Machine tool thermal error step-by-step prediction method and system for cross-working condition migration

Abstract

The present application belongs to the field of machine tool linear feed axis thermal error prediction, and provides a machine tool thermal error step-by-step prediction method and system across working conditions, which acquires thermal error data and time-temperature distribution data of each temperature measuring point of the linear feed axis under natural cooling and forced cooling working conditions; decouples the thermal error data under each working condition into linear components and nonlinear deviation components; quantifies the inhibitory effect of low-temperature water on the temperature rise of the screw based on the heat conduction and convection heat transfer coupling mechanism, and calculates the temperature rise inhibition coefficient; based on the inhibition coefficient, maps the original temperature rise data and nonlinear deviation components under the natural cooling working condition to the equivalent temperature rise characteristic space under the forced cooling working condition; predicts the linear components and nonlinear deviation components across working conditions according to the equivalent temperature rise characteristic space, and superimposes to obtain the linear feed axis thermal error prediction value. High-precision prediction of the linear feed axis thermal error under different cooling working conditions is realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of machine tool linear feed axis thermal error prediction, and particularly relates to a machine tool thermal error step-by-step prediction method and system for cross-working condition migration. BACKGROUND

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

[0003] The existing machine tool linear feed axis thermal error prediction methods mainly include two research paths of mechanism driving and data driving; the mechanism driving method constructs a temperature-deformation mapping model based on heat conduction theory, and the physical relationship between temperature rise and thermal error of the linear feed axis is derived by establishing a heat source distribution equation and a structure thermal resistance network; this kind of method has an explainable advantage under the condition of steady-state temperature field, but it is difficult to accurately describe the local temperature gradient mutation phenomenon caused by forced convection of the low-temperature water circulation system in the face of non-steady-state heat transfer process under the condition of cooling condition switching. The data-driven method directly establishes the correlation model of temperature data and error value by using machine learning algorithm, although it can capture the nonlinear relationship under complex working conditions, but it lacks the mechanism level constraint on the differential thermal response characteristics of key components such as screw and guide under natural cooling and forced cooling modes, resulting in the problem of decreased model generalization ability in cross-working condition prediction.

[0004] In summary, the common limitations of the current technology are: on the one hand, the essential difference between the heat exchange modes of natural cooling and forced cooling working conditions leads to significant differences in the temperature field evolution of the linear feed axis, the mechanism driving relies on air natural convection and radiation, and the data driving is based on forced convection of cooling liquid, and the traditional single modeling method cannot effectively describe the thermal error generation mechanism of the two working conditions; on the other hand, the dynamic intervention of the low-temperature water circulation system will change the heat conduction path of the linear feed axis, and the nonlinear coupling relationship exists between the temperature rise suppression effect and parameters such as cooling liquid flow and heat exchange area, and the existing method cannot establish a quantitative representation mechanism of the cross-working condition correlation characteristics in the model. In addition, the coupling mechanism of the linear component and the nonlinear deviation component in the thermal error has not been fully decoupled, and the direct use of end-to-end modeling strategy will introduce error component confusion problem, affecting the physical consistency of the prediction model. SUMMARY

[0005] In order to solve at least one of the technical problems in the background art, the present application provides a machine tool thermal error step-by-step prediction method and system for cross-working condition migration, which decouples and step-by-step models and cooperatively predicts the thermal error; at the same time, the inhibition effect of the low-temperature water circulation system on the temperature rise of the linear feed axis is combined to establish a feature distribution consistency mapping mechanism of the cross-working condition data set, and then the high-precision prediction of the linear feed axis thermal error under different cooling working conditions is realized, and the generalization ability and multi-working condition applicability of the prediction model are significantly enhanced.

[0006] To achieve the above object, the present application adopts the following technical solutions:

[0007] The first aspect of the present application provides a machine tool thermal error step-by-step prediction method for cross-condition migration, comprising the following steps:

[0008] Obtain thermal error data of a linear feed axis of a machine tool under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measurement point of the linear feed axis;

[0009] Decouple the thermal error data under each condition into a linear component and a nonlinear deviation component; filter key temperature measurement points based on the decoupled linear component and nonlinear deviation component, construct a data set based on the filtered key temperature measurement points, and train a nonlinear deviation prediction model based on the constructed data set to obtain a trained nonlinear deviation prediction model;

[0010] According to the coupling mechanism of heat conduction and convective heat transfer, the inhibitory effect of low-temperature water on the temperature rise of the screw, the nut and the bearing is quantified, and the corresponding temperature rise inhibition coefficient is calculated based on the temperature rise data under natural cooling and forced cooling conditions;

[0011] Based on the inhibition 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.

[0012] According to the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, the cross-condition nonlinear deviation component is predicted, and the linear component is superimposed to obtain the linear feed axis thermal error prediction value.

