CN110543140B - Time characteristic-based numerical control machine tool spindle system thermal key point selection modeling method - Google Patents
Time characteristic-based numerical control machine tool spindle system thermal key point selection modeling method Download PDFInfo
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Abstract
The invention discloses a time characteristic-based method for selecting and modeling a thermal key point of a spindle system of a numerical control machine tool, which comprises the following steps of: the temperature data of all temperature measuring points collected under a standard rotating speed map are sorted from small to large according to the time required for reaching the highest temperature, the temperature measuring points are divided into several classes by a fuzzy c-means clustering and other clustering methods, then, for the temperature measuring points in each class, the points with high sorting are selected as the thermal key points of the class according to the sorting height, the temperature data of the selected thermal key points and the corresponding thermal error data are used as training sets, and a thermal error model is established by using a regression method such as a support vector machine. The invention improves the robustness of the model, so that the selected thermal error key point can have higher precision when predicting the thermal errors under other rotating speed maps.
Description
Technical Field
The invention belongs to the technical field of numerical control machine tools, and particularly relates to a time characteristic-based method for selecting and modeling a thermal key point of a spindle system of a numerical control machine tool.
Background
With the development of the numerical control machine tool in the high-speed and precise direction, the thermal error becomes the most important component of the machine tool error. Thermal errors can account for 40-70% of the total machine tool errors, and geometric errors due to temperature effects can account for 75% of the total geometric errors of the workpiece. And the friction between the main shaft and the bearing is inevitable from the source when the main shaft rotates. Therefore, active control of thermal errors in a compensating manner based on methods such as thermal error modeling is a main approach to reduce thermal errors.
The thermal error modeling is to establish a multivariate nonlinear relation model between thermal key point temperature data and thermal error data under a certain rotating speed map by using a regression method. In order to ensure the robustness of the model, the model is also required to be applied to the thermal error prediction of other rotating speed maps. Therefore, the collection of temperature and thermal error data, the selection of thermal key points and the establishment of a thermal error model are the main contents of the thermal error modeling.
The sinosaurus of Shanghai university of transportation and the like think through a heating experiment that the correlation coefficient between the temperature change of the optimal measuring point and the thermal deformation of the main shaft is the largest; the Hokkaido and the like at Shanghai engineering technology university select thermal key points by analyzing correlation coefficients among temperature measuring points; thermal key points are determined by fuzzy clustering and grey correlation degree analysis of Ravery, university of Rivern State; the Suyufeng of Zhengzhou university and the like establish a thermal error compensation model through a BP neural network; establishing a thermal error model by a support vector machine for Miao Enming and the like of the university of fertilizer industry; the Yang army and the like of the Western-Ann university of transportation determine a thermal key point through fuzzy clustering and correlation coefficients; integrating BP neural networks into Tan Peak and the like of Sichuan university, and establishing a thermal error model of a horizontal processing center; zhang Jie, university of Huazhong science and technology, and the like establish a thermal error model based on a genetic RBF neural network.
The temperature measuring point selection and thermal error modeling method mainly comprises the steps of classifying the temperature measuring points by using a fuzzy clustering method, and then selecting one point in each class as a thermal key point by using a method of sorting according to correlation coefficients or grey correlation degrees between temperature data and thermal error data. The methods can ensure certain precision when self-prediction is carried out (namely training data and prediction data come from data under the same rotating speed map). However, in the case of cross prediction (that is, the training data and the prediction data are from data under different rotational speed maps), because the thermal key point selected under the previous rotational speed map has a strong correlation with the thermal error data under the previous rotational speed map, but cannot ensure that the thermal key point under the next rotational speed map has a strong correlation with the thermal error data, the accuracy and robustness cannot be ensured during thermal error modeling.
Therefore, a method for modeling the thermal key point selection of the spindle system of the numerical control machine tool based on the time characteristic needs to be provided.
