A single-temperature-sensor-based thermal error modeling method for longitudinal cutting automatic lathe

Abstract

The application 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. The thermal error experimental data of the longitudinal cutting automatic lathe are acquired, the influence of the ambient temperature and the spindle speed on the thermal error is based on respectively, transverse difference is carried out, the ambient temperature thermal error model is acquired, the spindle speed thermal error model is further acquired by substituting the ambient temperature thermal error model to remove the influence of the ambient temperature fluctuation; 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 acquire a total model. The application provides a thermal error modeling method with low cost, low complexity and transparent model structure.

Description

Technical Field

[0001] This invention relates to the field of thermal error compensation and control technology for CNC machine tools, and more specifically to a method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor. Background Technology

[0002] With advancements in sensor and computer technologies, thermal error compensation methods have seen significant improvements in both computational 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 machine tool's thermal error. Common estimation methods are prediction strategies based on data-driven thermal error models. This method typically requires establishing a model relating the temperature of key machine tool points to the thermal error, and then inputting multiple sets of measured temperature values ​​into the model to predict the thermal error. Domestic and international scholars have conducted extensive and fruitful research on thermal error modeling methods. Currently, the main modeling methods developed include: least squares, multiple linear regression, artificial neural networks, and support vector machines.

[0003] However, mainstream methods in the field of thermal error modeling for longitudinally oriented automatic lathes have significant limitations. Traditional data-driven regression models based on least squares and multiple linear regression lack sufficient prediction accuracy under the complex stochastic conditions of actual machine tool operation, making it difficult to meet the requirements of high-precision machining. While machine learning methods such as neural networks and support vector machines can handle nonlinear relationships, their "black box" nature leads to unclear physical meaning of the model, difficulty in parameter tuning, and a reliance on a large number of samples for generalization ability, resulting in poor model interpretability and engineering applicability, making it difficult to effectively deploy, maintain, and apply in real-world engineering environments. Furthermore, the aforementioned data-driven modeling methods generally rely on multiple temperature sensors. For example, the stepwise regression method in related studies requires optimizing up to 12 temperature measurement points as model inputs, which not only significantly increases hardware costs 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 model structure for thermal error modeling is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

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

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for modeling thermal errors in a longitudinally oriented automatic lathe based on a single temperature sensor, comprising:

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

[0009] The collected data on power-on time characteristics, ambient temperature, and spindle speed are preprocessed to further add time-series features corresponding to ambient temperature and spindle speed, generating a feature space matrix. Based on the feature space matrix, the thermal error data is decomposed to quantify the influence of ambient temperature and spindle speed on thermal error.

[0010] Based on the influence of ambient temperature on thermal error, data of the same rotation speed but different ambient temperatures are subjected to horizontal difference to obtain the first-level difference data. The first-level difference data is used as input to iteratively optimize the OS-SR model 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 subjected to lateral difference, and the influence of ambient temperature fluctuation is removed by substituting them into the ambient temperature thermal error model to obtain the second-level difference data. The OS-SR model is iteratively optimized using the second-level difference data as input to obtain the spindle speed thermal error model.

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

[0013] Preferably, the preprocessing of the startup time characteristic, ambient temperature, and spindle speed specifically includes processing the startup time characteristic t and ambient temperature T. amb Spindle speed N is used as one of the three basic feature vectors. Further, time-series features corresponding to ambient temperature and spindle speed are added, as detailed below:

[0014] Ambient temperature T amb The time lag characteristic of the spindle speed N is as follows: Represented as:

[0015]

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

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

[0018]

[0019] Where, mean T (k) represents the average ambient temperature at time k when the sliding window is 3; std T (k) represents the standard deviation of the ambient temperature at time k when the sliding window is 3; mean N (k) represents the average spindle speed at time k when the sliding window is 3; std N (k) represents 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 Represented as:

[0021]

[0022] Ambient temperature T amb The interaction characteristic of the spindle speed N is T amb (k)·N(k);

[0023] Using thermal state characteristics P st Indicates whether the temperature is rising or falling:

[0024]

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

[0026]

[0027] Preferably, the decomposition of 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 As an inherent trend, y amb The thermal error is caused by changes in ambient temperature. N The thermal error is caused by changes in spindle speed. v It is the irregular fluctuation caused by numerous accidental factors affecting thermal error.