[0013] Further, the linear component based on the decoupled linear component and the filtered key temperature measurement points comprises:

[0014] The absolute temperature measured by each initial temperature measurement point is density clustered to obtain a clustering result, and the key temperature measurement point with the highest correlation between the absolute temperature and the error curve slope k in each clustering result is selected according to the Pearson correlation coefficient calculation.

[0015] The relative temperature measured by each initial temperature measurement point is density clustered to obtain a clustering result, and the key temperature measurement point with the highest correlation between the relative temperature and the error curve intercept b in each clustering result is selected according to the Pearson correlation coefficient calculation.

[0016] Further, the linear component is fitted based on the time-temperature distribution data of each temperature measurement point and is expressed as:

[0017] ,

[0018] wherein, T is the absolute temperature at the critical temperature measurement point, is the temperature rise at the critical temperature measurement point, the slope and the intercept both vary with temperature, is the fitting coefficient of the absolute temperature at the nth critical temperature point, is the fitting coefficient of the temperature rise at the nth critical temperature point, is the constant term of the slope expression, is the constant term of the intercept expression.

[0019] Further, the screening of the critical temperature measurement points based on the decoupled nonlinear deviation component includes: screening, according to DBSCAN clustering combined with correlation coefficient calculation, the critical temperature measurement points with the highest correlation between the relative temperature and the deviation e at each error measurement point in each cluster, n taking the union of each critical temperature measurement point set to obtain the final critical temperature measurement point set of the deviation e , a total of p points.

[0020] Further, 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 c and the kernel function width g are optimized through the dream optimization algorithm, so as to select the most suitable kernel function parameters for modeling.

[0021] Further, the temperature rise suppression coefficients corresponding to the temperature rise data in the natural cooling and forced cooling states are calculated, including:

[0022] defining the Huber loss function, minimizing the sum of the Huber loss, introducing the weight, converting the minimization of the sum of the Huber loss into a weighted least squares problem, and calculating the corresponding temperature rise suppression coefficient through the iteratively reweighted least squares method, so that the adjusted temperature rise suppression coefficient satisfies as close as possible to , wherein, is the temperature rise data set under natural cooling, is the temperature rise data set under forced cooling.

[0023] Further, when mapping the data set under the natural cooling condition to the equivalent temperature rise feature space under the forced cooling condition, the original temperature rise k in the error curve slope b and error curve intercept Substitute for forced cooling equivalent temperature rise Finally, the deviation value under the forced cooling condition is resolved e .

[0024] The second aspect of the application provides a machine tool thermal error step-by-step prediction system for cross-condition migration, comprising:

[0025] A data acquisition module is configured to acquire thermal error data of a linear feed axis of a machine tool under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measurement point of the linear feed axis.

[0026] An error decoupling module is configured to decouple the thermal error data under each condition into a linear component and a nonlinear deviation component; filter key temperature measurement points based on the decoupled linear component and nonlinear deviation component; construct a data set based on the filtered key temperature measurement points; and train a nonlinear deviation prediction model based on the constructed data set to obtain a trained nonlinear deviation prediction model.

[0027] A mechanism analysis module is configured to quantify the inhibitory effect of low-temperature water on the temperature rise of a lead screw, a nut, and a bearing according to the heat conduction and convection heat transfer coupling mechanism, and calculate corresponding temperature rise inhibition coefficients based on the temperature rise data under natural cooling and forced cooling conditions.

[0028] A cross-condition prediction module is configured to map the data set under the natural cooling condition to an equivalent temperature rise feature space under the forced cooling condition to align the input feature distribution under different conditions.

[0029] The cross-condition nonlinear deviation component is predicted according to the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and the linear component under the cross-condition is superimposed to obtain the thermal error prediction value of the linear feed axis.

[0030] The third aspect of the application provides a computer readable storage medium.

[0031] A computer readable storage medium having a computer program stored thereon, the program being executed by a processor to implement the steps of a cross-condition migration machine tool thermal error step-by-step prediction method as described above.

[0032] The fourth aspect of the application provides a computer device.

[0033] A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the steps of a cross-condition migration machine tool thermal error step-by-step prediction method as described above.

[0034] Compared with the prior art, the beneficial effects of the application are:

[0035] 1、The present application quantifies the physical inhibition of the temperature rise of the screw by low-temperature water by decoupling the thermal error into a linear mechanism component and a nonlinear deviation component, calculating the temperature rise inhibition coefficient based on the heat conduction inhibition effect, aligning the characteristic distribution of the natural cooling working condition samples through the inhibition coefficient, establishing a cross-working condition consistency mapping mechanism, breaking through the dependence of traditional models on single working condition data, while retaining the physical law of the linear component, enhancing the dynamic capture ability of the nonlinear deviation by using an optimization algorithm, and realizing the model generalization performance improvement through cross-working condition characteristic space conversion, thereby providing a solution for machine tool thermal error compensation that takes into account the prediction accuracy and multi-working condition adaptability.

[0036] 2、The present application quantifies the physical inhibition of the temperature rise of the screw by low-temperature water by calculating the temperature rise inhibition coefficient based on the heat conduction inhibition effect, constructing a temperature rise equivalent conversion model between the natural cooling and forced cooling working conditions, and solving the problem of inconsistent cross-working condition data distribution.