Disclosure of Invention
The invention aims to improve the robustness of a model and enable a selected thermal error key point to have higher precision when predicting thermal errors under other rotating speed maps. The method does not substitute thermal error data when selecting the thermal key point, thereby ensuring that the self-prediction and the cross-prediction have higher precision. Especially for a special numerical control machine tool such as a peripheral grinding machine, the flange disc at the front end of the main shaft system can play an obvious cooling effect on the main shaft system when the main shaft system rotates at a high speed, so that the sequencing result according to the correlation coefficient or the grey correlation degree can be greatly influenced. The thermal key point selection method based on the time characteristic does not influence the point selection result no matter whether the thermal boundary condition of the spindle system is changed or not, and the defects are avoided.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the method for selecting and modeling the thermal key points of the numerical control machine tool spindle system based on the time characteristics comprises the following steps:
s1, collecting temperature data of each temperature measuring point under a standard rotating speed map, and sequencing the temperature data from small to large according to the time required for reaching the highest temperature, wherein the expression is as follows:
(1) in the formula: x is the number ofijIs the temperature at the ith measurement point at the jth minute, Int () is a rounding function, riIs the rank value of the ith measurement point, riThe larger the order, the less time is required for the ith measuring point to reach the highest temperature, and the higher the order is; for the point at which the highest temperature is reached at the same time, i.e. riThe same measuring points are sorted from large to small according to the temperature variation of the measuring points in the whole measuring time;
s2, classifying the temperature measuring points through a clustering method, selecting the points with high sequence as the thermal key points of each class according to the sequence in the step S1 for the temperature measuring points in each class, and selecting the thermal key points of each class according to the method to finally form the thermal key points of all the temperature measuring points;
and S3, taking the temperature data of the thermal key points selected by the method in the step S2 and the thermal error data corresponding to the temperature data as a training set, establishing a thermal error model by using a regression method, bringing the temperature data of the same thermal key points under a non-standard rotating speed map into the trained thermal error model, and predicting the thermal error.
Preferably, step S1 includes the following sub-steps,
s11, setting rotation speed maps in different running states, and ensuring that one rotation speed map is GB/T17421.3-2009 part 3 of machine tool inspection general rule: determination of thermal effect standard speed map specified in;
s12, the numerical control machine tool respectively operates according to the rotating speed map in the step S11, and when the numerical control machine tool operates, the temperature sensor and the displacement sensor simultaneously acquire corresponding data;
s13, acquiring a thermal error of a main shaft extension end of the main shaft system by using a displacement sensor, taking an average value of a period of time as a thermal error value at the moment, and enabling the displacement sensor to be in a zero setting state before the numerically-controlled machine tool operates;
and S14, acquiring the temperature of each point on the surface of the main shaft system and the ambient temperature at a certain distance from the main shaft system by using a temperature sensor, wherein the sampling frequency of temperature data is the same as the frequency obtained by averaging displacement data, and the temperature measuring points comprise measuring points which are not limited to positions close to front and rear bearings, ambient temperature measuring points and measuring points with other heat sources.
Preferably, the displacement sensor is a non-contact displacement sensor, and the temperature sensor is a contact temperature sensor.
Preferably, in step S12, the cnc machine is stationary for a period of time for cooling before operating according to the tachograph in step S11, respectively.
Preferably, the temperature data obtained in step S14 is a temperature data variation during the temperature sensor acquisition.
Preferably, the clustering method of step S2 adopts a fuzzy c-means clustering method.
Preferably, the implementation process of classifying the temperature measurement points by the fuzzy c-means clustering method in step S2 is as follows:
the objective function of fuzzy clustering is represented as:
(2) wherein c is the number of clusters, h is the fuzzy weight index, uijIs a temperature vector x formed by the temperature of the ith temperature measuring pointiMembership, d, belonging to the jth fuzzy classijIs a temperature vector xiDistance from the jth fuzzy class;
dij＝||xi-vj|| (3)
(3) in the formula, viIs the cluster center of the ith ambiguity class,
the classification process is as follows:
(4) in the formula (5), a clustering number c and a fuzzy weight index h are given;
b. randomly giving a membership matrix U;
c. calculating a clustering center matrix V;
d. calculating a membership matrix U;
e. repeating the steps c and d until the difference between the membership degree matrixes of the two times is less than the given minimum variation, namely | | | Ul +1-Ul| | < epsilon, or the iteration times have reached the maximum iteration times;
after the temperature measuring points are classified, the number of the classified categories of the temperature measuring points is the number of the thermal key points.
Preferably, the regression method adopted in step S3 is a support vector machine regression method.
