechanism-driven models rely on natural air convection and radiation, while data-driven models rely on forced coolant convection. Traditional single-modeling approaches cannot effectively and uniformly describe the thermal error generation mechanisms for both operating conditions. Second, the dynamic intervention of the low-temperature water circulation system alters the heat conduction path of the linear feed axis. The resulting temperature rise suppression effect exhibits a nonlinear coupling relationship with parameters such as coolant flow rate and heat exchange area. Existing methods fail to establish a quantitative representation mechanism for these cross-condition correlation characteristics within the model. Furthermore, the coupling mechanism between the linear component and the nonlinear deviation component in the thermal error has not been fully decoupled. Directly adopting an end-to-end modeling strategy introduces error component confusion, impacting the physical consistency of the prediction model. Summary of the Invention

[0005] In order to solve at least one technical problem existing in the above-mentioned background technology, the present invention provides a step-by-step prediction method and system for machine tool thermal errors with cross-working condition migration. The method decouples the thermal error and performs step-by-step modeling and collaborative prediction. At the same time, combined with the inhibitory effect of the low-temperature water circulation system on the temperature rise of the linear feed shaft, a feature distribution consistency mapping mechanism across working condition data sets is established, thereby achieving high-precision prediction of the thermal error of the linear feed shaft under different cooling conditions, significantly enhancing the generalization ability and multi-working condition applicability of the prediction model.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: A first aspect of the present invention provides a step-by-step prediction method for machine tool thermal errors across working conditions, comprising the following steps: Obtain thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions, as well as time-temperature distribution data of each temperature measurement point of the linear feed axis; Decoupling the thermal error data under each operating condition into a linear component and a nonlinear deviation component; screening key temperature measurement points based on the decoupled linear and nonlinear deviation components; constructing a data set based on the screened key temperature measurement points; and training a nonlinear deviation prediction model based on the constructed data set to obtain a trained nonlinear deviation prediction model. Based on the coupling mechanism of heat conduction and convection, the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing is quantified. The corresponding temperature rise suppression coefficient is calculated by combining the temperature rise data under natural cooling and forced cooling. Based on the suppression coefficient, the dataset under natural cooling conditions is mapped to the equivalent temperature rise feature space under forced cooling conditions to align the input feature distributions under different conditions. The nonlinear deviation component across working conditions is predicted based on the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and the thermal error prediction value of the linear feed axis is obtained by superimposing the linear component across working conditions.

[0007] Furthermore, the linear components obtained based on decoupling and screening of key temperature measurement points include: Perform density clustering on the absolute temperature measured at each initial temperature measurement point to obtain the clustering result. Calculate the absolute temperature and error curve slope in each clustering result based on the Pearson correlation coefficient. k The most relevant key temperature measurement points; Perform density clustering on the relative temperature measured at each initial temperature measurement point to obtain the clustering result. Calculate the Pearson correlation coefficient and filter the intercept of the relative temperature and error curve in each clustering result. b Critical temperature measurement points of greatest relevance.

[0008] Furthermore, the linear component is fitted with the time-temperature distribution data of each temperature measurement point and is expressed as: , in, is the absolute temperature at the key temperature measurement point, is the temperature rise at the key temperature measurement point, the slope and intercept will change with the change of temperature. is the fitting coefficient of the absolute temperature at the nth key temperature point, is the fitting coefficient of temperature rise at the nth key temperature point, is the constant term in the slope expression, is the constant term in the intercept expression.

[0009] Furthermore, the nonlinear deviation component obtained by decoupling is used to screen the key temperature measurement points, including: according to DBSCAN clustering combined with correlation coefficient calculation, the relative temperature in each cluster and the deviation at each error measurement point are screened out. e The most relevant n The key temperature measurement point sets are combined to obtain the final deviation. e The key temperature measurement point set is p points.

[0010] Furthermore, when the nonlinear deviation prediction model is trained based on the constructed data set, the hyperparameters of the support vector machine regression prediction model, including the penalty coefficient, are optimized by the dream optimization algorithm. c and kernel width g Optimize and select the most appropriate kernel function parameters for modeling.