[0037] The advantages of the additional aspects of the present application will be partially given in the following description, partially become obvious from the following description, or be learned through the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0038] The accompanying drawings, which form a part of the specification, are included to provide a further understanding of the application, and are incorporated herein by reference. The illustrations are shown to explain the present application and are not intended to be an undue limitation on the application.

[0039] Figure 1 is a flowchart of a machine tool thermal error step-by-step prediction method provided by an embodiment of the present application for cross-working condition migration;

[0040] Figure 2 is a schematic diagram of the thermal error decomposition into a linear component L and a deviation component e provided by an embodiment of the present application;

[0041] Figure 3 is a flowchart of the selection of key temperature measurement points for the slope k , the intercept b , and the deviation e at each position of the linear feed axis provided by an embodiment of the present application;

[0042] Figure 4 is a DOA-SVM model modeling flowchart for deviation e prediction provided by an embodiment of the present application. DETAILED DESCRIPTION

[0043] The present application will be further described below in conjunction with the drawings and embodiments.

[0044] It should be noted that the following detailed description is illustrative only, and is intended to provide further description in connection with the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the application belongs.

[0045] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0046] The existing thermal error prediction methods for linear feed axes of machine tools 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, and deduces the physical relationship between temperature rise and thermal error of the linear feed axis by establishing heat source distribution equation and structure thermal resistance network. This method has the advantage of explainability under the condition of steady-state temperature field, but it is difficult to accurately describe the local temperature gradient mutation phenomenon caused by forced convection of low-temperature water circulation system in the non-steady-state heat transfer process when the cooling condition switches. The data-driven method directly establishes the correlation model between temperature data and error value by using machine learning algorithm, which can capture the nonlinear relationship under complex working conditions, but lacks mechanism-level constraints on the differential thermal response characteristics of key components such as lead screws and guide rails under natural cooling and forced cooling modes, resulting in a decrease in model generalization ability when predicting across working conditions.

[0047] In summary, the common limitations of current technologies are: on the one hand, the essential difference in heat exchange mode between natural cooling and forced cooling working conditions leads to significant differences in temperature field evolution of linear feed axes. Mechanism-driven relies on air natural convection and radiation, while data-driven is based on forced convection of cooling liquid. Traditional single modeling method cannot effectively describe the thermal error generation mechanism of both working conditions. On the other hand, the dynamic intervention of low-temperature water circulation system changes the heat conduction path of linear feed axis, and the nonlinear coupling relationship exists between the temperature rise suppression effect and parameters such as cooling liquid flow and heat exchange area. Existing methods fail to establish a quantitative representation mechanism for such cross-condition correlation characteristics in the model. In addition, the coupling mechanism of linear components and nonlinear deviation components in thermal error has not been fully decoupled, and direct end-to-end modeling strategy may introduce error component confusion problem, affecting the physical consistency of the prediction model.

[0048] The application provides a mechanism and data double-driven fusion machine tool linear feed axis thermal error cross-condition prediction method. 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, adaptive modeling and high-precision prediction of the nonlinear deviation are realized; meanwhile, based on the thermal conduction suppression effect, the temperature rise suppression coefficient is calculated to quantify the physical suppression effect of low-temperature water on the temperature rise of the screw, and the temperature rise equivalent conversion model between natural cooling and forced cooling conditions is constructed to solve the cross-condition data distribution inconsistency problem. Further through the suppression coefficient α The feature distribution of the natural cooling condition sample is aligned, the cross-condition consistency mapping mechanism is established, and the dependence of the traditional model on single-condition data is broken through. The method innovatively combines the advantages of thermodynamic mechanism constraint and data-driven modeling, retains the physical law of the linear component, enhances the dynamic capture ability of the nonlinear deviation by using the optimization algorithm, and realizes the model generalization performance improvement through cross-condition feature space conversion, thereby providing a solution for machine tool thermal error compensation with consideration of prediction accuracy and multi-condition adaptability.

[0049] Embodiment one

[0050] Please refer to Figure 1 , Figure 1 The cross-condition migration machine tool thermal error step-by-step prediction method flowchart is shown, and the method comprises the following steps:

[0051] S1: obtaining thermal error data of a 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;

[0052] The thermal error data of the machine tool linear feed axis under natural cooling and forced cooling conditions is obtained in the following manner:

[0053] To reduce the temperature rise of the machine tool linear feed axis and suppress thermal error, low-temperature water can be circulated through the internal circulating low-temperature water pipeline of the key components of the linear feed axis such as the ball screw, screw nut, etc., to improve the heat dissipation efficiency of the linear feed axis. The natural cooling and forced cooling conditions correspond to air natural cooling and circulating low-temperature water forced cooling, respectively.

