Longitudinal cutting automatic lathe thermal error modeling method based on single temperature sensor

Abstract

The invention discloses a longitudinal cutting automatic lathe thermal error modeling method based on a single temperature sensor, and relates to the technical field of numerical control machine tool thermal error compensation control. Thermal error experimental data of a longitudinal cutting automatic lathe are obtained, and transverse difference is carried out based on the influence of the environment temperature and the main shaft rotating speed on thermal errors; obtaining an environment temperature thermal error model, and further substituting the environment temperature thermal error model to remove the influence of environment temperature fluctuation so as to obtain a main shaft rotating speed thermal error model; and synthesizing the environment temperature thermal error model, the main shaft rotating speed thermal error model and the inherent trend obtained by decomposing the thermal error data with irregular fluctuation to obtain a total model. The thermal error modeling method provided by the invention has the advantages of low cost, low complexity and transparent model structure.

Description

Technical Field

[0001] The present invention relates to the technical field of thermal error compensation control of numerically controlled machine tools, and more particularly to a thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor. Background Art

[0002] With advances in sensor and computer technology, thermal error compensation methods have significantly improved in both accuracy and speed. Due to their low cost and ease of implementation, they have become an effective way to improve machine tool accuracy. The key to thermal error compensation technology lies in accurately estimating the thermal error of a machine tool. Common estimation methods are prediction strategies based on data-driven thermal error models. Implementing this method typically requires establishing a relationship model between the temperature of key machine tool points and thermal error, then inputting multiple sets of measured temperature values ​​into the model to predict thermal error. Domestic and international scholars have conducted extensive and fruitful research on thermal error modeling methods. The main modeling methods currently under development include least squares, multivariate linear regression, artificial neural networks, and support vector machines.

[0003] However, the mainstream methods in the field of thermal error modeling of longitudinal automatic lathes have significant limitations. Traditional data-driven regression models based on least squares and multivariate linear regression have insufficient prediction accuracy under the complex random working conditions of the actual operation of the machine tool, making it difficult to meet the requirements of high-precision processing. Although machine learning methods such as neural networks and support vector machines can handle nonlinear relationships, their "black box" characteristics lead to unclear physical meaning of the model, difficulty in parameter debugging, and generalization ability relying on a large number of samples, resulting in poor model interpretability and engineering applicability, making it difficult to effectively deploy, maintain and apply in actual engineering environments. In addition, the above-mentioned data-driven modeling methods generally rely on multiple temperature sensors. For example, the stepwise regression method in related research needs to optimize up to 12 temperature measurement points as model input, which not only significantly increases the hardware cost and the complexity of installation and wiring, but also increases the difficulty of system maintenance and introduces more potential failure points.

[0004] Therefore, how to provide a low-cost, low-complexity and transparent thermal error modeling method is an urgent problem that technicians in this field need to solve. Summary of the Invention

[0005] In view of this, the present invention provides a thermal error modeling method for a longitudinal automatic lathe based on a single temperature sensor, so as to solve the problems existing in the background technology.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A thermal error modeling method for a longitudinal automatic lathe based on a single temperature sensor includes:

[0008] Acquire thermal error experimental data of a longitudinal automatic lathe, and use input variable characteristic data and thermal error data in the thermal error experimental data as source domain data; the source domain data includes power-on time characteristics, ambient temperature, spindle speed, and thermal error data;

[0009] Preprocessing the collected data of the power-on time characteristics, ambient temperature, and spindle speed to further add time series characteristics corresponding to the ambient temperature and spindle speed to generate a feature space matrix; decomposing the thermal error data based on the feature space matrix to quantify the effects of the ambient temperature and spindle speed on the thermal error;

[0010] Based on the influence of ambient temperature on thermal error, the data of different ambient temperatures at the same speed are transversely differentiated to obtain the first-level differential data. The OS-SR model is iteratively optimized with the first-level differential data as input to obtain the ambient temperature thermal error model.

[0011] Based on the influence of spindle speed on thermal error, the data of different speeds and different ambient temperatures are horizontally differentiated and substituted into the ambient temperature thermal error model to remove the influence of ambient temperature fluctuations. The second-level differential data is obtained. The second-level differential data is used as input to iteratively optimize the OS-SR model to obtain the spindle speed thermal error model.