[0030] Preferably, obtaining the first-level differential data specifically includes: determining a set of thermal error data y collected at a constant rotation speed. 1 As a baseline trend for thermal error, assuming that irregular fluctuations are stable and have minimal impact, several sets of data collected at the same spindle speed and different ambient temperatures as the baseline thermal error are subjected to lateral differencing to remove the influence of trends, spindle speed, and irregular fluctuations. Assuming there are p sets of data, the first-level differencing data is obtained:

[0031]

[0032] At the same time, the transverse difference also yields ΔT amb , These are, respectively, the horizontal difference data of ambient temperature and the horizontal difference data of ambient temperature lag characteristics.

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

[0034]

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

[0036]

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

[0038]

[0039] Where, ΔN, These are the lateral difference data of the spindle speed time series data and the lateral difference data of the spindle speed lag characteristics, respectively.

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

[0041]

[0042] Among them, y N The thermal error is caused by changes in spindle speed. v It is the irregular fluctuation caused by numerous accidental factors affecting thermal error.

[0043] As can be seen from the above technical solution, compared with the prior art, this invention discloses a method for thermal error modeling of a longitudinal slitting automatic lathe based on a single temperature sensor. A high-precision thermal error prediction model can be constructed using a single temperature sensor, thereby effectively reducing hardware costs, simplifying installation and maintenance, and improving system reliability. Simultaneously, by combining "two-level transverse difference" feature construction with "offspring selection symbolic regression" modeling, the complex nonlinear characteristics of thermal errors are effectively captured, generating a white-box model with a clear mathematical expression. This makes the model structure transparent and its physical meaning clearer, significantly improving the model's applicability in real-world industrial environments. Ultimately, this invention aims to achieve prediction accuracy comparable to or even higher than multi-sensor solutions to meet the urgent need for real-time thermal error compensation in high-precision machining equipment such as Swiss-type longitudinal slitting lathes, possessing clear industrial application value. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0045] Figure 1 Flowchart of the two-stage transverse difference and offspring selection symbolic regression thermal error modeling method provided by this invention;

[0046] Figure 2 The thermal error prediction curve of the model provided by this invention under 2000 rpm conditions;

[0047] Figure 3 The thermal error prediction curve of the model provided by this invention under 4000 rpm conditions;

[0048] Figure 4 The thermal error prediction curve of the model provided by this invention under 6000 rpm conditions. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] This invention discloses a method for thermal error modeling of a longitudinally oriented automatic lathe based on a single temperature sensor. Please refer to [link / reference]. Figure 1 As shown, the thermal error prediction modeling method for longitudinal automatic lathes includes the following steps:

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

[0052] The source dataset D contains only four variables. The input variables include the power-on time feature t and the ambient temperature variable T. amb The dataset includes a spindle speed variable N and one output variable y, which is the thermal error variable in the X direction. It contains 761 sets of data, including data at the same spindle speed under different ambient temperatures and data at different spindle speeds under different ambient temperatures.

[0053] Step S2, Data Preprocessing and Feature Engineering. This involves processing the power-on time feature t and the ambient temperature feature T. amb Spindle speed N is used as one of the three basic feature vectors. Further, time-series features corresponding to ambient temperature and spindle speed are added.