[0011] Furthermore, the temperature rise data under natural cooling and forced cooling are combined to calculate the corresponding temperature rise suppression coefficient, including: Define the Huber loss function, minimize the sum of Huber losses, introduce weights, transform the minimization of the sum of Huber losses into a weighted least squares problem, and calculate the corresponding temperature rise suppression coefficient by iterative reweighted least squares method, so that the adjusted temperature rise suppression coefficient satisfy As close as possible ,in, is the temperature rise data set under natural cooling, is the temperature rise data set under forced cooling.

[0012] Furthermore, when the data set under natural cooling conditions is mapped to the equivalent temperature rise feature space under forced cooling conditions, the slope of the error curve under natural cooling conditions is converted to k and the error curve intercept b The original temperature rise in the relationship Replaced with forced cooling equivalent temperature rise , and finally the deviation value adapted to the forced cooling condition is analyzed e . A second aspect of the present invention provides a step-by-step prediction system for machine tool thermal errors that migrate across working conditions, comprising: A data acquisition module is used to obtain thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measurement point of the linear feed axis; An error decoupling module is used to decouple the thermal error data under each operating condition into a linear component and a nonlinear deviation component; based on the decoupled linear and nonlinear deviation components, key temperature measurement points are selected, a data set is constructed based on the selected key temperature measurement points, and a nonlinear deviation prediction model is trained based on the constructed data set to obtain a trained nonlinear deviation prediction model; The mechanism analysis module is used to quantify the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing based on the coupling mechanism of heat conduction and convection heat transfer. It also calculates the corresponding temperature rise suppression coefficient by combining the temperature rise data under natural cooling and forced cooling conditions. A cross-condition prediction module, which is used to map the data set under natural cooling conditions to the equivalent temperature rise feature space under forced cooling conditions to align the input feature distribution under different conditions; The nonlinear deviation component across working conditions is predicted based on the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and the thermal error prediction value of the linear feed axis is obtained by superimposing the linear component across working conditions.

[0013] A third aspect of the present invention provides a computer-readable storage medium.

[0014] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned step-by-step prediction method for thermal errors of machine tools that migrate across working conditions.

[0015] A fourth aspect of the present invention provides a computer device.

[0016] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-described step-by-step prediction method for thermal errors of machine tools that migrate across working conditions are implemented.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention decouples thermal errors into linear mechanism components and nonlinear deviation components. Based on the heat conduction suppression effect, it calculates the temperature rise suppression coefficient to quantify the physical suppression of low-temperature water on the screw temperature rise. This suppression coefficient aligns the characteristic distribution of natural cooling condition samples, establishing a cross-condition consistency mapping mechanism and overcoming the traditional model's reliance on single-condition data. While retaining the physical laws of the linear component, it utilizes an optimization algorithm to enhance the dynamic capture of nonlinear deviations, and improves model generalization performance through cross-condition feature space transformation. This provides a solution for machine tool thermal error compensation that balances prediction accuracy and adaptability to multiple conditions.

[0018] 2. Based on the heat conduction inhibition effect, the present invention calculates the temperature rise inhibition coefficient to quantify the physical inhibition effect of low-temperature water on the temperature rise of the screw, constructs an equivalent temperature rise conversion model between natural cooling and forced cooling conditions, and solves the problem of inconsistent data distribution across working conditions.

[0019] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0021] Figure 1 This is a flow chart of a step-by-step prediction method for machine tool thermal errors across working conditions provided by an embodiment of the present invention; Figure 2 The thermal error provided by the embodiment of the present invention is decomposed into linear components L and deviation components e Schematic diagram of; Figure 3 The embodiment of the present invention provides a method for selecting a slope. k ,intercept b And the deviation of each position of the linear feed axis e Flow chart of key temperature measurement points; Figure 4 The embodiment of the present invention provides a method for deviation e Flowchart of modeling of the predicted DOA-SVM model. DETAILED DESCRIPTION

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0024] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0025] Existing thermal error prediction methods for machine tool linear feed axes mainly include two research paths: mechanism-driven and data-driven. The mechanism-driven method constructs a temperature-deformation mapping model based on heat conduction theory. By establishing a heat source distribution equation and a structural thermal resistance network, it derives the physical relationship between the temperature rise and thermal error of the linear feed axis. This method has the advantage of interpretability under steady-state temperature field conditions, but it is difficult to accurately describe the local temperature gradient mutation caused by forced convection in the low-temperature water circulation system when facing the unsteady-state heat transfer process when cooling conditions are switched. The data-driven method uses machine learning algorithms to directly establish a correlation model between temperature data and error values. Although it can capture nonlinear relationships under complex working conditions, it lacks mechanistic constraints on the differentiated thermal response characteristics of key components such as screws and guide rails under natural cooling and forced cooling modes, resulting in a decrease in model generalization ability when predicting across working conditions.