[0054] The thermal error data is measured by a laser interferometer at a short time interval during the long-time operation of the machine tool, i.e., the thermal error of the linear feed axis under different temperature states is measured. The complete thermal error data includes the thermal error values of each error measurement point on the linear feed axis at different measurement times (different temperature states).

[0055] In this embodiment, the specific method of data collection is: set the feed speed of the linear feed axis to 1500 mm / rev, the stroke length to 1000 mm, and the linear feed axis to reciprocate, with a duration of 5 hours. During this period, the linear feed axis thermal error is measured every 30 minutes using an XL-80 laser interferometer, and the error measurement point interval of the laser interferometer is set to 100 mm, i.e. there are 11 error measurement points in the 1000 mm stroke.

[0056] The same data collection method is used under both natural cooling and forced cooling conditions, the difference being that the circulating low-temperature water system needs to be turned on under the forced cooling condition.

[0057] Among them, the time-temperature distribution data of each temperature measurement point of the linear feed axis contains the temperature data collected by the initial temperature measurement points on the linear feed axis over time;

[0058] 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 state. Magnetic suction type thermistor temperature sensors are arranged on the motor, workbench, bed, front bearing, rear bearing, slider, guide rail front end, and guide rail rear end of the machine tool linear feed axis to collect temperature data; the front end, middle end, and rear end of the ball screw use non-contact infrared temperature measurement guns to collect temperature data due to high-speed rotation during operation; a total of 11 initial temperature measurement points.

[0059] S2: decouple the thermal error into a linear component L and a nonlinear deviation component e ;

[0060] Among them, the linear component L is fitted with a linear function, and the nonlinear deviation component e is modeled and predicted using the Dreaming Optimization Algorithm (DOA) - Support Vector Machine (SVM) algorithm;

[0061] Please refer to Figure 2 , which specifically includes the following steps:

[0062] S21, plot the collected thermal error data into a point-line graph, and fit the error curves under different states with a linear function as:

[0063] ,

[0064] Among them, n is the number of times the thermal error is measured under different temperature states, Let be the slope of the error curve at the nth temperature condition. Let be the intercept of the error curve at the nth temperature condition. This represents the position of the linear axis.

[0065] S22. Perform density clustering on the absolute temperatures measured at each initial temperature measurement point to obtain clustering results. Calculate the Pearson correlation coefficient and filter the absolute temperature versus error curve slope in each clustering result. k The key temperature measurement points with the highest correlation;

[0066] like Figure 3 As shown, in this embodiment, the absolute temperature of each initial temperature measurement point is subjected to DBSCAN cluster analysis, dividing the 11 initial temperature measurement points into 4 clusters. Based on the Pearson correlation coefficient, the absolute temperature and slope in each cluster are selected. k The key temperature measurement points with the highest correlation were used to obtain the slope. k Key temperature measurement point set ( - ).

[0067] S23. Perform the intercept according to the method in S22. b Selection of key temperature measurement points;

[0068] Intercept b When selecting the key temperature measurement points, only the absolute temperature in the S22 analysis process is replaced with the relative temperature, i.e., the temperature rise value, to obtain the intercept. b Key temperature measurement point set ( - ).

[0069] S24, Final Combined Slope k and intercept b The linear component of the thermal error of the linear feed axis is obtained. L ( x ) is represented as:

[0070] ,

[0071] in, The absolute temperature at the key temperature measurement point. The slope represents the temperature rise at key temperature measurement points. and intercept All of these will change with temperature. and Using T and Δ respectively T The multivariate linear function representation, For the first n The fitting coefficients of the absolute temperature at key temperature points. For the firstn the fitting coefficients of the temperature rise at the key temperature points, the constant term of the slope expression, the constant term of the intercept expression.

[0072] S25, the collected thermal error data Subtract the linear component L ( x ), that is, the nonlinear deviation component of each error measurement point on the linear feed axis under different temperature states , expressed as:

[0073] ,

[0074] S26, the nonlinear deviation component of each measurement point under different temperature states The key temperature measurement points are screened;

[0075] In this embodiment, when predicting the deviation e , it is necessary to simultaneously establish the mapping relationship between the value of each error measurement point and the temperature of each temperature measurement point. According to the DBSCAN clustering combined with the Pearson correlation coefficient calculation, the e key temperature measurement point set with the highest correlation between the relative temperature and the deviation e of each error measurement point in each cluster is screened out. The union of each key temperature measurement point set is taken to obtain the final key temperature measurement point set of the deviation n , a total of e points. p

[0076] 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 the deviation component based on the trained DOA-SVM prediction model;

[0077] In this embodiment, the DOA-SVM prediction algorithm used for predicting the deviation component e , specifically optimizes the hyperparameters of the support vector machine regression prediction model, including the penalty coefficient c and the kernel function width g , so as to select the most suitable kernel function parameters for modeling and improve the prediction accuracy of the prediction model;

[0078] Please refer to Figure 4 , which specifically includes the following steps:

[0079] S271, constructing a training data set and a test data set based on the screened key temperature measurement set, and expressing the data set and the test data set as: ​

[0080] ,

[0081] in, For the first m A subset of data at a given moment. For the first m At this moment n Temperature rise at key temperature measurement points The first on the linear axis p Location of each error measurement point The first on the linear axis p The error measurement point is located at the position of the [number]th error measurement point. m The deviation component at time t, m This is a sequence of temperature measurement times. p Number of error measurement points;

[0082] S272. Input the training dataset to optimize the DOA hyperparameters and determine the optimized DOA hyperparameters.