Preferably, the specific method for establishing the thermal error regression model comprises the following steps:
the following regression function was constructed:
y＝f(X) (6)
(6) in the formula, X is a q-dimensional vector formed by the temperature of the thermal key point at any moment, q is the number of the thermal key points, and y is a thermal error value at the same moment;
the nonlinear support vector machine regression model can be expressed as:
(7) in the formula (I), the compound is shown in the specification,
is a coefficient, xiAs a support vector, K (X, X)i) Is a kernel function;
selecting a Gaussian radial basis kernel function as a kernel function of a regression model of a support vector machine, wherein the expression is as follows:
K(X,Xi)＝exp(-||Xi-X||2/σ2) (8)
(8) wherein σ is a width parameter, and 1/σ is expressed2Is a nuclear parameter g;
taking a data set acquired under a standard rotating speed map as a training set to be brought into a support vector machine, and adopting a K classification cross validation method2-4～24And selecting a penalty coefficient C and a kernel function parameter g in the range.
The beneficial technical effects of the invention are as follows: the invention improves the robustness of the regression model of the support vector machine, so that the selected thermal error key point can have higher precision when predicting the thermal errors under other rotating speed maps, and the thermal error data is not substituted when selecting the thermal key point, thereby ensuring that the self-prediction and the cross-prediction have higher precision.
Drawings
FIG. 1 is a flow chart showing steps of embodiment 1 of the present invention.
Fig. 2 is a flowchart illustrating step S1 in embodiment 1 of the present invention.
Fig. 3 is a schematic diagram showing the arrangement of the temperature sensor on the surface of the headstock in embodiment 2 of the present invention.
FIG. 4 is a schematic diagram showing the temperature increase at 16 measurement points under the tachogram A in example 2 of the present invention.
FIG. 5 is a schematic diagram showing a comparison of two point selection methods in example 2 of the present invention.
Fig. 6 is a schematic diagram showing the modeling accuracy of the data set a self-prediction (when 3 thermal key points are selected based on the time characteristics) in embodiment 2 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to fig. 1 to 6 of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example (b):
as shown in fig. 1 and 2, the method for selecting and modeling the thermal key point of the spindle system of the numerical control machine tool based on the time characteristic comprises the following steps:
s1, collecting temperature data of each temperature measuring point under a standard rotating speed map, and sequencing the temperature data from small to large according to the time required for reaching the highest temperature, wherein the expression is as follows:
(1) in the formula: x is the number ofijIs the temperature at the ith measurement point at the jth minute, Int () is a rounding function, riIs the rank value of the ith measurement point, riThe larger the order, the less time is required for the ith measuring point to reach the highest temperature, and the higher the order is; for the point at which the highest temperature is reached at the same time, i.e. riThe same measuring points are sorted from large to small according to the temperature variation of the measuring points in the whole measuring time;
s2, classifying the temperature measuring points through a clustering method, selecting the points with high sequence as the thermal key points of each class according to the sequence in the step S1 for the temperature measuring points in each class, and selecting the thermal key points of each class according to the method to finally form the thermal key points of all the temperature measuring points;
and S3, taking the temperature data of the thermal key points selected by the method in the step S2 and the thermal error data corresponding to the temperature data as a training set, establishing a thermal error model by using a regression method, bringing the temperature data of the same thermal key points under a non-standard rotating speed map into the trained thermal error model, and predicting the thermal error.
Preferably, step S1 includes the following sub-steps,
s11, setting rotation speed maps in different running states, and ensuring that one rotation speed map is GB/T17421.3-2009 part 3 of machine tool inspection general rule: determination of thermal effect standard speed map specified in;
s12, the numerical control machine tool respectively operates according to the rotating speed map in the step S11, and when the numerical control machine tool operates, the temperature sensor and the displacement sensor simultaneously acquire corresponding data;
s13, acquiring a thermal error of a main shaft extension end of the main shaft system by using a displacement sensor, taking an average value of a period of time as a thermal error value at the moment, and enabling the displacement sensor to be in a zero setting state before the numerically-controlled machine tool operates;
and S14, acquiring the temperature of each point on the surface of the main shaft system and the ambient temperature at a certain distance from the main shaft system by using a temperature sensor, wherein the sampling frequency of temperature data is the same as the frequency obtained by averaging displacement data, and the temperature measuring points comprise measuring points which are not limited to positions close to front and rear bearings, ambient temperature measuring points and measuring points with other heat sources.
Preferably, the displacement sensor is a non-contact displacement sensor, and the temperature sensor is a contact temperature sensor.
Preferably, in step S12, the cnc machine is stationary for a period of time for cooling before operating according to the tachograph in step S11, respectively.
Preferably, the temperature data obtained in step S14 is a temperature data variation during the temperature sensor acquisition.
