Mechanism-driven online evolution method for time-varying thermal error model of machine tool feed axis

Abstract

A mechanism-driven online evolution method for a time-varying thermal error model of a machine tool feed axis includes the following steps: Establishing a mechanism-driven time-varying thermal error model of the machine tool feed axis based on frictional heating, heat conduction, and convection cooling mechanisms; determining the lead screw temperature as the key intermediate dependent variable based on online direct measurement and the principle of approximating the final dependent variable; actively identifying the accuracy of the mechanism-driven model based on the consistency between the model's calculated value and the online measured value of the intermediate dependent variable; if the consistency is poor, the model accuracy is poor; if the consistency is good, the model accuracy is good; based on the active identification result of the model accuracy, if the model accuracy is poor, the model parameters are updated online; if the model accuracy is good, the model remains unchanged. This invention enables the mechanism-driven time-varying thermal error model of the machine tool feed axis to have online evolution capability, providing a specific solution to improve the robustness of the time-varying thermal error model in long-term operation and ensure long-term accurate compensation of the machine tool's time-varying thermal error.

Description

Technical Field

[0001] This invention belongs to the field of CNC machine tool error compensation technology, and relates to a mechanism-driven online evolution method for the time-varying thermal error model of machine tool feed axes. Background Technology

[0002] Time-varying thermal error is a significant factor affecting the accuracy and stability of machine tools. The presence of time-varying thermal error not only easily leads to out-of-tolerance machining accuracy for single pieces but also causes fluctuations in the accuracy of batch machining. Error compensation is an effective means of controlling time-varying thermal error in CNC machine tools.

[0003] The prerequisite for implementing time-varying thermal error compensation for CNC machine tools is establishing an accurate time-varying thermal error model. Domestic and international scholars have conducted extensive research on time-varying thermal error modeling for machine tools. Currently, established time-varying thermal error models for CNC machine tools can be divided into two categories: mechanism-driven time-varying thermal error models and data-driven time-varying thermal error models. Among them, mechanism-driven time-varying thermal error models have unique advantages in saving training time, reducing temperature measurement points, and improving the robustness of error compensation. Under the error modeling conditions, mechanism-driven time-varying thermal error compensation has produced satisfactory results. However, due to the complexity of machine tool operating conditions, in long-term application, the actual working conditions of the machine tool may differ from the experimental conditions used for empirical model derivation due to factors such as seasonal changes, wear of moving parts, and changes in cooling and lubrication conditions. How to ensure that the mechanism-driven time-varying thermal error model of the machine tool always adapts to the working state of the machine tool during long-term operation is a key issue that requires in-depth research and is crucial for the long-term accurate compensation of time-varying thermal errors in machine tools.

[0004] A search revealed existing research on online updates of data-driven models. For example, the invention patent "An Online Update Method for Principal Component Analysis Monitoring Model" (patent number: CN201210080056.3) discloses an online update method for multivariate statistical process monitoring models to ensure that principal component analysis adapts to the slow drift of process variables caused by external environmental factors such as catalyst degradation and equipment aging and dust accumulation during actual production. The invention patent "Evolutionary Machine Learning Model" (patent number: CN201980027832.3) discloses a machine learning model evolution method for the field of machine learning. The invention patent "An Adaptive Model Online Reconstruction Robust Filtering Method, Device, and System" (patent number: CN202210448169.8) discloses an adaptive model online reconstruction robust filtering method in the field of information fusion, used to balance navigation accuracy, robustness, and computational efficiency to improve the long-term operational capability of underwater robots. However, the above methods are all applicable to the online evolution of data-driven models; no research has yet been found specifically on the online evolution of mechanism-driven models. Summary of the Invention