[0083] Specifically, it includes:

[0084] 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:

[0085] ,

[0086] Where rand is a uniformly distributed random number in the range [0,1]. The initial value of c is randomly generated. Explore the lower bound of the space for the value of c. for c The upper bound of the exploration space, Randomly generated g initial value, for g The lower bound of the exploration space, for g The upper bound of the value exploration space;

[0087] S2722, fitness calculation;

[0088] For each individual X i =[ c i , g i ], using the training dataset D train the SVM regression model with RBF kernel: , calculate the fitness (5-fold cross-validation MSE): where, is the expression of RBF kernel, and are two input samples (vectors), representing the feature vectors of the i th and j th sample, respectively, is the fitness of individual X i, is the number of samples in the k th fold, is the predicted value of the model in the k th fold,

[0089] S2723, DOA iterative optimization;

[0090] Perform a loop ( t = 1, 2, …, T max ):

[0091] (1) Exploration phase (first T d = 0.9 T max iterations):

[0092] Memory strategy: the population is divided into 5 groups, and each group is updated to the position of the historical best individual in the group .

[0093] Forget and supplement: randomly select dimensions in each group ( representing the number of forgotten dimensions in the exploration phase q group) to update:

[0094] ,

[0095] where, represents the position of the i th individual in the j th dimension at iteration t+1, represents the position of the best individual in the groupq th dimension at iteration t, represents the position of the i-th individual in the j-th dimension at the t-th iteration, 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, represents the maximum number of iterations of the exploration phase;

[0096] Dream sharing: with probability u =0.9, the above strategy is executed, otherwise the dimension information is randomly exchanged:

[0097] ,

[0098] where, m is a randomly selected individual number;

[0099] (2) Development phase (after T max - T d iterations):

[0100] Global optimal guidance: all individuals move towards the global optimal X t best :

[0101] ,

[0102] represents the best individual in the entire population at the t-th iteration.

[0103] Forgetful supplementary update: randomly select k r dimension ( k r represents the number of dimensions forgotten in the development phase) update:

[0104] ,

[0105] represents the position of the individual in the j-th dimension in the entire population at the t-th iteration.

[0106] (3) Boundary processing (if the parameter is out of bounds):

[0107] ,

[0108] (4) Update global optimum: record the minimum fitness corresponding .

[0109] S273, combine the optimized DOA hyperparameters and the test data set to train the final SVM model, and predict the final bias component based on the SVM model.

[0110] S3: According to the heat conduction and convection heat transfer coupling mechanism, the temperature rise suppression effect of low-temperature water on the screw, nut and bearing is quantified, and the temperature rise suppression coefficient is calculated combined with the temperature rise data in the natural cooling and forced cooling states; specifically including the following steps:

[0111] S31, quantifying the temperature rise suppression effect of low-temperature water on the screw, nut and bearing, including:

[0112] S311, quantifying the temperature rise suppression effect of low-temperature water on the screw, and obtaining the temperature rise suppression coefficient of the screw

[0113] The thermal error of the machine tool linear feed shaft is mainly caused by the thermal deformation of the ball screw due to temperature rise during long-term operation.

[0114] Assuming that the heat input of the linear feed shaft during the entire operation process is , under natural cooling conditions, the heat is dissipated through natural convection and radiation of the screw outer wall to the environment, and the temperature rise can be represented as:

[0115] ,

[0116] wherein, is the environmental convection thermal resistance, is the environmental convection heat transfer coefficient, is the screw outer wall heat dissipation area;

[0117] When low-temperature water is added to the ball screw, the heat is dissipated through the screw outer wall to the circulating low-temperature water pipeline, and then dissipated through forced convection, and the total thermal resistance is represented as:

[0118] ,

[0119] wherein, is the total thermal resistance, is the convection thermal resistance, and are the outer radius and inner radius of the screw, is the thermal conductivity of the screw, is the low-temperature water convection heat transfer coefficient, is the circulating low-temperature water pipeline inner wall area, is the screw length.

[0120] At this time, the temperature rise of the ball screw with low-temperature water under the heat is:

[0121] ,​

[0122] Substitute the above formula into the temperature rise calculation formula under natural cooling conditions, eliminate Q , and obtain:

[0123] ,

[0124] The inhibition effect of low-temperature water on the temperature rise of the screw can be quantified, i.e., the inhibition coefficient of the screw.