[0026] In summary, the common limitations of current technologies are as follows: First, the essential differences in heat exchange patterns between natural cooling and forced cooling conditions lead to significantly different temperature field evolution patterns in linear feed axes. Mechanism-driven models rely on natural air convection and radiation, while data-driven models rely on forced coolant convection. Traditional single-modeling approaches cannot effectively and uniformly describe the thermal error generation mechanisms for both operating conditions. Second, the dynamic intervention of the low-temperature water circulation system alters the heat conduction path of the linear feed axis. The resulting temperature rise suppression effect exhibits a nonlinear coupling relationship with parameters such as coolant flow rate and heat exchange area. Existing methods fail to establish a quantitative representation mechanism for these cross-condition correlation characteristics within the model. Furthermore, the coupling mechanism between the linear component and the nonlinear deviation component in the thermal error has not been fully decoupled. Directly adopting an end-to-end modeling strategy introduces error component confusion, impacting the physical consistency of the prediction model.

[0027] The present invention proposes a cross-operating condition prediction method for the thermal error of the linear feed axis of a machine tool that integrates dual-drive mechanisms and data. By decoupling the thermal error into a linear mechanism component and a nonlinear deviation component, the DOA algorithm is used to dynamically optimize the SVM hyperparameters to achieve adaptive modeling and high-precision prediction of the nonlinear deviation; at the same time, based on the heat conduction inhibition effect, the temperature rise inhibition coefficient is calculated to quantify the physical inhibition effect of low-temperature water on the temperature rise of the screw, and an equivalent temperature rise conversion model between natural cooling and forced cooling working conditions is constructed to solve the problem of inconsistent data distribution across working conditions. Further, through the inhibition coefficient α By aligning the feature distributions of natural cooling condition samples and establishing a cross-condition consistency mapping mechanism, this approach breaks through the traditional model's reliance on single-condition data. This innovative approach combines the constraints of thermodynamic mechanisms with the advantages of data-driven modeling. While preserving the physical laws of linear components, it leverages optimization algorithms to enhance the dynamic capture of nonlinear deviations. Furthermore, through cross-condition feature space transformation, it improves model generalization performance, providing a solution for machine tool thermal error compensation that balances prediction accuracy with adaptability to multiple conditions.

[0028] Example 1 Please refer to Figure 1 , Figure 1 A flow chart of a step-by-step prediction method for machine tool thermal errors across working conditions is shown. The method includes the following steps: S1: Obtain the thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions for long-term operation, as well as the time-temperature distribution data of each temperature measurement point of the linear feed axis; The method for obtaining the thermal error data of the machine tool linear feed axis under long-term operation in natural cooling and forced cooling conditions is as follows: To reduce the temperature rise of a machine tool's linear feed axis and suppress thermal errors, low-temperature water can be forced to circulate through the circulating low-temperature water pipes inside key linear feed axis components, such as the ball screw and screw nut, improving the axis's heat dissipation efficiency. Natural cooling and forced cooling correspond to natural air cooling and forced cooling with circulating low-temperature water, respectively.

[0029] Thermal error data is measured using a laser interferometer at short intervals during long machine operation. This data is used to measure the thermal error of the linear feed axis at different temperatures. Complete thermal error data includes the thermal error values ​​corresponding to each error measurement point on the linear feed axis at different measurement times (at different temperatures).

[0030] In this example, the specific data acquisition method is as follows: the linear feed axis is set to a feed rate of 1500 mm / rev and a stroke length of 1000 mm. The linear feed axis performs reciprocating motion for 5 hours. During this period, the linear feed axis thermal error is measured every 30 minutes using an XL-80 laser interferometer. The error measurement points of the laser interferometer are set to 100 mm intervals, meaning that there are 11 error measurement points within the 1000 mm stroke.