[0005] This invention addresses the urgent need for long-term accurate compensation of time-varying thermal errors in CNC machine tools by providing a novel mechanism-driven online evolution method for the time-varying thermal error model of machine tool feed axes. This method proactively identifies the accuracy of the mechanism-driven model by judging the consistency between the calculated dataset of the intermediate dependent variable and the measured dataset. Furthermore, it uses the actual measured values ​​of the intermediate dependent variable to update the parameters of the degenerate model online, ensuring the accuracy of the feed axis time-varying thermal error model throughout the long-term operation of the machine tool.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A mechanism-driven online evolution method for a time-varying thermal error model of a machine tool feed axis involves the following steps: First, a mechanism-driven time-varying thermal error model of the machine tool feed axis is established based on the mechanisms of frictional heating, heat conduction, and convection cooling. Then, according to the derivation process of the time-varying thermal error model, machine tool temperature is selected as the key intermediate dependent variable. Next, the model calculation dataset and the online measurement dataset of the intermediate dependent variable are obtained. Then, based on the consistency between the model calculation dataset and the online measurement dataset, the accuracy of the mechanism-driven model is actively identified. If the model calculation dataset and the online measurement dataset are inconsistent, the model is judged to have poor accuracy; if they are consistent, the model is judged to have good accuracy. Finally, based on the active identification result of the model accuracy, it is decided whether to perform online updates of the model parameters. If the model accuracy is poor, online updates of the model parameters are performed; if the model accuracy is good, the model remains unchanged. The method includes the following steps:

[0008] The first step is to establish a mechanism-driven time-varying thermal error model for the machine tool feed axis;

[0009] With the origin of the machine tool feed axis as the origin, a coordinate system Ox is established along the direction of the motion axis. A micro segment dx is taken at a distance x from the origin O. Based on the theories of frictional heat generation, heat conduction and convective heat transfer, the frictional heat generation, heat conduction and convective heat transfer of the micro segment dx are calculated. Combined with the law of conservation of energy, the thermal deformation of the micro segment dx is calculated and integrated within the range of the feed axis stroke to establish a mechanism-driven time-varying thermal error model of the CNC machine tool feed axis.

[0010] The lead screw segment dx at position x generates heat Q through friction with the nut during the time interval (t-Δt,t). f (x,t) can be represented as:

[0011]

[0012] In the formula, Q0 is the heat generated by the nut rubbing against the lead screw segment dx once; N is the average number of friction cycles between the nut and the lead screw segment dx per unit time.

[0013] The heat transfer of the lead screw micro-segment during the time interval (t-Δt,t) is as follows:

[0014]

[0015]

[0016] In the formula, Q t (x,t) represents the heat conducted at position x during the time interval (t-Δt,t); Q t (x+dx,t) represents the heat transferred at position x+dx during the time interval (t-Δt,t); λ is the thermal conductivity coefficient of the lead screw; R s The equivalent diameter of the leadscrew; Let x be the temperature gradient value at position x at time t. Let x be the temperature gradient value at position x+dx at time t;

[0017] The heat transfer Q during the combined radiation and convection heat transfer process within the time interval (t-Δt,t) is... cr (x,t) can be represented as:

[0018]

[0019] In the formula, k is the factor that increases the intensity of convective heat transfer during the movement of the lead screw; h is the convective heat transfer coefficient between the lead screw and the air; T s (x,t) is the temperature of the lead screw at position x at time t; T f (t) is the air temperature in contact with the lead screw surface at time t;

[0020] The heat increment ΔQ(x,t) of the lead screw segment dx during the time interval (t-Δt,t) is:

[0021]

[0022] In the formula, c is the specific heat capacity of the lead screw material; ρ is the density of the lead screw material; It is the rate of change of the temperature of the lead screw at position x of the lead screw at time t with time;

[0023] Based on the law of conservation of energy, and combining equations (1) to (5), the temperature field of the lead screw is obtained:

[0024]

[0025] Thermal expansion error of the lead screw at any time t:

[0026]

[0027] In the formula, coff is the coefficient of thermal expansion of the leadscrew; l is the calculation range of thermal expansion error of the linear feed axis; Tst (x,t) is the measured temperature of the lead screw at position x at time t; T st (x,0) is the measured value of the lead screw temperature at position x at the initial moment.

[0028] The second step is to determine the key intermediate dependent variables in the mechanism-driven time-varying thermal model of the feed shaft.