[0125] S312, the inhibition effect of low-temperature water on the temperature rise of the nut is quantified, and the temperature rise inhibition coefficient of the nut is obtained ;

[0126] The screw nut is also subjected to forced cooling. Assuming that the structure and cooling parameters of the screw nut do not change during the movement of the linear feed shaft, according to the differences in thermal resistance and under different conditions, the relationship between the temperature rises of the nut under natural cooling and forced cooling can be obtained:

[0127] ,

[0128] is the temperature rise of the nut under forced cooling, is the inhibition coefficient of the nut, is the temperature rise of the nut under natural cooling.

[0129] S313, the inhibition effect of low-temperature water on the temperature rise of the bearing is quantified, and the temperature rise inhibition coefficient of the bearing is obtained ;

[0130] The front and rear bearings of the linear feed shaft are directly connected to the ball screw. The low-temperature water will reduce the thermal resistance of the entire system, thereby significantly inhibiting the temperature rise at the end of the bearing. Therefore, the temperature rises under natural cooling and forced cooling conditions also have a similar proportional relationship:

[0131] ,

[0132] is the temperature rise of the bearing under forced cooling, is the inhibition coefficient of the bearing, is the temperature rise of the bearing under natural cooling;

[0133] S32, the temperature rise inhibition coefficients corresponding to the temperature rise data under the natural cooling and forced cooling conditions are calculated;

[0134] In this embodiment, the robust regression method is combined to calculate the values of the corresponding temperature rise inhibition coefficients. Taking the calculation of as an example:​​​

[0135] The temperature rise data set of a certain temperature measuring point on the lead screw under natural cooling and forced cooling conditions is respectively:

[0136] ,

[0137] Among them, is the temperature rise data set of the temperature point under natural cooling, is the temperature rise of the temperature point at the m moment under natural cooling, is the temperature rise data set of the temperature point under forced cooling, is the temperature rise of the temperature point at the m moment under forced cooling;

[0138] The solution problem of the inhibition coefficient can be converted into solving a coefficient , so that the adjusted is as close as possible to . Define the Huber loss function as:

[0139] ,

[0140] Among them, delta is the threshold parameter, usually taken as multiple of the median absolute deviation (MAD) of data residual (for example delta =1.345×MAD); , is the temperature rise of the m temperature point under forced cooling; i is the temperature rise of the m temperature point under natural cooling. i The target is to minimize the sum of Huber loss:

[0141]

[0142] ,

[0143] By introducing the weight w i , it is converted into a weighted least squares problem, where the weight w i is dynamically adjusted with the residual, and the influence of outliers is suppressed;

[0144] ,

[0145] The robust coefficient α is calculated by iterative reweighted least squares (IRLS):

[0146] ,

[0147] ​​The obtained robust coefficient α That is, the suppression coefficient of the screw;

[0148] In the present embodiment, the data sets of the temperature rise of a certain temperature measurement point on the screw within 5 hours under natural cooling and forced cooling (water cooling temperature 33°C) conditions are measured respectively as follows:

[0149]

[0150]

[0151] According to the above steps, the suppression coefficient of the screw is obtained. The calculation process undergoes three iterations, and at the third iteration, the weight .

[0152] The solving process of the temperature rise suppression coefficient of the nut and bearing is the same as that of the temperature rise suppression coefficient of the screw . Details are not described here. According to the same method, the temperature rise suppression coefficient of the nut and the temperature rise suppression coefficient of the bearing are obtained.

[0153] S4: Based on the suppression coefficient, map the data set under the natural cooling condition to the equivalent temperature rise characteristic space under the forced cooling condition to align the input feature distribution under different conditions;

[0154] When performing the bias prediction modeling, the input of the test set is the temperature rise , the linear feed axis position , and the model output is . However, for the forced cooling condition, since the forced convection heat transfer significantly suppresses the temperature rise of the screw, if the training set D directly uses the original temperature rise data under the natural cooling condition and the bias for modeling, it will cause the feature distribution deviation between the training set and the prediction set. Therefore, based on the suppression coefficient α , the original temperature rise data Δ T under the natural cooling condition and the bias are mapped to the equivalent temperature rise characteristic space under the forced cooling condition. The consistency alignment of the input feature distribution under different conditions is achieved.

[0155] Taking the temperature rise suppression coefficient of the screw as an example, the conversion rule of the bias is explained as follows:

[0156] The temperature change of the ball screw produces thermal deformation. The change form of the thermal error before and after forced cooling is idealized as the equivalent form of thermal deformation, and then the following is obtained: ​​

[0157] ,

[0158] wherein, is the thermal deformation of the screw under forced cooling, is the thermal expansion coefficient of the screw, is the original length of the screw, is the temperature rise of the screw under forced cooling, is the thermal deformation of the screw under natural cooling, is the thermal error of the linear shaft under forced cooling, is the thermal error of the linear shaft under natural cooling;

[0159] Since k and b are both linear functions of temperature rise, the deviation e is determined by k and b . In the forced cooling condition, the original temperature rise k and b in the relationship of are replaced by the equivalent temperature rise of forced cooling through the characteristic mapping rule of the heat conduction model. Finally, the deviation value e adapted to the forced cooling condition is analyzed as follows:

[0160] ,

[0161] wherein, is the slope of the thermal error curve under forced cooling, is the intercept of the thermal error curve under forced cooling;

[0162] The temperature rise suppression coefficient corresponding to the nut and bearing maps the original temperature rise data Δ T and the deviation of the natural cooling condition to the equivalent temperature rise characteristic space under the forced cooling condition, and the temperature rise suppression coefficient of the screw is the same;

[0163] S105: The superposition of the linear component mechanism prediction and the deviation component data prediction is output to obtain the thermal error prediction value of the linear feed shaft.