[0031] The same data acquisition method was used for both natural cooling and forced cooling. The difference was that the circulating low-temperature water system needed to be turned on for forced cooling. Among them, the time-temperature distribution data of each temperature measurement point of the linear feed axis includes the temperature change data collected from the numerous temperature measurement points initially set on the linear feed axis over time; It should be noted that, in this embodiment, the temperature measurement method of different temperature measurement points should be selected according to their location and operating status. Magnetic thermal resistor temperature sensors are arranged on the motor, worktable, bed, front bearing, rear bearing, slider, front end and rear end of the guide rail of the machine tool linear feed axis to collect temperature data; since the screw rotates at high speed during operation, non-contact infrared temperature measuring guns are used to collect temperature data at the front, middle and rear ends of the ball screw; there are a total of 11 initial temperature measurement points.

[0032] S2: Decoupling thermal errors into linear components L and nonlinear deviation components e ; Among them, the linear component L A linear function is used for fitting, and the nonlinear deviation component e The Dreaming Optimization Algorithm (DOA)-Support Vector Machine (SVM) algorithm is used for modeling and prediction; See Figure 2 , specifically including the following steps: S21. The collected thermal error data is plotted into a dot-line graph, and a linear function is used to fit the error curves under different states: , in, n is the number of times thermal error is measured at different temperature states, is the slope of the error curve under the nth temperature state, is the intercept of the error curve under the nth temperature state, is the position of the linear axis.

[0033] S22. Perform density clustering on the absolute temperature measured at each initial temperature measurement point to obtain clustering results. Calculate the absolute temperature and error curve slope in each clustering result based on the Pearson correlation coefficient. k The most relevant key temperature measurement points; like Figure 3 As shown, in this embodiment, the absolute temperature of each initial temperature measurement point is subjected to DBSCAN cluster analysis, and the 11 initial temperature measurement points are divided into 4 clusters. The absolute temperature and slope in each cluster are screened out according to the Pearson correlation coefficient. k The key temperature measurement point with the highest correlation, and finally the slope k The key temperature measurement point set ( - ).

[0034] S23. According to the method of S22, intercept b Selection of key temperature measurement points; Intercept b When selecting the key temperature measurement points, only the absolute temperature in the S22 analysis process is replaced by the relative temperature, that is, the temperature rise value, to obtain the intercept b The key temperature measurement point set ( - ).

[0035] S24, final binding slope k and intercept b Get the linear component of the thermal error of the linear feed axis L ( x ) is expressed as: , in, is the absolute temperature at the key temperature measurement point, is the temperature rise at the key temperature measurement point, the slope and intercept will change with the change of temperature. and Use about T and Δ respectively T The multivariate linear function representation of For the n The fitting coefficient of the absolute temperature at the key temperature points, For the n The fitting coefficient of temperature rise at each key temperature point, is the constant term in the slope expression, is the constant term in the intercept expression.

[0036] S25, collect the thermal error data Subtract the linear component L (x ), the nonlinear deviation component under different temperature conditions at each error measurement point on the linear feed axis can be obtained , expressed as: , S26, nonlinear deviation component at different temperature conditions at each measurement point Screening of key temperature measurement points; In this embodiment, the deviation e When making predictions, it is necessary to simultaneously establish all error measurement positions within the full range of measurement. e The mapping relationship between the value and the temperature of each temperature measurement point. According to the DBSCAN clustering combined with the Pearson correlation coefficient calculation, the relative temperature in each cluster and the deviation at each error measurement point are screened out. e The most relevant n The key temperature measurement point sets are combined to obtain the final deviation. e The key temperature measurement point set is p points.