[0012] The ambient temperature thermal error model, the spindle speed thermal error model, and the inherent trend and irregular fluctuation obtained by decomposing the thermal error data are synthesized to obtain an overall model.

[0013] Preferably, the pre-processing of the power-on time feature, ambient temperature and spindle speed specifically includes the power-on time feature t, ambient temperature T amb , and spindle speed N are used as the three basic feature vectors. The time series features corresponding to ambient temperature and spindle speed are further added as follows:

[0014] Ambient temperature T amb , the time lag characteristic of the spindle speed N is Expressed as:

[0015]

[0016] Where k is the current moment, τ is the lag coefficient; when τ = 1, it is the k-1 moment;

[0017] Ambient temperature T amb , the sliding window statistical characteristics of the spindle speed N are mean T 、std T 、mean N 、std N , expressed as:

[0018]

[0019] Among them, mean T (k) is the average value of the ambient temperature when the sliding window is 3 at time k; std T (k) is the standard deviation of the ambient temperature when the sliding window is 3 at time k; mean N (k) is the average spindle speed when the sliding window is 3 at time k; std N (k) is the standard deviation of the ambient temperature when the sliding window is 3 at time k;

[0020] Ambient temperature T amb , the longitudinal differential characteristics of the spindle speed N are respectively Expressed as:

[0021]

[0022] Ambient temperature T amb , the interaction characteristics of the spindle speed N are T amb (k)·N(k);

[0023] Thermal state characteristics P st Characterizes the stage of heating up or cooling down:

[0024]

[0025] Preferably, generating the feature space matrix specifically includes: the feature space matrix χ is an n×m matrix, each row corresponds to a different feature, wherein m is the number of features, n is the amount of collected data, the time lag feature is set to k-1 to k-4, and the sliding window size is set to 3, which is specifically expressed as:

[0026]

[0027] Preferably, the decomposing the thermal error data based on the feature space matrix specifically includes:

[0028] y=y ten +y amb +y N +y v ;

[0029] Where y is the total thermal error, y ten is the inherent trend, y amb is the thermal error caused by the change of ambient temperature, y N is the thermal error caused by the change of spindle speed, y v It is the irregular fluctuation of thermal error caused by many accidental factors.

[0030] Preferably, the acquisition of the first-level differential data specifically includes: determining a set of thermal error data y collected at a constant speed 1 Assuming that irregular fluctuations are stable and have little impact as the benchmark trend of thermal error, several groups of data collected at the same spindle speed and different ambient temperatures as the benchmark thermal error are horizontally differentiated to remove the influence of trend, spindle speed, and irregular fluctuations. Assuming there are p groups of data, the first-level differential data is obtained:

[0031]

[0032] At the same time, the lateral difference also obtains ΔT amb 、 They are the lateral difference of ambient temperature and the lateral difference data of ambient temperature hysteresis characteristics.

[0033] Preferably, the step of obtaining the ambient temperature thermal error model specifically includes:

[0034]

[0035] Preferably, the obtaining of the second-level differential data specifically includes:

[0036]

[0037] Preferably, the spindle speed thermal error model specifically includes:

[0038]

[0039] Among them, ΔN, They are the horizontal difference of the spindle speed time series data and the horizontal difference data of the spindle speed hysteresis characteristics.

[0040] Preferably, the obtaining of the overall model specifically includes:

[0041]

[0042] Among them, y N is the thermal error caused by the change of spindle speed, y v It is the irregular fluctuation of thermal error caused by many accidental factors.

[0043] Through the above technical solutions, it can be seen that compared with the prior art, the present invention discloses a method for modeling thermal errors of longitudinal automatic lathes based on a single temperature sensor, which can build a high-precision thermal error prediction model through a single temperature sensor, thereby effectively reducing hardware costs, simplifying installation and maintenance, and improving system reliability. At the same time, by combining the "two-level lateral difference" feature construction with the "offspring selection symbol regression" modeling, the complex nonlinear characteristics of thermal errors are effectively captured, and a white box model with a clear mathematical expression is generated, making the model structure transparent and the physical meaning clearer, which significantly improves the applicability of the model in actual industrial environments. Ultimately, the present invention strives to achieve prediction accuracy comparable to or even higher than that of a multi-sensor solution, in order to meet the urgent needs of high-precision machining equipment such as Swiss-type longitudinal lathes for real-time compensation of thermal errors, and has clear industrial application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0045] Figure 1 Flowchart of the two-stage lateral difference and progeny selection signed regression thermal error modeling method provided by the present invention;