[0164] The prediction of the linear component L is realized by a linear function fitting, and the prediction of the deviation component is realized according to the data distribution alignment and the DOA-SVM algorithm across conditions. Finally, the prediction value of the thermal error E can be expressed as the sum of the linear component L and the deviation component , and the accurate prediction of the thermal error E of the machine tool linear feed shaft is completed.

[0165] ​Embodiment two

[0166] The embodiment provides a machine tool thermal error step-by-step prediction system for cross-condition migration, comprising:

[0167] a data acquisition module configured to acquire thermal error data of a linear feed axis of a machine tool under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measurement point of the linear feed axis;

[0168] an error decoupling module configured to decouple the thermal error data under each condition into a linear component and a nonlinear deviation component, filter key temperature measurement points based on the decoupled linear component and nonlinear deviation component, construct a data set based on the filtered key temperature measurement points, and train a nonlinear deviation prediction model based on the constructed data set to obtain a trained nonlinear deviation prediction model;

[0169] a mechanism analysis module configured to quantize the inhibitory effect of low-temperature water on temperature rise of a lead screw, a nut and bearings respectively according to a heat conduction and convection heat exchange coupling mechanism, and calculate corresponding temperature rise inhibition coefficients in combination with temperature rise data under natural cooling and forced cooling conditions;

[0170] a cross-condition prediction module configured to map the data set under the natural cooling condition to an equivalent temperature rise feature space under the forced cooling condition to align input feature distributions under different conditions;

[0171] a cross-condition nonlinear deviation component is predicted according to the equivalent temperature rise feature space and the trained nonlinear deviation prediction model, and a linear component is superimposed to obtain a linear feed axis thermal error prediction value.

[0172] It should be noted that the specific implementation mode of the machine tool thermal error step-by-step prediction system for cross-condition migration of the embodiment of the present application is similar to that of the machine tool thermal error step-by-step prediction method for cross-condition migration of the embodiment of the present application, and specific reference can be made to the description in the method part. In order to reduce redundancy, this part is not described here.

[0173] Embodiment three

[0174] The embodiment provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to realize the steps in the machine tool thermal error step-by-step prediction method for cross-condition migration.

[0175] Embodiment four

[0176] The embodiment provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor realizes the steps in the machine tool thermal error step-by-step prediction method for cross-condition migration when executing the program.

[0177] Example Five

[0178] The present embodiment provides a program product, which is a computer program product comprising a computer program which, when executed by a processor, implements the steps of a cross-condition migration machine tool thermal error step-and-repeat prediction method as described above.

[0179] Those skilled in the art will appreciate that embodiments of the present application can be supplied as a method, a system, or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, magnetic disks and optical storage media and the like) embodying computer program instructions.

[0180] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system) and computer program product according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagrams, as well as combinations of flows and / or blocks in the flowchart 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 apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified in the flowchart and / or block diagram block or blocks.

[0181] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions means which implement the function specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified in the flowchart and / or block diagram block or blocks.

[0182] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the function specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified in the flowchart and / or block diagram block or blocks.

[0183] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by a computer program instructing relevant hardware, and the program can be stored in a computer readable storage medium. When the program is executed, the program can include the processes of the above-mentioned embodiment methods. The storage medium can be a magnetic disc, an optical disc, a read-only memory (ROM), a random access memory (RAM), or the like.

[0184] The above only describes the preferred embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A machine tool thermal error stepwise prediction method for cross- work-condition migration, characterized in that, The method comprises the following steps: obtaining thermal error data of a linear feed axis of a machine tool under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measuring point of the linear feed axis; decoupling the thermal error data under each condition into a linear component and a nonlinear deviation component; screening key temperature measuring points based on the decoupled linear component and nonlinear deviation component, constructing a data set based on the screened key temperature measuring points, training a nonlinear deviation prediction model based on the constructed data set, and obtaining a trained nonlinear deviation prediction model; quantifying the temperature rise suppression of low-temperature water on the screw, nut and bearing according to the coupling mechanism of heat conduction and convective heat transfer, and calculating the corresponding temperature rise suppression coefficient based on the temperature rise data under the natural cooling and forced cooling conditions; mapping the data set under the natural cooling condition to the equivalent temperature rise characteristic space under the forced cooling condition based on the suppression coefficient to align the input feature distribution under different conditions; predicting the cross-condition nonlinear deviation component according to the equivalent temperature rise characteristic space and the trained nonlinear deviation prediction model, and superimposing the cross-condition linear component to obtain the thermal error prediction value of the linear feed axis.