[0037] S27, constructing a training data set based on the screened key temperature measurement point set, training the DOA-SVM prediction model based on the constructed training data set, and predicting a deviation component based on the trained DOA-SVM prediction model; In this embodiment, the deviation component e The DOA-SVM prediction algorithm used in the prediction is to optimize the hyperparameters of the support vector machine regression prediction model, including the penalty coefficient, through the dream optimization algorithm. c and kernel width g Optimize to select the most appropriate kernel function parameters for modeling and improve the prediction accuracy of the prediction model; See Figure 4 , specifically including the following steps: S271. Construct a training data set and a test data set based on the selected key temperature measurement set, and express both the data set and the test data set as: , in, For the m The data subset at the time, For the m Time n The temperature rise at the key temperature measurement points, The first p The error measurement point position, The first p The error measurement point is located at m The deviation component at the moment,m is the sequence of temperature measurement moments, p is the number of error measurement points; S272, inputting the training data set to perform DOA hyperparameter optimization, and determining the optimized DOA hyperparameters; Specifically include: S2721, DOA initialization, including parameter definition: search space c ∈[10 -5 ,10 5 ], g ∈[10 -5 ,1 05 ], population size N =30, maximum iterations T max = 100. Randomly generate the initial population: each individual X i =[ c i , g i The initial value of ] is: , Among them, rand is a uniformly distributed random number between [0,1]. is the randomly generated initial value of c, is the lower bound of the exploration space for the value of c, for c The upper bound of the value exploration space, Randomly generated g The initial value of for g The lower bound of the value exploration space, for g The upper bound of the value exploration space; S2722, fitness calculation; For each individual X i =[ c i , g i ], using the training dataset D Train the SVM regression model with RBF kernel function: , calculate the fitness (5-fold cross-validation MSE): ,in, is the expression of RBF kernel function, and are two input samples (vectors), representing the i and j The feature vector of the samples, For individualsX The fitness of i, For the k The number of folded samples, For the model k The predicted value of the fold, S2723, DOA iterative optimization; Execute loop ( t =1,2,…, T max ): (1) Exploration stage (preliminary T d =0.9 T max iterations): Memory strategy: The population is divided into 5 groups, and the individuals in each group are updated to the position of the historical best individual in the group .

[0038] Forget and supplement: Random selection for each group Dimensions ( Indicates the exploration phase q The number of forgetting dimensions of the group) is updated: , in, Indicates the i Individuals in the iteration t+1 j The location of the dimension, Indicates that at iteration t, groupq The best individual is located in the jth dimension, represents the position of the i-th individual in the j-th dimension after t iterations, represents the upper bound of the j-th dimension search space, represents the lower bound of the j-th dimension search space, represents the total maximum number of iterations, Indicates the maximum number of iterations in the exploration phase; Dream Sharing: Based on Probability u = 0.9 executes the above strategy, otherwise randomly swaps dimension information: , in, m Number the randomly selected individuals; (2) Development stage (post T max - T d iterations): Global optimal guidance: All individuals move towards the global optimal X t best near: , represents the best individual in the entire population at iteration t.

[0039] Oblivion Supplement Update: Random Selection k r Dimensions ( k r Indicates the number of forgotten dimensions during the development phase) Update: , Indicates the individual position of the entire population in the jth dimension in the tth iteration.

[0040] (3) Boundary processing (if the parameter is out of bounds): , (4) Update the global optimum: record the minimum fitness corresponding to .

[0041] S273. Combine the optimized DOA hyperparameters and the test data set to train the SVM to obtain the final SVM model, and predict the final deviation component based on the SVM model.

[0042] S3: Based on the coupling mechanism of heat conduction and convection heat transfer, quantify the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing respectively. Combined with the temperature rise data under natural cooling and forced cooling, calculate the corresponding temperature rise suppression coefficient. The specific steps include the following: S31. Quantify the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing, including: S311. Quantify the inhibitory effect of low-temperature water on the temperature rise of the screw and obtain the temperature rise suppression coefficient of the screw ; The thermal error of the linear feed axis of a machine tool is mainly caused by the thermal deformation of the ball screw due to temperature rise during long-term operation.

[0043] Assume that the heat input of the linear feed axis during the entire operation is In the case of natural cooling, the heat is dissipated to the environment through natural convection and radiation on the outer wall of the screw, and the temperature rise It can be expressed as: , in, is the ambient convection thermal resistance, is the ambient convection heat transfer coefficient, is the heat dissipation area of ​​the outer wall of the screw; When low-temperature water is added to the ball screw, the heat is conducted through the outer wall of the screw to the circulating low-temperature water pipe, and then discharged through forced convection. The total thermal resistance Expressed as: , in, is the total thermal resistance, is the convection thermal resistance, and are the outer and inner radii of the screw, is the thermal conductivity of the screw, is the low-temperature water convective heat transfer coefficient, is the inner wall area of ​​the circulating low-temperature water pipe, is the screw length.

[0044] At this time, the ball screw after the low temperature water is passed through the heat Temperature rise under for: , Substitute the above formula into the temperature rise calculation formula under natural cooling conditions and eliminate Q , we can get: , in, The suppression effect of low-temperature water on the temperature rise of the screw can be quantified, that is, the suppression coefficient of the screw.