[0029] There are two principles for selecting key intermediate dependent variables for active identification of model accuracy: a. Intermediate dependent variables are easy to measure directly online; b. Intermediate dependent variables should be as close as possible to the final dependent variable to ensure that the model parameters required to solve for intermediate dependent variables include key parameters that affect the mechanism of the research object.

[0030] Based on the derivation process of the time-varying thermal error model of the machine tool feed axis driven by the mechanism, and according to the selection principle of key intermediate dependent variables, the temperature T of the leadscrew is selected. s (x,t) is used as an intermediate dependent variable; in addition, T is solved. s When (x,t), all unknown parameters K are used. n =[R s [,Q0,h,λ,k] can ensure that key parameters are updated when model parameters are updated.

[0031] The third step is to obtain the model calculation dataset and online measurement dataset for the intermediate dependent variables;

[0032] During machine tool operation, the temperature of the leadscrew is used as a key intermediate variable T. s (x,t), whose model calculation values ​​are obtained by the mechanism-driven time-varying thermal error model of the feed shaft, and form a dataset T. sc Intermediate dependent variable T s Online measurement of (x,t) is achieved using an infrared temperature sensor, and a dataset T is generated. sm ;T s Model computation dataset T of (x,t) sc With online measurement dataset T sm It is stored until the consistency judgment period is reached, and then it proceeds to the next step of data processing.

[0033] The fourth step is to determine the model calculation dataset T for the intermediate dependent variable. sc and online measurement dataset T sm Consistency;

[0034] The consistency evaluation method (Bland-Altman method) is adopted, based on the lead screw temperature T. s Model computation dataset T of (x,t) sc With infrared temperature sensor measurement dataset T smThe mean M of the difference between the two sets of data and the width W between the consistency boundaries are used to determine the consistency between the two sets of data. The threshold M0 of the mean difference between the model calculated value and the measured value and the threshold W0 of the width between the consistency boundaries are obtained experimentally. The calculation methods of M, W, M0 and W0 are as follows:

[0035]

[0036] In the formula, m is the amount of data obtained from model calculation and sensor measurement within the consistency judgment period T0; n is the amount of data obtained from model calculation and sensor measurement during the experiment when solving for thresholds M0 and W0; T sc (x,t i ) and T sc (x,t j ) are respectively t i and t j The calculated value of the lead screw temperature at any given time; T sm (x,t i ) and T sm (x,t j ) are respectively t i and t j The sensor readings of the constant lead screw temperature;

[0037] The mechanism-driven time-varying thermal error model of the feed axis during operation, when the screw temperature T... s Model computation dataset T of (x,t) sc With infrared temperature sensor measurement dataset T sm If the mean M of the difference between the two values ​​and the width W between the consistency boundary satisfy M > M0 or W > W0, then the model is considered to have poor accuracy; otherwise, the model is considered to have good accuracy.

[0038] Fifth, update the time-varying thermal model parameters of the mechanism-driven feed axis online;

[0039] When the mechanism-driven time-varying thermal error model degrades during long-term operation, it is necessary to update the model parameters online using data measured by an infrared temperature sensor; the objective function for optimizing the model parameters is:

[0040]

[0041] The beneficial effects of this invention are:

[0042] (1) Enable the mechanism-driven time-varying thermal error model of the machine tool feed axis to have online evolution capability, ensure that the model always adapts to the working conditions of the CNC machine tool during long-term operation, and improve the robustness of the time-varying thermal error model;

[0043] (2) A solution was provided for the long-term robust compensation of time-varying thermal error of CNC machine tools, and the implementation method of using the time-varying thermal error model for long-term accurate compensation of time-varying thermal error of CNC machine tool feed axis was clarified.

[0044] (3) The method provided by this invention has a certain degree of universality and can be extended to the online evolution of mechanism-driven models in other fields. Attached Figure Description

[0045] Figure 1 Flowchart of an online evolution method for a time-varying thermal error model of a machine tool feed axis driven by a mechanism.

[0046] Figure 2 A schematic diagram illustrating the online evolution principle of the time-varying thermal error model for machine tool feed axes driven by mechanism. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings.