2. A machine tool thermal error step-wise prediction method for cross- situation migration as claimed in claim 1, wherein, The screening of the key temperature measuring points based on the decoupled linear component comprises: The absolute temperatures measured at each initial temperature measurement point are subjected to density clustering to obtain clustering results, and the absolute temperatures and error curve slopes in each clustering result are screened according to Pearson correlation coefficient calculation k The key temperature measurement points with the highest correlation The relative temperatures measured at each initial temperature measurement point are subjected to density clustering to obtain clustering results, and the relative temperatures in each clustering result are screened according to the calculation of the Pearson correlation coefficient and the error curve intercept b The key temperature measurement points with the highest correlation.

3. A cross-condition migrated machine tool thermal error step-wise prediction method according to claim 1, characterized in that, The linear component is fitted based on the time-temperature distribution data of each temperature measuring point and is expressed as: ， wherein T is the absolute temperature at the critical temperature measurement point, ΔT is the temperature rise at the critical temperature measurement point, the slope and the intercept both vary with temperature, Tn is the fitting coefficient of the absolute temperature at the nth critical temperature point, ΔTn is the fitting coefficient of the temperature rise at the nth critical temperature point, is the constant term of the expression of the slope, is the constant term of the expression of the intercept.

4. A machine tool thermal error step-wise prediction method for cross- situation migration as claimed in claim 1, wherein, The nonlinear deviation component obtained based on decoupling is used to screen key temperature measurement points, including: screening out the relative temperature and the deviation at each error measurement point in each cluster according to DBSCAN clustering combined with Pearson correlation coefficient calculation e The correlation is the highest n The key temperature measurement point set, and the union of each key temperature measurement point set is obtained to obtain the final deviation e The key temperature measurement point set has a total of p Points.

5. A machine tool thermal error step-wise prediction method that migrates across working conditions as claimed in claim 1, wherein, When training the nonlinear bias prediction model based on the constructed dataset, the hyperparameters of the support vector machine regression prediction model, including the penalty coefficient c and the kernel function width g are optimized by the dream optimization algorithm, so as to select the most appropriate kernel function parameters for modeling.

6. A machine tool thermal error step-wise prediction method that migrates across working conditions as recited in claim 1, wherein, The temperature rise suppression coefficient is calculated based on the temperature rise data under the natural cooling and forced cooling conditions, and comprises: The Huber loss function is defined, the sum of Huber losses is minimized, weights are introduced, the sum of Huber losses is converted into a weighted least square problem, the corresponding temperature rise inhibition coefficients are calculated through an iterative reweighted least square method, and the adjusted temperature rise inhibition coefficients satisfy as close as possible wherein, is a temperature rise data set under natural cooling, is a temperature rise data set under forced cooling.

7. A machine tool thermal error step-wise prediction method that migrates across working conditions as claimed in claim 1, wherein, When mapping the data set of the natural cooling condition to the equivalent temperature rise characteristic space of the forced cooling condition, the error curve slope k and the error curve intercept b of the natural cooling condition are replaced by the original temperature rise of the forced cooling equivalent temperature rise in the relationship formula, and the deviation value adapted to the forced cooling condition is finally analyzed e .

8. A machine tool thermal error step-wise prediction system that migrates across working conditions, characterized by, It comprises: a data acquisition module for acquiring thermal error data of a linear feed axis of a machine tool under natural cooling and forced cooling conditions and time-temperature distribution data of each temperature measuring point of the linear feed axis; an error decoupling module for decoupling the thermal error data under each condition into a linear component and a nonlinear deviation component; screening key temperature measuring points based on the decoupled linear component and nonlinear deviation component, constructing a data set based on the screened key temperature measuring points, training a nonlinear deviation prediction model based on the constructed data set, and obtaining a trained nonlinear deviation prediction model; a mechanism analysis module for quantifying the temperature rise suppression of low-temperature water on the screw, nut and bearing according to the coupling mechanism of heat conduction and convective heat transfer, and calculating the corresponding temperature rise suppression coefficient based on the temperature rise data under the natural cooling and forced cooling conditions; a cross-condition prediction module for mapping the data set under the natural cooling condition to the equivalent temperature rise characteristic space under the forced cooling condition to align the input feature distribution under different conditions; predicting the cross-condition nonlinear deviation component according to the equivalent temperature rise characteristic space and the trained nonlinear deviation prediction model, and superimposing the cross-condition linear component to obtain the thermal error prediction value of the linear feed axis.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the steps in the cross-condition migration machine tool thermal error step-by-step prediction method according to any one of claims 1-7.

10. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps in the cross-condition migration machine tool thermal error step-by-step prediction method according to any one of claims 1-7.

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