[0045] S312. Quantify the inhibitory effect of low-temperature water on the temperature rise of the nut and obtain the temperature rise inhibition coefficient of the nut ; The screw nut also uses forced cooling. Assuming that the structure and cooling parameters of the screw nut do not change during the motion of the linear feed axis, the thermal resistance under different conditions and The difference between the nut temperature rise under natural cooling and forced cooling can be obtained: , in, is the temperature rise of the nut under forced cooling, is the suppression coefficient of the nut, is the temperature rise of the nut under natural cooling.

[0046] S313. Quantify the inhibitory effect of low-temperature water on bearing temperature rise and obtain the bearing temperature rise suppression coefficient. ; The front and rear bearings of the linear feed axis are directly connected to the ball screw. Considering the bearing and screw as a whole, low-temperature water will reduce the thermal resistance of the entire system, thereby significantly suppressing the temperature rise at the bearing end. Therefore, there is a similar proportional relationship between the temperature rise in the natural cooling state and the forced cooling state: , in, is the bearing temperature rise under forced cooling, is the bearing's suppression coefficient, is the bearing temperature rise under natural cooling; S32. Calculate the corresponding temperature rise suppression coefficient based on the temperature rise data under the natural cooling and forced cooling states; In this embodiment, the robust regression method is used to calculate the value of the corresponding temperature rise suppression coefficient. The calculation is as follows: Assume that the data sets of temperature rise at a temperature measurement point on the screw under natural cooling and forced cooling conditions are: , in, is the temperature rise data set of this temperature point under natural cooling, is the temperature rise of the temperature point at the mth moment under natural cooling, is the temperature rise data set of this temperature point under forced cooling, is the temperature rise of the temperature point at the mth moment under forced cooling; Suppression coefficient The problem of solving can be converted into solving a coefficient , so that the adjusted As close as possible . Define the Huber loss function for: , in, δ is a threshold parameter, usually taken as a multiple of the median absolute deviation (MAD) of the data residuals (e.g. δ =1.345×MAD); , For forced cooling i Temperature rise at each temperature point; For natural cooling i The temperature rise of a temperature point.

[0047] The goal is to minimize the sum of Huber losses: , By introducing weights w i , transformed into a weighted least squares problem, where the weights w i Dynamically adjust with residuals to suppress the influence of outliers; , The robust coefficients are calculated by iteratively reweighted least squares (IRLS) α : , The robust coefficient obtained α That is, the suppression coefficient of the screw; In this implementation case, the data sets of the temperature rise at a certain temperature measurement point on the screw measured within 5 hours under natural cooling and forced cooling (water cooling temperature 33°C) are respectively: , , According to the above steps, the suppression coefficient of the screw can be obtained The calculation process goes through 3 iterations. In the third iteration, the weight .

[0048] The solution process for the temperature rise suppression coefficient of nuts and bearings and the temperature rise suppression coefficient of screws The solution process is the same as that of , so it will not be repeated here. Using the same method, the nut temperature rise suppression coefficient can be obtained , bearing temperature rise suppression coefficient .

[0049] S4: Based on the suppression coefficient, the data set under the natural cooling condition is mapped to the equivalent temperature rise feature space under the forced cooling condition to align the input feature distribution under different conditions; In the process of deviation When predicting modeling, the input of the test set is temperature rise , linear feed axis position , the model output is However, for the forced cooling condition, since forced convection heat transfer significantly suppresses the temperature rise of the screw, if the training set D Directly use the original temperature rise data and deviation of natural cooling conditions Modeling will cause a shift in the feature distribution between the training set and the prediction set. Therefore, based on the suppression coefficient α , the original temperature rise data of natural cooling condition Δ T and deviation Map to the equivalent temperature rise feature space under forced cooling conditions. Achieve consistent alignment of input feature distributions under different conditions.

