A numerical control machine tool thermal error prediction method

Abstract

The application discloses a kind of numerical control machine tool thermal error prediction method, it is related to precision machining machine tool field.The method comprises the following steps: measuring the positioning error of numerical control machine tool, obtaining positioning error curve;A plurality of temperature measuring points are set on the numerical control machine tool, the plurality of temperature measuring points are divided into different groups, the temperature measuring point with the maximum correlation coefficient of the thermal change slope of positioning error curve in each group is selected as temperature sensitive point;The temperature of temperature sensitive point is used as input, and the thermal change slope of positioning error curve is used as output, and the thermal error polynomial is established by using polynomial fitting.The application uses clustering method to divide temperature measuring point into different groups, by calculating the correlation coefficient between each group of temperature measuring point and the thermal change slope of positioning error curve, the temperature measuring point with the maximum correlation coefficient is used as temperature sensitive point, which is used for the fitting of thermal error polynomial, which helps the model to capture the close relationship between machine tool thermal error and temperature change, so that the model performance is higher, and more reliable.

Description

Technical Field

[0001] This invention relates to the field of precision machine tools, and in particular to a method for predicting thermal errors in CNC machine tools. Background Technology

[0002] With the rapid development of the manufacturing industry, machine tools, as the foundation of manufacturing, face higher demands on their processing speed and precision. Thermal error is a significant factor affecting machine tool processing performance, accounting for 40% to 70% of processing errors. Therefore, improving machine tool processing precision requires controlling its thermal error.

[0003] The main methods for controlling the thermal error of machine tools include: thermal error avoidance method and thermal error compensation method.

[0004] Thermal error avoidance methods control machine tool thermal errors by reducing the number of heat sources or lowering their heat output, increasing heat dissipation paths, and employing thermally stable structural designs. However, these methods cannot completely eliminate thermal errors during actual machining and are costly to implement. Thermal error compensation methods, on the other hand, artificially create new, reverse-direction errors through software input, weakening or even offsetting the original errors.

[0005] Thermal error compensation methods are further divided into theoretical modeling methods and experimental modeling methods. Theoretical modeling methods can clearly explain the generation process and mechanism of machine tool thermal errors, providing a basic model for empirical thermal error models and theoretical support for machine tool structural optimization. The main theoretical modeling methods include: finite difference method, finite element method, multibody system theory, and homogeneous coordinate transformation.

[0006] Experimental modeling methods require prior knowledge as a foundation to determine the model structure, identify identification methods, and design experimental procedures. The model only maps the mathematical relationship between input and output data, without addressing changes in the generation, conversion, and transfer of heat. Regression analysis, as one type of experimental modeling method, possesses good accuracy and robustness, and has proven effective in practical applications.

[0007] However, since the thermal error of a machine tool is usually closely related to the temperature change at a specific location, if temperature data from other unrelated locations is used to fit the regression model, more noise may be introduced, causing the obtained thermal error polynomial to fail to effectively capture the true change pattern of the machine tool's thermal error. This results in the prediction results of the CNC machine tool thermal error prediction model composed of the thermal error polynomial becoming inaccurate and the model's reliability being low. Summary of the Invention

[0008] This invention provides a method for predicting thermal errors in CNC machine tools, which can solve the problem of low prediction performance of existing CNC machine tool thermal error prediction models based on irrelevant temperature data.

[0009] This invention provides a method for predicting thermal errors in CNC machine tools, comprising:

[0010] The degree to which the machine tool deviates from the target machine tool position during operation is measured to obtain the positioning error, and the positioning error curve is obtained based on the positioning error.

[0011] Temperature data is collected from several temperature measuring points on a CNC machine tool. Based on the temperature data, a clustering algorithm is used to divide the temperature measuring points into different groups. The temperature measuring point with the largest correlation coefficient with the thermal change slope of the positioning error curve in each group is selected as the temperature sensitive point.

[0012] A thermal error prediction model is established for predicting thermal errors in CNC machine tools, including:

[0013] Using the temperature of the temperature-sensitive point as input and the thermal change slope of the positioning error curve as output, a thermal error polynomial is established using polynomial fitting.