[0046] Figure 2 This is a thermal error prediction curve diagram of the model provided by the present invention at 2000rpm;

[0047] Figure 3 This is a thermal error prediction curve diagram of the model provided by the present invention at 4000rpm;

[0048] Figure 4 This is a thermal error prediction curve diagram of the model provided by the present invention under 6000rpm conditions. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0050] The embodiment of the present invention discloses a thermal error modeling method for a longitudinal automatic lathe based on a single temperature sensor. Figure 1 As shown in FIG, the thermal error prediction modeling method of the longitudinal cutting automatic lathe includes the following steps:

[0051] Step S1: Arrange and install temperature measurement sensors and thermal error sensors on the longitudinal cutting automatic lathe, collect power-on time, ambient temperature time series data, X-direction thermal error time series data, and spindle speed time series data, and generate the above data together as a source data set D.

[0052] The source data set D only includes 4 variables. Among them, the input variables include the boot time feature t, the ambient temperature variable T amb The output variable is the X-direction thermal error variable y. The data set contains 761 sets of data at the same speed and different ambient temperatures, and at different speeds and different ambient temperatures.

[0053] Step S2: Data preprocessing and feature engineering. amb , and spindle speed N as the three basic feature vectors. Further add the time series features corresponding to ambient temperature and spindle speed.

[0054] Ambient temperature T amb , the time lag characteristic of the spindle speed N is Expressed as:

[0055]

[0056] Where k is the current moment, τ is the lag coefficient; when τ = 1, it is the k-1 moment;

[0057] Ambient temperature T amb , the sliding window statistical characteristics of the spindle speed N are mean T 、std T 、mean N 、std N , expressed as:

[0058] mean T (k)=[T amb (k-1)+T amb (k)+T amb (k+1)]3;

[0059]

[0060] mean N (k)=[N(k-1)+N(k)+N(k+1)]3;

[0061]

[0062] Among them, mean T (k) is the average value of the ambient temperature when the sliding window is 3 at time k; stdT (k) is the standard deviation of the ambient temperature when the sliding window is 3 at time k; mean N (k) is the average spindle speed when the sliding window is 3 at time k; std N (k) is the standard deviation of the ambient temperature when the sliding window is 3 at time k;

[0063] Ambient temperature T amb , the longitudinal differential characteristics of the spindle speed N are respectively Expressed as:

[0064]

[0065]

[0066] Ambient temperature T amb , the interaction characteristics of the spindle speed N are T amb (k)·N(k);

[0067] Thermal state characteristics P st Characterizes the stage of heating up or cooling down:

[0068]

[0069] The expanded feature space matrix χ is an n×m matrix, where each row corresponds to a different feature, where m is the number of features, n is the amount of collected data, the time lag feature is set to k-1 to k-4, and the sliding window size is set to 3. It can be specifically expressed as:

[0070]

[0071] The feature space matrix is ​​presented in detail in steps 2 and 3 and will be used in steps 5, 6, 7, and 8.

[0072] Step S3, model decomposition. The thermal error time series data is considered to be composed of the inherent trend of thermal error caused by internal heat sources, the influence of external ambient temperature changes, the influence of spindle speed changes, and irregular fluctuations. Its additive decomposition method is as follows:

[0073] y=y ten +y amb +y N +y v ;

[0074] Where y is the total thermal error, y ten It is an inherent tendency of thermal error to continue to develop and change over a period of time after power-on. amb is the thermal error caused by the change of ambient temperature, y N is the thermal error caused by the change of spindle speed; vIt is the influence of many accidental factors on thermal error.

[0075] Step S4, first-level lateral difference. Perform lateral difference on 320 sets of data of 6 working conditions with the same speed but different ambient temperatures to obtain the first differential data. Although the longitudinal cutting automatic lathe is placed in a workshop with ambient temperature control (heating in winter and air conditioning in summer), the ambient temperature span in experiments in different seasons is still large. Therefore, the experiment mainly collected three sets of data in winter, spring and summer. The spindle speed is set at 2 levels. The experimental data of ambient temperature model identification are shown in Table 1. A total of 4 sets of data are obtained after differentiating the two speeds.