Preferably, the clustering method of step S2 adopts a fuzzy c-means clustering method.
Preferably, the implementation process of classifying the temperature measurement points by the fuzzy c-means clustering method in step S2 is as follows:
the objective function of fuzzy clustering is represented as:
(2) wherein c is the number of clusters, h is the fuzzy weight index, uijIs a temperature vector x formed by the temperature of the ith temperature measuring pointiMembership, d, belonging to the jth fuzzy classijIs a temperature vector xiDistance from the jth fuzzy class;
dij＝||xi-vj|| (3)
(3) in the formula, viIs the cluster center of the ith ambiguity class,
the classification process is as follows:
(4) in the formula (5), a clustering number c and a fuzzy weight index h are given;
b. randomly giving a membership matrix U;
c. calculating a clustering center matrix V;
d. calculating a membership matrix U;
e. repeating the steps c and d until the difference between the membership degree matrixes of the two times is less than the given minimum variation, namely | | | Ul +1-Ul| | < epsilon, or the iteration times have reached the maximum iteration times;
after the temperature measuring points are classified, the number of the classified categories of the temperature measuring points is the number of the thermal key points.
Preferably, the regression method adopted in step S3 is a support vector machine regression method.
Preferably, the specific method for establishing the thermal error regression model comprises the following steps:
the following regression function was constructed:
y＝f(X) (6)
(6) in the formula, X is a q-dimensional vector formed by the temperature of the thermal key point at any moment, q is the number of the thermal key points, and y is a thermal error value at the same moment;
the nonlinear support vector machine regression model can be expressed as:
(7) in the formula (I), the compound is shown in the specification,
is a coefficient of，xiAs a support vector, K (X, X)i) Is a kernel function;
selecting a Gaussian radial basis kernel function as a kernel function of a regression model of a support vector machine, wherein the expression is as follows:
K(X,Xi)＝exp(-||Xi-X||2/σ2)(8)
(8) wherein σ is a width parameter, and 1/σ is expressed2Is a nuclear parameter g;
taking a data set acquired under a standard rotating speed atlas as a training set to be brought into a support vector machine, and adopting a K classification cross validation method at 2-4～24And selecting a penalty coefficient C and a kernel function parameter g in the range.
Example 2:
on the basis of the embodiment 1, a numerical control indexable insert peripheral grinding machine spindle system is taken as an example.
(1) Temperature and thermal error data acquisition
And (4) setting up a temperature and thermal error measuring platform. The non-contact laser displacement sensor is used for collecting the axial thermal error of the extension end of the main shaft system, the sampling frequency is 1500Hz, and the average value of all sampling data in one minute is taken as the thermal error value at the moment. The PT100 magnetic-type temperature sensor is used for collecting the temperature of each point on the surface of the spindle system and the ambient temperature at a certain distance from the spindle system. The temperature data sampling frequency was 1/60 Hz.
The headstock surface temperature sensor arrangement is shown in fig. 3. The No. 1 sensor and the No. 4 sensor are respectively positioned on the surface of the spindle box and close to the front bearing and the rear bearing of the spindle; 2. the No. 3 sensors are uniformly distributed between the No. 1 and the No. 4 sensors; 5. sensors No. 6, 7 and 8 are respectively positioned at grooves on the surface of the spindle box below the sensors No. 1, 2, 3 and 4; the No. 9 sensor is positioned at the joint of the spindle box and the front end cover and is close to the front bearing; 10. the sensors 11, 12 and 13 are arranged at the joint of the spindle box and the base bolt; 14. the No. 15 sensor is positioned at two ends of a connecting flange of the spindle motor and the spindle box; and the No. 16 sensor is arranged at a certain distance from the spindle box and used for measuring the ambient temperature.
The thermal error experiment is carried out under 3 rotating speed maps in three days, and the temperature and the position of the displacement sensor are kept unchanged in the experimental process. The rotating speed spectrum A and the rotating speed spectrum B are standard rotating speed spectra, the running time is 270min totally, the machine is stopped and cooled for 90min after the running is finished, the maximum rotating speed of the rotating speed spectrum A is 3000r/min, and the maximum rotating speed of the rotating speed spectrum B is 2000 r/min. The rotating speed spectrum C is constant rotating speed 2000r/min, the running time is 240min totally, and the machine is stopped and cooled for 90min after the running is finished.
(2) Thermal key point selection
In order to prove the effectiveness of the thermal key point selection method, a method based on Pearson correlation coefficient sorting is selected for comparison.