[0050] The temperature rise suppression coefficient of the screw For example, the deviation The conversion rules are as follows: The temperature change of the ball screw produces thermal deformation. If the change of thermal error before and after forced cooling is idealized into an equivalent form of thermal deformation, we can obtain: , in, In order to force cooling of the thermal deformation of the screw, is the thermal expansion coefficient of the screw, is the original length of the screw, To force cooling of the temperature rise of the screw, To reduce the thermal deformation of the screw under natural cooling, is the thermal error of the linear axis under forced cooling, is the thermal error of the linear axis under natural cooling; because k and b are characterized as a linear function of temperature rise, and the deviation e is through k and b Under forced cooling conditions, the characteristic mapping rules of the heat conduction model are used to convert the natural cooling conditions into k and b The original temperature rise in the relationship Replaced with forced cooling equivalent temperature rise Finally, the deviation value adapted to the forced cooling condition is analyzed. e ,for: , in, is the slope of the thermal error curve fitted under forced cooling, is the intercept of the thermal error curve fitted under forced cooling; The temperature rise suppression coefficient corresponding to the nut and bearing will be the original temperature rise data of the natural cooling condition Δ T and deviation The process of mapping to the equivalent temperature rise characteristic space under forced cooling conditions and the temperature rise suppression coefficient of the screw same; S105: Outputting the predicted value of the thermal error of the linear feed axis by superimposing the linear component mechanism prediction and the deviation component data prediction.

[0051] The linear component L is predicted by a linear function fitting, and the deviation component is realized by aligning the data distribution across working conditions and the DOA-SVM algorithm. The predicted value of the final thermal error E can be expressed as the linear component L and the deviation component The sum of the thermal error E of the machine tool linear feed axis is accurately predicted.

[0052] Example 2 This embodiment provides a step-by-step prediction system for machine tool thermal errors that migrate across working conditions, including: A data acquisition module is used to obtain thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measurement point of the linear feed axis; An error decoupling module is used to decouple the thermal error data under each operating condition into a linear component and a nonlinear deviation component; based on the decoupled linear and nonlinear deviation components, key temperature measurement points are selected, a data set is constructed based on the selected key temperature measurement points, and a nonlinear deviation prediction model is trained based on the constructed data set to obtain a trained nonlinear deviation prediction model; The mechanism analysis module is used to quantify the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing based on the coupling mechanism of heat conduction and convection heat transfer. It also calculates the corresponding temperature rise suppression coefficient by combining the temperature rise data under natural cooling and forced cooling conditions. A cross-condition prediction module, which is used to map the data set under natural cooling conditions to the equivalent temperature rise feature space under forced cooling conditions to align the input feature distribution under different conditions; The nonlinear deviation component across working conditions is predicted based on the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and the thermal error prediction value of the linear feed axis is obtained by superimposing the linear component across working conditions.

[0053] It should be noted that the specific implementation method of a step-by-step prediction system for machine tool thermal errors across working conditions in an embodiment of the present invention is similar to the specific implementation method of a step-by-step prediction method for machine tool thermal errors across working conditions in an embodiment of the present invention. Please refer to the description of the method section for details. In order to reduce redundancy, it will not be repeated here.

[0054] Example 3 This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps in the above-mentioned step-by-step prediction method for machine tool thermal errors with cross-operating state migration are implemented.

[0055] Example 4 This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the above-described step-by-step prediction method for machine tool thermal errors across working conditions are implemented.

[0056] Example 5 This embodiment provides a program product, which is a computer program product, including a computer program. When the computer program is executed by a processor, the steps in the step-by-step prediction method for machine tool thermal errors across working conditions as described above are implemented.

[0057] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage and optical storage, etc.) containing computer-usable program code.

[0058] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0059] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0060] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0061] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0062] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A step-by-step prediction method for machine tool thermal errors across working conditions, characterized in that: The steps include: Obtain thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions, as well as time-temperature distribution data of each temperature measurement point of the linear feed axis; Decoupling the thermal error data under each operating condition into a linear component and a nonlinear deviation component; screening key temperature measurement points based on the decoupled linear and nonlinear deviation components; constructing a data set based on the screened key temperature measurement points; and training a nonlinear deviation prediction model based on the constructed data set to obtain a trained nonlinear deviation prediction model. Based on the coupling mechanism of heat conduction and convection, the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing is quantified. The corresponding temperature rise suppression coefficient is calculated by combining the temperature rise data under natural cooling and forced cooling. Based on the suppression coefficient, the dataset under natural cooling conditions is mapped to the equivalent temperature rise feature space under forced cooling conditions to align the input feature distributions under different conditions. The nonlinear deviation component across working conditions is predicted based on the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and the thermal error prediction value of the linear feed axis is obtained by superimposing the linear component across working conditions.