[0048] Taking the Z-axis of a certain type of vertical milling machine as an example, the implementation of the present invention is described in detail. The CNC system of this vertical milling machine is model GJ301. The Z-axis adopts a semi-closed-loop control method and has no cooling system. The lead screw is fixed at both ends, with a stroke range of -347mm to -909mm (machine coordinate values), and a maximum traverse speed of 10000mm / min. The complete process of online evolution of the mechanism-driven time-varying thermal error model of the CNC machine tool is as follows: Figure 1 As shown. The specific steps are as follows:

[0049] (1) Establish a mechanism-driven time-varying thermal error model for the feed axis of a CNC machine tool;

[0050] The Z-axis thermal error was tested using a Renishaw XL80 laser interferometer. The machine tool coordinate range was -360mm to -850mm, and the warm-up range was -500mm to -750mm. The warm-up speed was 6000mm / min, and both the warm-up and cool-down cycles were 10 minutes each, for a total of 8 warm-up cycles and 5 cool-down cycles. An adsorption-type temperature sensor was placed on the machine bed near the Z-axis leadscrew to acquire Z-axis temperature information, with a temperature acquisition period of 10 seconds. The time-varying thermal error model for the Z-axis is as follows:

[0051] The lead screw segment dz at position z generates heat Q through friction with the nut during the time interval (t, t+τ). f (z,t) is represented as:

[0052]

[0053] In the formula, Q0 is the heat generated by the nut rubbing against the lead screw segment dz once; N is the average number of friction cycles between the nut and the lead screw segment dz per unit time.

[0054] The heat transfer of the lead screw micro-segment during the time interval (t, t+τ) is as follows:

[0055]

[0056]

[0057] In the formula, Q t (z,t) represents the heat conducted at position z during the time interval (t-Δt,t); Q t (z+dz,t) represents the heat transferred at position z+dz during the time interval (t-Δt,t); λ is the thermal conductivity coefficient of the Z-axis lead screw; R s The equivalent diameter of the leadscrew; Let z be the temperature gradient at position z at time t. Let z be the temperature gradient value at position z+dz at time t;

[0058] The heat transfer Q during the combined radiation and convection heat transfer process within the time interval (t, t+τ) is... cr (z,t):

[0059]

[0060] In the formula, k is the factor that increases the intensity of convective heat transfer during the movement of the lead screw; h is the convective heat transfer coefficient between the Z-axis lead screw and the air; T s (z,t) is the temperature of the lead screw at position z at time t; T f (t) is the air temperature in contact with the lead screw surface at time t;

[0061] The heat increment ΔQ(z,t) of the lead screw microsegment dz during the time interval (t,t+τ) is:

[0062]

[0063] In the formula, c is the specific heat capacity of the lead screw material; ρ is the density of the lead screw material; It is the rate of change of the temperature of the lead screw at position z of the lead screw at time t with time;

[0064] Based on the law of conservation of energy, and combining equations (1) to (5), the temperature field of the lead screw is obtained:

[0065]

[0066] Thermal expansion error of the lead screw at any time t:

[0067]

[0068] In the formula, coff is the coefficient of thermal expansion of the leadscrew; l is the calculation range of thermal expansion error of the linear feed axis; T st (z,t) is the measured temperature of the lead screw at position z at time t; T st (z,0) is the measured value of the lead screw temperature at position z at the initial moment.

[0069] The parameter K in the above model is known. y =[c,ρ,coff,l]=[460,7850,11.7,10], unknown parameter K n =[R s Using Z-axis thermal error and temperature test data, the unknown parameter K of the model is calculated. n = [1.368×10 -2 ,1.334,8.023,2.144×10 -5 ,2.880].

[0070] (2) Determine the key intermediate dependent variables of the mechanism-driven time-varying thermal model of the feed shaft;

[0071] Based on the derivation process of the Z-axis time-varying thermal error model and the principle for determining key intermediate dependent variables, the screw temperature T at the z-coordinate position is selected. s (z,t) is used as an intermediate dependent variable. During machine tool operation, the lead screw temperature at the z-coordinate position can be measured online using an infrared temperature sensor. Based on the actual installation position of the infrared temperature sensor, the z-value here is -421mm. Solve for T. s When (-421,t), all unknown parameters K are used. n =[R s [,Q0,h,λ,k] can ensure that key parameters are updated when model parameters are updated.