1) Firstly, sorting 16 temperature measuring points acquired under a rotating speed map A by respectively utilizing a Pearson correlation coefficient method and a sorting method based on time characteristics.
The pearson correlation coefficient may be expressed as:
(9) in the formula, XiIs the temperature value of any temperature measuring point at the moment i, YiAre the thermal error values corresponding to the same time.
The data of 16 temperature measuring points acquired under the rotating speed map A are shown in figure 4. The results of the two sorting methods are shown in table 1, based on the temperature data.
TABLE 1 results of ranking
2) And classifying the 16 temperature measuring points by using a fuzzy c-means clustering method. The classification numbers are assigned to 3, 4, and 5, respectively. Taking fuzzy weight index m as 2, and membership degree minimum variation epsilon as 1e-6Maximum number of iterations 300.
3) Based on the sorting result of 1), selecting the point with the top sorting in each category of the sorting result of 2) as a thermal key point, wherein the sorting and point selecting results are shown in table 2.
TABLE 2 Classification and Point selection results
Figure 5 shows the stability of the time-based characteristic of the method for selecting points in the selection of the thermal error key points. In the point selection method based on the time characteristic, the thermal key points comprise 4 points, 9 points and 16 points when 3 points, 4 points and 5 points are taken, the 4 points and the 9 points are respectively close to the rear bearing and the front bearing, and the 16 points are ambient temperature measuring points.
(3) Thermal error modeling
The thermal key point temperature data and the thermal error data collected under the rotating speed map A, B, C respectively form a data set A, B, C. Wherein the first column of each data set is thermal error data and the remaining columns are temperature data. Data set a and data set B comprise 360 rows of data, and data set C comprises 330 rows of data. And training the support vector machine by taking the data set A as a training set.
Taking the prediction of the data set A under the time characteristic-based point selection method as an example, when the number of the thermal key points is 3, the penalty coefficient C selected by the cross validation is 20.5Kernel function parameter g 21.4142The ratio of the predicted value to the measured value is shown in fig. 6. The root mean square error between the predicted value and the measured value is used as an index for evaluating the modeling accuracy, and the root mean square error value is 0.44 μm.
The temperature data of the thermal key points selected by the two point selection methods are respectively utilized to perform thermal error modeling, the data set A is taken as a training set, the A itself, the data set B and the data set C are respectively predicted, the root mean square error between a predicted value and an actually measured value is taken as an index for evaluating modeling precision, and the prediction results are shown in Table 3.
As can be seen from table 3, when the thermal key points are 3, 4, and 5 respectively, and a is used as a training set pair A, B, C for 18 times of predictions in 9 groups, 8 groups of predictions use the root mean square error of time characteristic method for point selection to be smaller than the point selection using the correlation coefficient method, which proves the effectiveness and robustness of the time characteristic-based point selection method described in this patent.
TABLE 3 prediction accuracy (μm) of two point selection methods
In the description of the present invention, it is to be understood that the terms "counterclockwise", "clockwise", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate orientations or positional relationships based on those shown in the drawings, and are used for convenience of description only, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be considered as limiting.
Claims (9)
1. The method for selecting and modeling the thermal key points of the numerical control machine tool spindle system based on the time characteristics is characterized by comprising the following steps of:
s1, collecting temperature data of each temperature measuring point under a standard rotating speed map, and sequencing the temperature data from small to large according to the time required for reaching the highest temperature, wherein the expression is as follows:
(1) in the formula: x is the number ofijIs the temperature at the ith measurement point at the jth minute, Int () is a rounding function, riIs the rank value of the ith measurement point, riThe larger the order, the less time is required for the ith measuring point to reach the highest temperature, and the higher the order is; for the point at which the highest temperature is reached at the same time, i.e. riThe same measuring points are sorted from large to small according to the temperature variation of the measuring points in the whole measuring time;
s2, classifying the temperature measuring points through a clustering method, selecting the points with high sequence as the thermal key points of each class according to the sequence in the step S1 for the temperature measuring points in each class, and selecting the thermal key points of each class according to the method to finally form the thermal key points of all the temperature measuring points;
and S3, taking the temperature data of the thermal key points selected by the method in the step S2 and the thermal error data corresponding to the temperature data as a training set, establishing a thermal error model by using a regression method, bringing the temperature data of the same thermal key points under a non-standard rotating speed map into the trained thermal error model, and predicting the thermal error.