2. The step-by-step prediction method for machine tool thermal errors across working conditions according to claim 1, characterized in that: The linear component obtained based on decoupling and screening of key temperature measurement points include: Perform density clustering on the absolute temperature measured at each initial temperature measurement point to obtain the clustering result. Calculate the absolute temperature and error curve slope in each clustering result based on the Pearson correlation coefficient. k The most relevant key temperature measurement points; Perform density clustering on the relative temperature measured at each initial temperature measurement point to obtain the clustering result. Calculate the Pearson correlation coefficient and filter the intercept of the relative temperature and error curve in each clustering result. b Critical temperature measurement points of greatest relevance.

3. The step-by-step prediction method for machine tool thermal errors across working conditions according to claim 1, characterized in that: The linear component is fitted with the time-temperature distribution data of each temperature measurement point and is expressed as: ， in, is the absolute temperature at the key temperature measurement point, is the temperature rise at the key temperature measurement point, the slope and intercept will change with the change of temperature. is the fitting coefficient of the absolute temperature at the nth key temperature point, is the fitting coefficient of temperature rise at the nth key temperature point, is the constant term in the slope expression, is the constant term in the intercept expression.

4. The step-by-step prediction method for machine tool thermal errors across working conditions according to claim 1, characterized in that: The nonlinear deviation component based on decoupling is used to screen the key temperature measurement points, including: screening the relative temperature in each cluster and the deviation at each error measurement point according to DBSCAN clustering combined with Pearson correlation coefficient calculation e The most relevant n The key temperature measurement point sets are combined to obtain the final deviation. e The key temperature measurement point set is p points.

5. The step-by-step prediction method for machine tool thermal errors across working conditions according to claim 1, characterized in that: When training the nonlinear deviation prediction model based on the constructed data set, the hyperparameters of the support vector machine regression prediction model, including the penalty coefficient, are optimized by the dream optimization algorithm. c and kernel width g Optimize and select the most appropriate kernel function parameters for modeling.

6. The step-by-step prediction method for machine tool thermal errors across working conditions according to claim 1, characterized in that: Combining the temperature rise data under natural cooling and forced cooling, calculate the corresponding temperature rise suppression coefficient, including: Define the Huber loss function, minimize the sum of Huber losses, introduce weights, transform the minimization of the sum of Huber losses into a weighted least squares problem, and calculate the corresponding temperature rise suppression coefficient by iterative reweighted least squares method, so that the adjusted temperature rise suppression coefficient satisfy As close as possible ,in, is the temperature rise data set under natural cooling, is the temperature rise data set under forced cooling.

7. The step-by-step prediction method for machine tool thermal errors across working conditions according to claim 1, characterized in that: When mapping the data set under natural cooling conditions to the equivalent temperature rise feature space under forced cooling conditions, the slope of the error curve under natural cooling conditions is k and the error curve intercept b The original temperature rise in the relationship Replaced with forced cooling equivalent temperature rise , and finally the deviation value adapted to the forced cooling condition is analyzed e .

8. A step-by-step prediction system for machine tool thermal errors that migrates across working conditions, characterized in that: include: A data acquisition module is used to obtain thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measurement point of the linear feed axis; An error decoupling module is used to decouple the thermal error data under each operating condition into a linear component and a nonlinear deviation component; based on the decoupled linear and nonlinear deviation components, key temperature measurement points are selected, a data set is constructed based on the selected key temperature measurement points, and a nonlinear deviation prediction model is trained based on the constructed data set to obtain a trained nonlinear deviation prediction model; The mechanism analysis module is used to quantify the inhibitory effect of low-temperature water on the temperature rise of the screw, nut, and bearing based on the coupling mechanism of heat conduction and convection heat transfer. It also calculates the corresponding temperature rise suppression coefficient by combining the temperature rise data under natural cooling and forced cooling conditions. A cross-condition prediction module, which is used to map the data set under natural cooling conditions to the equivalent temperature rise feature space under forced cooling conditions to align the input feature distribution under different conditions; The nonlinear deviation component across working conditions is predicted based on the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and the thermal error prediction value of the linear feed axis is obtained by superimposing the linear component across working conditions.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the step-by-step prediction method for thermal errors of machine tools that migrate across working conditions as described in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the step-by-step prediction method for machine tool thermal errors across working condition migration according to any one of claims 1 to 7 are implemented.

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