[0072] (3) Obtain the model calculation dataset and online measurement dataset for the intermediate dependent variable;

[0073] During the machine tool's operation, the key intermediate dependent variable T s The model calculation value of (-421,t) is obtained by the mechanism-driven time-varying thermal error model of the feed shaft, and forms the dataset T. sc Intermediate dependent variable T s The online measurement of (-421,t) was achieved using an infrared temperature sensor, and a dataset T was generated. sm ;T s The model computation set T of (-421,t) sc With online measurement set T sm It is stored until the consistency judgment period is reached, and then it proceeds to the next step of data processing.

[0074] (4) Determine the consistency between the model calculation dataset and the online measurement dataset for the intermediate dependent variable;

[0075] The lead screw temperature T is defined as 5 minutes. s The model calculation cycle (-421,t) and infrared temperature acquisition cycle are used to calculate the lead screw temperature T by continuously storing 5 hours of data. s The (-421,t) model calculates the threshold M0 for the mean difference between the dataset and the measured dataset, and the threshold W0 for the width between the consistency boundaries, along with the lead screw temperature T. s The model calculates the dataset T using the formula (-421,t). sc Compared with the measured dataset T sm As shown in Table 1:

[0076] Table 1. Model calculation dataset and measured dataset of lead screw temperature stored continuously for 5 hours.

[0077]

[0078]

[0079] The threshold M0 for the mean difference between the dataset and the measured dataset and the threshold W0 for the width between the consistency boundaries are calculated according to the calculation model of equation (8):

[0080]

[0081] Rounded to the nearest whole number, the screw temperature T is taken as follows. s The threshold values ​​for the mean difference between the calculated dataset and the measured dataset (-421,t) are M0 = 0.2, and the threshold values ​​for the width between consistency boundaries are W0 = 2; the consistency judgment period is set to 0.5 hours, and the screw temperature T is... s The model calculation cycle and infrared temperature acquisition cycle for (-421,t) were set to 1 minute. During the online evolution mechanism of the model, the consistency between the lead screw temperature calculation dataset and the measured dataset was checked every 0.5 hours. The results of the consistency check within a certain period are shown in Table 2.

[0082] Table 2 records the model calculation dataset and the measured dataset for the lead screw temperature over 0.5 hours.

[0083]

[0084] Calculate the lead screw temperature T according to formula (8). s The model calculates the mean difference M between the (-421,t) dataset and the measured dataset, as well as the width W between the consistency boundaries:

[0085]

[0086] According to the Bland - Altman method, when the mean value M of the difference between the model calculation data set of the lead screw temperature T s (-421, t) and the measurement data set of the infrared temperature sensor and the width W between the consistency boundaries satisfy M < M0 and W < W0, the consistency is good, that is, the model accuracy is good, and the model does not need to evolve; however, at this time, M = 1.9673 > M0 and W = 1.2586 < W0, which does not meet the condition of good consistency, so the next - step data operation is required at this time.

[0087] (5) Online update the parameters of the time - varying thermal error model of the feed axis driven by the mechanism;

[0088] When the time - varying thermal error model driven by the mechanism degrades during long - term operation, use the measurement data of the infrared temperature sensor to update the model parameters online. The objective function for model parameter optimization is:

[0089]

[0090] The model parameters after online update are K n ′ = [1.442×10 -2 , 1.689, 7.232, 1.989×10 -5 , 2.127]; The calculation data set and the measured data set of the lead screw temperature during the consistency judgment period are obtained by using the infrared temperature sensor and the updated time - varying thermal error model of the feed axis as shown in Table 3:

[0091] Table 3 records the model calculation data set and the measured data set of the lead screw temperature for 0.5 hours

[0092]

[0093] Calculate the mean value M of the difference between the model calculation data set of the lead screw temperature T s (-421, t) and the measured data set and the width W between the consistency boundaries according to Equation (8):

[0094]

[0095] At this time, the mean value M of the difference between the model calculation data set of the lead screw temperature T s (-421, t) and the measured data set is M < M0 and the width W between the consistency boundaries is W < W0. The calculation accuracy of the model after online parameter update is good.