2. The method for modeling thermal key point selection for a numerically controlled machine tool spindle system according to claim 1, wherein step S1 includes the following sub-steps,
s11, setting rotation speed maps in different running states, and ensuring that one rotation speed map is GB/T17421.3-2009 part 3 of machine tool inspection general rule: determination of thermal effect standard speed map specified in;
s12, the numerical control machine tool respectively operates according to the rotating speed map in the step S11, and when the numerical control machine tool operates, the temperature sensor and the displacement sensor simultaneously acquire corresponding data;
s13, acquiring a thermal error of a main shaft extension end of the main shaft system by using a displacement sensor, taking an average value of a period of time as a thermal error value at the moment, and enabling the displacement sensor to be in a zero setting state before the numerically-controlled machine tool operates;
and S14, acquiring the temperature of each point on the surface of the main shaft system and the ambient temperature at a certain distance from the main shaft system by using a temperature sensor, wherein the sampling frequency of temperature data is the same as the frequency obtained by averaging displacement data, and the temperature measuring points comprise measuring points which are not limited to positions close to front and rear bearings, ambient temperature measuring points and measuring points with other heat sources.
3. The time characteristic-based modeling method for selecting thermal key points of a spindle system of a numerical control machine tool according to claim 2, wherein the displacement sensor is a non-contact displacement sensor, and the temperature sensor is a contact temperature sensor.
4. The method of claim 2, wherein the cnc machine is allowed to stand still for a period of time for cooling before operating according to the tachograph of step S11 in step S12.
5. The method for modeling selection of thermal key point of numerical control machine tool spindle system according to claim 2, wherein the temperature data obtained in step S14 is the variation of temperature data during the collection process of the temperature sensor.
6. The time characteristic-based modeling method for selecting thermal key points of the spindle system of the numerically-controlled machine tool according to claim 1, wherein the clustering method in step S2 is a fuzzy c-means clustering method.
7. The time characteristic-based method for selecting and modeling the thermal key points of the spindle system of the numerical control machine tool according to claim 6, wherein the fuzzy c-means clustering method in step S2 is implemented for classifying the temperature measuring points by the following steps:
the objective function of fuzzy clustering is represented as:
(2) wherein c is the number of clusters, h is the fuzzy weight index, uijIs a temperature vector x formed by the temperature of the ith temperature measuring pointiMembership, d, belonging to the jth fuzzy classijIs a temperature vector xiDistance from the jth fuzzy class;
dij＝||xi-vj|| (3)
(3) in the formula, viIs the cluster center of the ith ambiguity class,
the classification process is as follows:
(4) in the formula (5), a clustering number c and a fuzzy weight index h are given;
b. randomly giving a membership matrix U;
c. calculating a clustering center matrix V;
d. calculating a membership matrix U;
e. repeating the steps c and d until the difference between the membership degree matrixes of the two times is less than the given minimum variation, namely | | | Ul+1-Ul| | < epsilon, or the iteration times have reached the maximum iteration times;
after the temperature measuring points are classified, the number of the classified categories of the temperature measuring points is the number of the thermal key points.
8. The method for modeling selection of thermal key points of a numerical control machine tool spindle system based on time characteristics according to claim 1, wherein the regression method adopted in step S3 is a support vector machine regression method.
9. The time characteristic-based method for modeling and selecting the thermal key point of the spindle system of the numerical control machine tool according to claim 8, wherein the specific method for establishing the thermal error regression model is as follows:
the following regression function was constructed:
y＝f(X) (6)
(6) in the formula, X is a q-dimensional vector formed by the temperature of the thermal key point at any moment, q is the number of the thermal key points, and y is a thermal error value at the same moment;
the nonlinear support vector machine regression model can be expressed as:
(7) in the formula (I), the compound is shown in the specification,
is a coefficient, xiAs a support vector, K (X, X)i) Is a kernel function;
selecting a Gaussian radial basis kernel function as a kernel function of a regression model of a support vector machine, wherein the expression is as follows:
K(X,Xi)＝exp(-||Xi-X||2/σ2) (8)
(8) wherein σ is a width parameter, and 1/σ is expressed2Is a nuclear parameter g;
taking a data set acquired under a standard rotating speed atlas as a training set to be brought into a support vector machine, and adopting a K classification cross validation method at 2-4～24And selecting a penalty coefficient C and a kernel function parameter g in the range.
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