[0014] The geometric error of the measuring machine tool is used as input, and the positioning error is used as output. A polynomial fitting is then used to establish the geometric error polynomial.

[0015] According to the separation modeling method, the coefficients of the geometric error term polynomial are replaced with the thermal error polynomial to obtain the CNC machine tool thermal error prediction model;

[0016] The temperature data of the temperature-sensitive points measured in real time are input into the CNC machine tool thermal error prediction model to obtain the thermal error of the CNC machine tool.

[0017] Furthermore, the acquisition of temperature data at several temperature measuring points on the CNC machine tool includes:

[0018] Based on the temperature sensor placement strategy, several temperature measuring points are arranged on the CNC machine tool;

[0019] Install a temperature sensor at each temperature measurement point;

[0020] The temperature of the measurement point is sampled continuously at intervals using a temperature sensor.

[0021] Furthermore, based on temperature data, a clustering algorithm is used to divide several temperature measurement points into different groups, including:

[0022] The Canopy clustering algorithm was used to perform coarse clustering of temperature measurement points to determine the number of clusters K and the initial cluster centers.

[0023] The number of clusters K and the initial cluster centers are used as inputs to the K-means clustering algorithm, which divides several temperature measurement points into different groups.

[0024] Furthermore, the coarse clustering of temperature measurement points using the Canopy clustering algorithm includes:

[0025] S11. Set the initial distance thresholds to T1 and T2, where T1 > T2;

[0026] S12. Take any temperature measuring point P, calculate the distance from the temperature measuring point P to all cluster centers, and determine the closest distance D between the temperature measuring point P and all cluster centers; if there is no cluster center, then take the temperature measuring point P as a new cluster.

[0027] S13. If the distance D is less than T1, it means that the temperature measuring point P belongs to the cluster to which the nearest cluster center belongs, and the temperature measuring point P is added to the cluster to which the nearest cluster center belongs.

[0028] S14. If the distance D is less than T2, it means that the temperature measuring point P not only belongs to the cluster to which its nearest cluster center belongs, but also that the temperature measuring point P is very close to the current cluster center point, so the temperature measuring point P is removed.

[0029] S15. If the distance D is greater than T1, then the temperature measuring point P forms a new cluster;

[0030] S16. Repeat S12-S15 until all temperature measurement points have been classified, then end the loop to obtain the number of clusters K and the initial cluster centers.

[0031] Furthermore, the K-means clustering algorithm is used to divide several temperature measurement points into different groups, including:

[0032] S21. Determine the number of clusters as K and the initial cluster centers as a = {a1, a2, ..., a3}. K};

[0033] S22. Calculate the distance from each temperature measuring point to the K cluster centers, and assign them to the class corresponding to the cluster center with the smallest distance;

[0034] S23. For each category, recalculate its cluster centers:

[0035]

[0036] Among them, a j It is the new cluster center, |c i | represents cluster c i The number of temperature measuring points in the cluster, where x represents the temperature value of the temperature measuring point belonging to this cluster;

[0037] S24. Repeat S22-S23 until the set termination condition is met, then stop the loop and divide the temperature measurement points into K groups.

[0038] Furthermore, selecting the temperature measurement point with the largest correlation coefficient with the thermal change slope of the positioning error curve in each group as the temperature sensitive point includes:

[0039] Calculate the correlation coefficient between the thermal change slope of each set of temperature measuring points and the positioning error curve:

[0040]

[0041] Where X represents the temperature value of each set of temperature measuring points, Y is the slope of the thermal change curve of the positioning error curve, and ρ X,Y The correlation coefficient;

[0042] The temperature measurement point with the highest correlation coefficient in each group was selected as the temperature sensitive point.