[0054] Ambient temperature T amb The time lag characteristic of the spindle speed N is as follows: Represented as:

[0055]

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

[0057] Ambient temperature T amb The sliding window statistical characteristics of the spindle speed N are as follows: T std T mean N std N , represented 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] Where, mean T (k) represents the average ambient temperature at time k when the sliding window is 3; stdT (k) represents the standard deviation of the ambient temperature at time k when the sliding window is 3; mean N (k) represents the average spindle speed at time k when the sliding window is 3; std N (k) represents 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 Represented as:

[0064]

[0065]

[0066] Ambient temperature T amb The interaction characteristic of the spindle speed N is T amb (k)·N(k);

[0067] Using thermal state characteristics P st Indicates whether the temperature is rising or falling:

[0068]

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

[0070]

[0071] The feature space matrix is ​​shown 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 consist of the inherent trend of thermal error caused by internal heat sources, the influence of external environmental temperature variations, the influence of spindle speed changes, and irregular fluctuations. The 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 This is an inherent trend in thermal error that continues to develop and change over a period of time after power-on. amb Thermal error caused by changes in ambient temperature, y N The thermal error is caused by changes in spindle speed; y vThe thermal error is caused by numerous accidental factors.

[0075] Step S4: First-level lateral differential analysis. 320 sets of data from six operating conditions at the same rotational speed but different ambient temperatures were laterally differentially analyzed to obtain the first differential data. Although the longitudinal cutting automatic lathe was placed in a workshop with ambient temperature control (heating in winter and air conditioning in summer), the ambient temperature range in different seasons was still significant. Therefore, the experiment mainly collected three sets of data from winter, spring, and summer. Two levels of spindle speed were set. The ambient temperature model identification experimental data are shown in Table 1. A total of four sets of data were obtained after differential analysis at the two speeds.

[0076] Table 1. Experimental data for the first-level transverse difference finite element method.

[0077] Data group season Ambient temperature range (°C) 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 transverse difference also yields ΔT amb , These are, respectively, the horizontal difference data of ambient temperature and the horizontal difference data of ambient temperature lag characteristics.

[0080] Step S5: Identify the time series data after the first-level horizontal differencing using the offspring selection symbolic regression method. First, configure the OS-SR model. Select the basic operators and determine the dynamic fitness function, and import the data from the previous step as the training set. Parameter settings are shown in Table 2.

[0081] Table 2 Parameter Settings

[0082] parameter value Population size 1000 Variation rate (%) 15 Crossover rate (%) 90 Maximum number of generations 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. An initial model is randomly generated, and new candidate models are generated through crossover and mutation. The fitness threshold is dynamically adjusted to ensure that offspring are superior to their parents. The model set is updated through continuous iterative optimization. Finally, an optimal ambient temperature model is output. The ambient temperature thermal error model obtained based on offspring selection-signed regression identification is as follows:

[0084]

[0085] In the formula, y amb (k) represents the thermal error caused by the ambient temperature difference at time k, t represents the start-up time characteristic, and at time k, t(k) = k, ΔT amb (k) represents the difference in ambient temperature between the two sets of data at time k. The hysteresis characteristic of the ambient temperature difference between the two sets of data is shown in Table 3, which represents 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 differential analysis. 441 sets of data under four operating conditions with different speeds and ambient temperatures were laterally differentially analyzed to obtain the second-level differential data. Five levels of spindle speed were set, resulting in a total of five sets of data. The experimental data for identifying the thermal error model of the spindle speed are shown in Table 4. K10 was used as the baseline data for the second-level differential analysis and differentially analyzed with the other four sets. A total of four sets of second-level differential data were obtained.

[0089] Table 4. Experimental data for identifying the thermal error model of spindle speed.

[0090]

[0091]

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

[0093] Step S9: Iterative Optimization and Output of the Optimal Spindle Speed ​​Model. An initial model is randomly generated, and new candidate models are generated through crossover and mutation. The fitness threshold is dynamically adjusted to ensure that offspring are superior to parents. The model set is updated through continuous iterative optimization. The time series data of the second-level difference also includes fluctuations in ambient temperature. The ambient temperature thermal error model obtained in the previous section needs to be incorporated to remove the influence of ambient temperature fluctuations. The second-level difference data, after removing the influence of ambient temperature fluctuations, is identified using offspring selection signed regression. The resulting spindle speed thermal error model can be expressed as:

[0094]

[0095]

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

[0097] Step S10: Synthesize the overall model. The model identification described above is based on the thermal error baseline trend y. 1A two-level difference model is performed, and the composite model consists of baseline data, an ambient temperature model, a spindle speed model, and irregular fluctuations. Since the thermal error caused by irregular fluctuations due to random factors cannot be predicted, it is considered the main source of the composite model's prediction residuals. Therefore, 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 The measured value representing the thermal error; This represents the predicted value of the thermal error; This represents the average value of the thermal error measurements.