[0076] Table 1 First-level transverse difference experimental data

[0077] Data Group season Ambient temperature range (℃) Spindle speed (rpm) K1 winter 17.13℃-20.65℃ 3000 K2 spring 19.06℃-22.03℃ 3000 K3 summer 23.21℃-23.69℃ 3000 K4 winter 16.44℃-18.89℃ 5000 K5 spring 24.81℃-25.44℃ 5000 K6 summer 26.16℃-25.33℃ 5000

[0078]

[0079] At the same time, the lateral difference also obtains ΔT amb 、 They are the lateral difference of ambient temperature and the lateral difference data of ambient temperature hysteresis characteristics.

[0080] Step S5: Use the offspring selection symbolic regression method to identify the time series data after the first-level horizontal difference. First, configure the OS-SR model. Select the basic operator and determine the dynamic fitness function. Import the data from the previous step as the training set. The parameter settings are shown in Table 2.

[0081] Table 2 Parameter settings

[0082] parameter value Number of individuals in the population 1000 Mutation rate (%) 15 Crossover rate (%) 90 Maximum genetic generation 100 Maximum tree depth 15 Maximum number of cotyledons 50 Operator Settings <![CDATA[+,-,×, / ,x 2 ]]>

[0083] Step S6: Iterative optimization and output of the optimal ambient temperature model. Initial models are randomly generated, and new candidate models are generated through crossover and mutation propagation. The fitness threshold is dynamically adjusted to ensure that the offspring outperforms the parent. Through continuous iterative optimization, the model set is updated. Ultimately, an optimal ambient temperature model is output. The ambient temperature thermal error model obtained based on offspring selection and symbolic regression identification is as follows:

[0084]

[0085] Where y amb (k) is the thermal error caused by the ambient temperature difference at time k, t is the power-on time characteristic, and at time k, t(k) = k, ΔT amb (k) is the ambient temperature difference between the two sets of data at time k, is the hysteresis characteristic of the ambient temperature difference between the two sets of data, that is, the temperature difference between time k-1 and time k-4. The model parameters are shown in Table 3.

[0086] Table 3 Model parameters

[0087]

[0088] Step S7: Second-level lateral differencing. 441 data sets from four operating conditions at different speeds and ambient temperatures were lateral-differentiated to obtain second-level differential data. Five spindle speed levels were set, resulting in five data sets. The experimental data for the spindle speed thermal error model identification are shown in Table 4. K10 was used as the baseline data for the second-level differential, and differentials were performed with the other four data sets. A total of four second-level differential data sets were obtained.

[0089] Table 4 Experimental data of spindle speed thermal error model identification

[0090]

[0091]

[0092] Step S8: Second OS-SR model configuration. Select the base operator and determine the dynamic fitness function. Import the data obtained from the second-level lateral difference as the training set. The hyperparameter settings are the same as in the previous section.

[0093] Step S9, iterative optimization and optimal spindle speed model output. Randomly generate an initial model, and generate a new candidate model through crossover and mutation reproduction. Dynamically adjust the fitness threshold to ensure that the offspring is better than the parent. Update the model set through continuous iterative optimization. The time series data of the second-level difference also contains fluctuations in ambient temperature. It is necessary to bring in the ambient temperature thermal error model obtained in the previous section to remove the influence of ambient temperature fluctuations. The second-level difference data without the influence of ambient temperature fluctuations is identified using offspring selection symbol regression. The obtained spindle speed thermal error model can be expressed as:

[0094]

[0095]

[0096] Where y N (k) is the thermal error caused by the spindle speed difference at time k, ΔN is the speed difference between the two sets of data, ΔT amb (k)·ΔN is the interaction feature at time k. The model parameters are shown in Table 3.

[0097] Step S10: Synthesize the total model. The above model identification is based on the thermal error benchmark trend y 1Performing two-level differentiation, the composite model consists of baseline data, an ambient temperature model, a spindle speed model, and irregular fluctuations. Since the irregular fluctuation thermal error caused by accidental factors cannot be predicted, it is considered the main source of the composite model's prediction residual. The overall model can be further expressed as:

[0098] y=y 1 +y amb +y N +y v ;

[0099] To evaluate the model, the following evaluation metrics were determined:

[0100]

[0101] Where m represents the number of sampling points; y j Represents a measure of thermal error; represents the predicted value of thermal error; Represents the average of the thermal error measurements.