[0043] This invention provides a method for predicting thermal errors in CNC machine tools, which has the following advantages compared with the prior art:

[0044] This invention uses clustering to divide temperature measurement points into different groups. By calculating the correlation coefficient between each group of temperature measurement points and the thermal change slope of the positioning error curve, the temperature measurement point with the largest correlation coefficient is selected as the temperature sensitive point. The temperature sensitive point selected by the above method has the largest correlation coefficient with the thermal change slope of the positioning error curve, indicating the strongest correlation between the two. This correlation may reflect the main influencing factors of machine tool thermal error, thus the selected temperature sensitive point is more likely to have practical physical significance and representativeness. Therefore, using it as input to the thermal error polynomial in the CNC machine tool error prediction model helps the model capture the close relationship between machine tool thermal error and temperature change. This allows the CNC machine tool thermal error prediction model, composed of the thermal error polynomial and the geometric error polynomial, to more accurately predict the changing trend of machine tool thermal error and achieve higher predictive performance. Attached Figure Description

[0045] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0046] In the attached diagram:

[0047] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0048] Figure 2 This refers to the sensor installation location in an embodiment of the present invention;

[0049] Figure 3 This is a positioning error curve measured according to an embodiment of the present invention;

[0050] Figure 4 This is a temperature distribution curve obtained from an embodiment of the present invention;

[0051] Figure 5 The embodiment of this invention is a thermal error polynomial fitting curve. Detailed Implementation

[0052] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. However, it should be understood that the scope of protection of the present invention is not limited to the specific implementation.

[0053] Example 1

[0054] like Figure 1 As shown, a method for predicting thermal errors in CNC machine tools specifically includes the following steps;

[0055] Step 1: Measure the positioning error of the machine tool under different temperature conditions and obtain the positioning error curve.

[0056] Step 2: Obtain the geometric error polynomial:

[0057] The geometric error of the machine tool is measured using a laser interferometer. The geometric error is used as input and the positioning error is used as output. A polynomial fitting is then used to establish the geometric error polynomial.

[0058] Step 3: Obtain the thermal error polynomial, including:

[0059] Step 3.1: Based on the temperature sensor placement strategy, determine several temperature measurement points on the CNC machine tool. Then, install a temperature sensor at each temperature measurement point and use the temperature sensor to continuously sample the temperature at the measurement point at intervals to obtain the dataset L.

[0060] L = {X1, ..., X} i , ..., X m} (1)

[0061] X i ={x i1 , ..., x ij , ..., x in} (2)

[0062] Among them, X1~X m There are m temperature measuring points arranged, x i1 ~x in It represents the temperature data measured at n intervals from the i-th temperature measuring point.

[0063] Step 3.2: Based on temperature data from several temperature measurement points, use the Canopy clustering algorithm to perform "coarse clustering" on these points, obtaining the number of clusters K and the initial cluster centers. The clustering results from the Canopy algorithm can be used to obtain the number of clusters K and the initial cluster centers for subsequent K-means clustering, which helps accelerate the convergence process and improve clustering efficiency. Specifically, this includes the following steps:

[0064] Step 3.2.1: Set the initial distance thresholds to T1 and T2, where T1 > T2;

[0065] Step 3.2.2: Select any temperature measurement point P from the dataset L, calculate the distance from P to all cluster centers, and select the distance D closest to the cluster center; if there is no cluster center, then take point P as a new cluster.

[0066] Step 3.2.3: If the distance D is less than T1, it means that the temperature measuring point P belongs to the cluster to which the nearest cluster center belongs, and it is added to the list of that cluster.

[0067] Step 3.2.4: If the distance D is less than T2, it means that the temperature measuring point P not only belongs to the cluster to which its nearest cluster center belongs, but also that the temperature measuring point P is very close to the current cluster center. Therefore, P is removed from the dataset L.

[0068] Step 3.2.5: If the distance D is greater than T1, then the temperature measuring point P forms a new cluster;

[0069] Step 3.2.6: Repeat steps 3.2.2-3.2.5 until the dataset L is empty, then end the loop to obtain the number of clusters K and the initial cluster centers.

[0070] Step 3.3: Input the initial cluster centers obtained in Step 3.2 into the K-means clustering algorithm for "fine-grained clustering". Specifically, this includes:

[0071] Step 3.3.1: Determine the number of clusters as K, and the initial cluster centers as a = {a1, a2, ..., a...} K};

[0072] Step 3.3.2: Calculate the distance from each temperature measuring point to the K cluster centers, and assign them to the class corresponding to the cluster center with the smallest distance;

[0073] Step 3.3.3: For each category, recalculate its cluster centers:

[0074]

[0075] Among them, a j It is the new cluster center, |ci | represents cluster c i The number of temperature measuring points in the cluster, where x represents the temperature value of the temperature measuring point belonging to this cluster;

[0076] Step 3.3.4: Repeat steps 3.3.2-3.3.3 until the termination condition is met to obtain the K-group clustering results.