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

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

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

[0105] The core innovation of this patent lies in proposing a two-stage transverse differential and offspring selection sign regression thermal error modeling method based on a single temperature sensor. Its essential differences and technical advantages from existing technologies are reflected in the following four points.

[0106] 1. Disruptive applications of single temperature sensors

[0107] Existing technologies rely on multiple temperature sensors to construct model inputs, while this patent is the first to achieve thermal error modeling using only a single temperature sensor. This breakthrough reduces hardware costs by more than 60%, simplifies system wiring complexity by 70%, and completely eliminates the problem of multi-sensor synchronization errors.

[0108] 2. Two-level lateral difference feature construction technique

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

[0110] 3. Symbolic regression generates analyzable white-box models.

[0111] The model replaces the black-box model with offspring selection symbolic regression (OS-SR), automatically generating thermal error equations with explicit mathematical expressions. This model has transparent physical meaning, supports field parameter tuning, and achieves a prediction error of ≤5μm under random operating conditions, improving accuracy by 35% compared to traditional models. Moreover, it can be deployed with only microcontroller-level computing power.

[0112] 4. Synergistic effect of technology combination

[0113] The two-level lateral difference and symbolic regression form a feature-model closed-loop optimization mechanism, which achieves the model accuracy level of multi-sensor schemes while ensuring the simplification of single sensors, thus resolving the technical contradiction that high accuracy and low complexity cannot be achieved simultaneously.

[0114] This patent achieves a breakthrough in the field of thermal error compensation through the synergistic application of a single temperature sensor, the construction of two-level lateral differential features, 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, high-precision modeling can be completed with only a single temperature sensor, directly reducing sensor procurement costs by more than 60%; at the same time, simplifying cable routing, signal acquisition modules and data fusion algorithms, the system installation cycle is shortened by 50% and maintenance costs are reduced, making it especially suitable for the precision structure of Swiss-type longitudinal lathes with limited space.

[0117] 2. Significantly improved accuracy and robustness of thermal error prediction

[0118] The thermal error of two-stage lateral differential depth mining is affected by the fluctuation of ambient temperature and the change of spindle speed. Explicit mathematical models generated by symbolic regression are used to predict the error stably within ≤5μm under complex working conditions such as random start-stop and variable speed machining. After compensation, the fluctuation range of workpiece size is narrowed to 1 / 3 of the original.

[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, thus completely solving problems such as difficult parameter debugging and blind spots in fault diagnosis associated with the black-box model.

[0121] 4. Breakthrough solutions to industry technological bottlenecks

[0122] Successfully resolving the dual contradiction between the need for multiple sensors for high precision and the need for a black-box model for strong robustness, this opens up a new path for the miniaturization of CNC machine tools and low-cost, high-precision compensation.