[0096] The schematic diagram of the principle of online evolution of the time - varying thermal error model of the numerically controlled machine tool driven by the mechanism is as Figure 2As shown, an adsorption-type temperature sensor is used to acquire the bed temperature beside the leadscrew, and is input together with the mechanical coordinate values ​​of the feed axis into a mechanism-driven time-varying error model to calculate the time-varying thermal error compensation value of the feed axis. During this process, the temperature field of the feed axis leadscrew can also be calculated by the model; at a distance l from the origin of the feed axis coordinate system... t An infrared temperature sensor is installed at the point to obtain the online measurement value T of the lead screw temperature. s (l t During the operation of the mechanism-driven time-varying thermal error model, the screw temperature T s (l t The model calculation values ​​and online measurement values ​​of (t) are stored; when the timing reaches the consistency judgment period T0, the screw temperature T is checked. s (l t The consistency between the model calculation dataset and the online measurement dataset is judged. When they are inconsistent, the parameters of the time-varying thermal error model are updated online. When they are consistent, the time-varying thermal error model remains unchanged.

[0097] Based on the above examples, the model calculation accuracy is good after online parameter updates, indicating that the present invention plays a significant role in ensuring the accuracy of time-varying thermal error models.

[0098] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A mechanism-driven machine tool feed axis time-varying thermal error model online evolution method, characterized in that, The online evolution method comprises the following steps: firstly, a mechanism-driven time-varying thermal error model of a machine tool feed shaft is established based on the mechanism of friction heat generation, heat conduction and convection heat dissipation; secondly, the temperature of the machine tool is selected as a key intermediate dependent variable according to the derivation process of the time-varying thermal error model of the feed shaft; thirdly, a model calculation data set and an online measurement data set of the intermediate dependent variable are obtained; fourthly, the accuracy of the mechanism-driven model is actively identified according to the consistency of the model calculation data set and the online measurement data set of the intermediate dependent variable; if the model calculation data set and the online measurement data set of the intermediate dependent variable are inconsistent, it is judged that the model accuracy is poor; if the model calculation data set and the online measurement data set of the intermediate dependent variable are consistent, it is judged that the model accuracy is good; finally, whether the model parameter is updated online is determined according to the active identification result of the model accuracy; if the model accuracy is poor, the model parameter is updated online; if the model accuracy is good, the model is kept unchanged. The specific process is as follows: Firstly, a mechanism-driven time-varying thermal error model of a machine tool feed shaft is established. A coordinate system O-x is established along the direction of the movement axis with the mechanical coordinate origin of the machine tool feed shaft as the origin, a micro section dx is taken at a distance x from the coordinate origin O, the friction heat generation, heat conduction and convection heat transfer of the micro section dx of the screw are calculated based on the theory of friction heat generation, heat conduction and convection heat transfer, the thermal deformation of the micro section dx of the screw is calculated in combination with the law of conservation of energy, and the mechanism-driven time-varying thermal error model of the numerical control machine tool feed shaft is established by integrating the thermal deformation of the micro section dx of the screw in the range of the feed shaft stroke. In the formula, Q0 is the heat generated by the nut friction screw micro section dx once; N is the average friction frequency of the nut and the screw dx section per unit time; The friction heat quantity Q generated by the micro section dx of the lead screw at the x position and the nut in the time period (t-Δt, t) f (x, t) is expressed as: The heat conduction heat of the micro section of the screw in the (t-Δt, t) time period is respectively: The heat increment ΔQ(x, t) of the micro section dx of the screw in the (t-Δt, t) time period is: wherein Q t (x, t) is the heat conduction heat at the x position in the (t - Δt, t) time period; Q t (x + dx, t) is the heat conduction heat at the x + dx position in the (t - Δt, t) time period; λ is the heat conduction coefficient of the screw rod; R s is the equivalent diameter of the screw rod; is the temperature gradient value at the x position at the