[0102] The thermal error prediction curve of the constructed model at 2000rpm is as follows Figure 2 shown.

[0103] The thermal error prediction curve of the constructed model at 4000rpm is as follows Figure 3 shown.

[0104] The thermal error prediction curve of the constructed model at 6000rpm is as follows Figure 4 shown.

[0105] The core innovation of this patent is to propose a two-stage lateral difference and offspring selection sign regression thermal error modeling method based on a single temperature sensor. Its essential difference and technical advantages over the existing technology are reflected in the following four points

[0106] 1. Disruptive application of single temperature sensor

[0107] While existing technologies rely on multiple temperature sensors to construct model inputs, this patented method is the first to enable thermal error modeling with only a single temperature sensor. This breakthrough reduces hardware costs by over 60%, simplifies system wiring complexity by 70%, and completely eliminates multi-sensor synchronization errors.

[0108] 2. Two-level lateral differential feature construction technology

[0109] To address the low information density of single-sensor data, this patent pioneers a two-level lateral differential feature construction process. The first-level differential extracts the temperature change rate feature, while the second-level differential extracts the spindle speed change rate fluctuation feature. This replaces the traditional multi-sensor spatial temperature distribution input and improves feature engineering efficiency.

[0110] 3. Symbolic regression generates a parsable white box model

[0111] Offspring Selection Symbolic Regression (OS-SR) replaces the black-box model and automatically generates a thermal error equation with a clear mathematical expression. This model is physically transparent and supports field parameter adjustment. Under random operating conditions, the prediction error is ≤ 5μm, a 35% improvement in accuracy over traditional models, and can be deployed with only microcontroller-level computing power.

[0112] 4. Technology combination synergy

[0113] Two-level lateral difference and symbolic regression form a feature-model closed-loop optimization mechanism. Under the premise of ensuring the simplification of a single sensor, the model accuracy reaches the level of a multi-sensor solution, solving the technical contradiction of achieving both high precision and low complexity.

[0114] This patent achieves breakthrough progress in thermal error compensation through the synergy of single temperature sensor application, two-level lateral differential feature construction, and symbolic regression white box modeling. Its significant effects are reflected in the following four aspects:

[0115] 1. Revolutionary reduction in hardware system cost and complexity

[0116] Completely abandoning the traditional multi-sensor solution, only a single temperature sensor is needed to complete high-precision modeling, directly reducing sensor procurement costs by more than 60%; simultaneously simplifying cable wiring, signal acquisition modules and data fusion algorithms, shortening the system installation cycle by 50% and reducing maintenance costs. It is especially suitable for the precision structure of Swiss-type sliding lathes with limited space.

[0117] 2. Thermal error prediction accuracy and robustness are significantly improved

[0118] Two-level lateral differential deep mining is used to explore the influence of ambient temperature fluctuations and spindle speed changes on thermal errors. Explicit mathematical models generated by symbolic regression are used. Under complex working conditions such as random start-stop and variable speed processing, the prediction error is stably controlled at ≤5μm. After compensation, the fluctuation range of workpiece size is narrowed to 1 / 3 of the original range.

[0119] 3. Leapfrog optimization of engineering practicality and maintainability

[0120] The white-box model provides human-readable mathematical expressions, allowing engineers to adjust coefficients on-site based on physical mechanisms, completely resolving problems such as difficulty in debugging black-box model parameters and blind spots in fault diagnosis.

[0121] 4. Breakthrough solutions to industry technical bottlenecks

[0122] It successfully resolves the dual contradictions between high precision requiring multiple sensors and strong robustness requiring a black box model, opening up a new path for miniaturization and low-cost high-precision compensation of CNC machine tools.