[0123] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0124] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for modeling thermal errors in a longitudinally oriented automatic lathe based on a single temperature sensor, characterized in that, include: Acquire thermal error experimental data of a longitudinal cutting automatic lathe, and use the input variable feature data and thermal error data in the thermal error experimental data as source domain data; the source domain data includes start-up time characteristics, ambient temperature, spindle speed and thermal error data; The collected data on power-on time characteristics, ambient temperature, and spindle speed are preprocessed to further add time series features corresponding to ambient temperature and spindle speed, generating a feature space matrix; The thermal error data is decomposed based on the feature space matrix to quantify the effects of ambient temperature and spindle speed on thermal error. Based on the influence of ambient temperature on thermal error, thermal error data with the same rotation speed but different ambient temperatures are subjected to horizontal difference to obtain first-level difference data. The first-level difference data is used as input to iteratively optimize the OS-SR model to obtain the ambient temperature thermal error model. Based on the influence of spindle speed on thermal error, thermal error data at different speeds and ambient temperatures are subjected to lateral difference. At the same time, the ambient temperature thermal error model is substituted to remove the influence of ambient temperature fluctuations and obtain second-level difference data. The OS-SR model is iteratively optimized using the second-level difference data as input to obtain the spindle speed thermal error model. The ambient temperature thermal error model, the spindle speed thermal error model, and the inherent trends and irregular fluctuations obtained by decomposing the thermal error data are synthesized to obtain the overall model.

2. The method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor according to claim 1, characterized in that, The preprocessing of the startup time characteristic, ambient temperature, and spindle speed specifically includes processing the startup time characteristic t and ambient temperature... Spindle speed N is used as one of the three basic feature vectors. Further, time-series features corresponding to ambient temperature and spindle speed are added, as detailed below: Ambient temperature The time lag characteristic of the spindle speed N is as follows: , , is represented as: ， ； Where k is the current time and τ is the lag coefficient. When τ=1, it is time k-1. Ambient temperature The sliding window statistical characteristics of the spindle speed N are as follows: , , , , is represented as: ； ； ； ； in, The average ambient temperature at time k when the sliding window is 3; Let be the standard deviation of the ambient temperature when the sliding window is 3 at time k; This represents the average spindle speed at time k when the sliding window is 3. Let be the standard deviation of the ambient temperature when the sliding window is 3 at time k; Ambient temperature The longitudinal differential characteristics of the spindle speed N are respectively , , is represented as: ； ； Ambient temperature The interaction characteristics of the spindle speed N are as follows: ; Thermal state characteristics Indicates whether the temperature is rising or falling: 。 3. The method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor according to claim 2, characterized in that, The generation of the feature space matrix specifically includes: the feature space matrix. It is The matrix is ​​such that each row corresponds to a different feature, where m is the number of features, n is the amount of data collected, the time lag features are set to k-1 to k-4, and the sliding window size is set to 3. Specifically, it is represented as follows: 。 4. The method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor according to claim 1, characterized in that, The decomposition of thermal error data based on the feature space matrix specifically includes: ； in, It is the total thermal error. As an inherent trend, This is due to thermal errors caused by changes in ambient temperature. This is due to thermal errors caused by changes in spindle speed. It is the irregular fluctuation caused by numerous accidental factors affecting thermal error.

5. The method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor according to claim 4, characterized in that, The acquisition of the first-level differential data specifically includes: determining a set of thermal error data collected at a constant rotation speed. As a baseline trend for thermal error, assuming that irregular fluctuations are stable and have minimal impact, several sets of data collected at the same spindle speed and different ambient temperatures as the baseline thermal error are subjected to lateral differencing to remove the influence of trends, spindle speed, and irregular fluctuations. Assuming there are p sets of data, the first-level differencing data is obtained: ； At the same time, the transverse difference also yields , These are, respectively, the horizontal difference data of ambient temperature and the horizontal difference data of ambient temperature lag characteristics.

6. The method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor according to claim 5, characterized in that, The specific components of the environmental temperature thermal error model include: 。 7. The method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor according to claim 6, characterized in that, The acquisition of the second-level difference data specifically includes: ； 。 8. The method for thermal error modeling 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: ； in, These are the lateral difference data of the spindle speed time series data and the lateral difference data of the spindle speed lag characteristics, respectively.

9. A method for thermal error modeling of a longitudinal automatic lathe based on a single temperature sensor, as described in claim 8, is characterized in that, The acquisition of the overall model specifically includes: ； in, This is due to thermal errors caused by changes in spindle speed. It is the irregular fluctuation caused by numerous accidental factors affecting thermal error.

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