t moment, is the temperature gradient value at the x + dx position at the t moment; The heat transfer amount Q of the radiation and convection combined heat transfer process in the (t-Δt, t) time period cr (x, t) is expressed as: where k is the increase multiple of the convective heat transfer intensity when the screw moves; h is the convective heat transfer coefficient between the screw and the air; T s (x, t) is the temperature of the screw at the position x of the screw at time t; T f (t) is the temperature of the air in contact with the surface of the screw at time t; In the formula, c is the specific heat capacity of the screw material; According to the law of conservation of energy, the screw temperature field is obtained in combination with formulas (1)-(5): p is the density of the screw material; is the rate of change of the temperature of the screw at the x position of the screw at time t; The thermal expansion error of the screw at any time t is: Secondly, the key intermediate dependent variable of the mechanism-driven time-varying thermal model of the feed shaft is determined. wherein coff is the thermal expansion coefficient of the screw; l is the thermal expansion error calculation range of the linear feed axis; T st (x, t) is the temperature measurement value of the screw at position x at time t; T st (x, 0) is the temperature measurement value of the screw at position x at the initial time Thirdly, a model calculation data set and an online measurement data set of the intermediate dependent variable are obtained. According to the derivation process of the mechanism-driven time-varying thermal error model of the feed axis of a machine tool, the temperature T s (x,t) of the screw is selected as the intermediate dependent variable according to the selection principle of the intermediate dependent variable; in addition, the temperature T s (x,t) is solved by using all unknown parameters K n =[R s ,Q0,h,λ,k], so that the key parameters can be updated when the model parameters are updated. The threshold value M0 of the difference between the model calculation value and the measured value and the threshold value W0 of the width between the consistency boundary are obtained through experiments, and the calculation method of M, W, M0 and W0 is as follows: During machine tool operation, the temperature of the leadscrew is used as a key intermediate variable T. s (x,t), whose model calculation values ​​are obtained by the mechanism-driven time-varying thermal error model of the feed shaft, and form a dataset T. sc Intermediate dependent variable T s Online measurement of (x,t) is achieved using an infrared temperature sensor, and a dataset T is generated. sm ;T s Model computation dataset T of (x,t) sc With online measurement dataset T sm It is stored until the consistency judgment period is reached, and then proceeds to the next step of data processing; Fourth step, judging the consistency of the model calculation dataset T of the intermediate dependent variable sc and the online measurement dataset T sm ; The consistency evaluation method is used to judge the consistency of the two groups of data according to the difference between the model calculation data set T s (x,t) of the screw temperature T sc and the infrared temperature sensor measurement data set T sm The mean value M of the difference between the two groups of data and the width W between the consistency boundaries are combined with the threshold value M0 of the difference between the model calculation value and the measured value and the threshold value W0 of the width between the consistency boundaries to judge the consistency of the two groups of data. The mechanism-driven time-varying thermal error model of the feed shaft is in the working process, when the temperature of the screw T s The model calculates the data set T sc The difference between the mean value M and the width W between the consistency boundary of the infrared temperature sensor measurement data set T sm When M>M0 or W>W0, it is considered that the model accuracy is poor; otherwise, it is considered that the model accuracy is good; In the formula, m is the data amount obtained by model calculation and sensor measurement in the consistency judgment period T0; n is the data amount obtained by model calculation and sensor measurement in the experiment when the threshold values M0 and W0 are solved. Fifthly, the parameters of the mechanism-driven time-varying thermal model of the feed shaft are updated online. T sc (x,t i ) and T sc (x,t j ) are the model calculated values of the screw temperature at time t i and t j ; T sm (x,t i ) and T sm (x,t j ) are the sensor measured values of the screw temperature at time t i and t j ; When the mechanism-driven time-varying thermal error model is degraded in the long-term operation process, the model parameters need to be updated online by using the measurement data of the infrared temperature sensor; and the objective function of the model parameter optimization is as follows: ​

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