[0123] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0124] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A thermal error modeling method for a longitudinal automatic lathe based on a single temperature sensor, characterized in that: include: Acquire thermal error experimental data of a longitudinal automatic lathe, and use input variable characteristic data and thermal error data in the thermal error experimental data as source domain data; the source domain data includes power-on time characteristics, ambient temperature, spindle speed, and thermal error data; Preprocessing the collected data of the power-on time characteristics, ambient temperature, and spindle speed, further adding time series characteristics corresponding to the ambient temperature and spindle speed, and generating a feature space matrix; Decomposing the thermal error data based on the characteristic space matrix, and quantifying the effects of the ambient temperature and the spindle speed on the thermal error respectively; Based on the influence of ambient temperature on thermal error, the data of different ambient temperatures at the same speed are transversely differentiated to obtain the first-level differential data. The OS-SR model is iteratively optimized with the first-level differential data as input to obtain the ambient temperature thermal error model. Based on the influence of spindle speed on thermal error, the data of different speeds and different ambient temperatures are horizontally differentiated and substituted into the ambient temperature thermal error model to remove the influence of ambient temperature fluctuations. The second-level differential data is obtained. The second-level differential data is used as input to iteratively optimize the OS-SR model to obtain the spindle speed thermal error model. The ambient temperature thermal error model, the spindle speed thermal error model, and the inherent trend and irregular fluctuation obtained by decomposing the thermal error data are synthesized to obtain an overall model.

2. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 1 is characterized in that: The pre-processing of the boot time feature, ambient temperature and spindle speed specifically includes: amb , and spindle speed N are used as the three basic feature vectors. The time series features corresponding to ambient temperature and spindle speed are further added as follows: Ambient temperature T amb , the time lag characteristic of the spindle speed N is Expressed as: Where k is the current moment, τ is the lag coefficient; when τ = 1, it is the k-1 moment; Ambient temperature T amb , the sliding window statistical characteristics of the spindle speed N are mean T 、std T 、mean N 、std N , expressed as: mean T (k)=[T amb (k-1)+T amb (k)+T amb (k+1)] / 3; mean N (k)=[N(k-1)+N(k)+N(k+1)] / 3; Among them, mean T (k) is the average value of the ambient temperature when the sliding window is 3 at time k; std T (k) is the standard deviation of the ambient temperature when the sliding window is 3 at time k; mean N (k) is the average spindle speed when the sliding window is 3 at time k; std N (k) is the standard deviation of the ambient temperature when the sliding window is 3 at time k; Ambient temperature T amb , the longitudinal differential characteristics of the spindle speed N are respectively Expressed as: Ambient temperature T amb , the interaction characteristics of the spindle speed N are T amb (k)·N(k); Thermal state characteristics P st Characterizes the stage of heating up or cooling down:

3. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 2 is characterized in that: The generating feature space matrix specifically includes: the feature space matrix χ is an n×m matrix, each row corresponds to a different feature, where m is the number of features, n is the amount of collected data, the time lag feature is set to k-1 to k-4, and the sliding window size is set to 3, which is specifically expressed as:

4. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 1, characterized in that: Decomposing the thermal error data based on the feature space matrix specifically includes: y=y ten +y amb +y N +y v ; Where y is the total thermal error, y ten is the inherent trend, y amb is the thermal error caused by the change of ambient temperature, y N is the thermal error caused by the change of spindle speed, y v It is the irregular fluctuation of thermal error caused by many accidental factors.

5. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 4 is characterized in that: The acquisition of the first-level differential data specifically includes: determining a set of thermal error data y collected at a constant speed 1 Assuming that irregular fluctuations are stable and have little impact as the benchmark trend of thermal error, several groups of data collected at the same spindle speed and different ambient temperatures as the benchmark thermal error are horizontally differentiated to remove the influence of trend, spindle speed, and irregular fluctuations. Assuming there are p groups of data, the first-level differential data is obtained: At the same time, the lateral difference also obtains ΔT amb 、 They are the lateral difference of ambient temperature and the lateral difference data of ambient temperature hysteresis characteristics.

6. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 5, characterized in that: The obtaining of the ambient temperature thermal error model specifically includes:

7. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 6, characterized in that: The obtaining of the second-level differential data specifically includes:

8. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 7, characterized in that: The spindle speed thermal error model specifically includes: Among them, ΔN, They are the horizontal difference of the spindle speed time series data and the horizontal difference data of the spindle speed hysteresis characteristics.

9. The thermal error modeling method of a longitudinal automatic lathe based on a single temperature sensor according to claim 8, characterized in that: The obtaining of the overall model specifically includes: Among them, y N is the thermal error caused by the change of spindle speed, y v It is the irregular fluctuation of thermal error caused by many accidental factors.

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