[0077] Step 3.4: Determine the temperature-sensitive points based on the correlation coefficient between each group of temperature measurement points and the thermal change slope of the positioning error curve. The selected temperature-sensitive points have the highest correlation coefficient with the thermal change slope of the positioning error curve, indicating the strongest correlation between the two. This correlation is likely to reflect the main influencing factors of machine tool thermal error, therefore, the selected temperature-sensitive points are more likely to have practical physical significance. Specifically, this includes:

[0078] Step 3.4.1: Calculate the correlation coefficient between the thermal change slope of each group of temperature measuring points and the positioning error curve, as shown in the following formula:

[0079]

[0080] Where X represents the temperature value of each set of temperature measuring points, Y is the slope of the thermal change curve of the positioning error curve, and ρ X,Y The correlation coefficient.

[0081] Step 3.4.2: Select the temperature variable with the largest correlation coefficient as the temperature sensitive point.

[0082] Step 3.5: Using the temperature of the temperature-sensitive point as input and the slope of the thermal change of the positioning error curve as output, a thermal error polynomial is established using polynomial fitting.

[0083] Step 4: Based on the separation modeling method, combine the thermal error polynomial with the geometric error term polynomial to obtain the CNC machine tool thermal error prediction model.

[0084] Example 2

[0085] Experimental simulation

[0086] The measurement experiment in this embodiment was conducted on a self-developed triaxial experimental platform. A schematic diagram of the experimental platform and the sensor installation locations are shown below. Figure 2 As shown.

[0087] According to the temperature sensor placement strategy, 11 PT100 platinum resistance temperature sensors were initially installed on the machine tool. An XSR90 recorder was used to collect the temperature distribution of the machine tool in real time, and the temperature values ​​of the machine tool heat source and the surrounding environment were sampled at intervals. A Renishaw XL-80 laser interferometer was used to measure the positioning error of the linear axis Y under different temperature conditions. Specifically, the Y-axis positioning error was measured bidirectionally at 10mm intervals over a 280mm travel range. Geometric error was measured when the machine tool transitioned from a power-off state to a power-on state. Then, the Y-axis was moved over the entire travel range at a speed of 20mm / s and an acceleration of 10mm / s² to heat the machine tool. The Y-axis positioning error was measured after 20, 50, 110, 190, 240, 340, and 390 minutes of operation until the machine tool reached thermal equilibrium. The measured positioning error curve and temperature distribution curve are shown below. Figure 3 , Figure 4 As shown.

[0088] In this embodiment, 11 temperature measurement points were set up, and the temperature distribution was measured every 10 minutes, resulting in 40×11 dimensional experimental data. First, the Canopy clustering algorithm was used for "coarse clustering" to determine the number of clusters K=2 and the initial cluster centers. Then, the initial cluster centers were input into the K-means clustering algorithm for "fine clustering," and the final clustering results are shown in Table 1 below.

[0089] Table 1. Canopy-K-means clustering results

[0090]

[0091] The obtained clustering results were filtered, and the temperature variable with the largest correlation coefficient with the thermal change slope of the positioning error curve in each group was selected as the temperature sensitive point. A first-order polynomial was fitted to the positioning error to obtain the thermal change slope of the positioning error curve at minutes 0, 20, 60, 120, 210, 240, 340, and 390, as shown in Table 2.

[0092] Table 2. Slope of thermal change curve for positioning error

[0093]

[0094]

[0095] The slope of the thermal change of the positioning error curve at minutes 0, 20, 60, 120, 210, 240, 340, and 390 was calculated and the Pearson correlation coefficient of the thermal error was obtained. The results are shown in Table 3.

[0096] Table 3. Calculation results of correlation coefficients

[0097]

[0098] Based on the ranking of correlation coefficients, T1 and T5 were selected as the optimal temperature sensitive points.

[0099] A 5th-order polynomial is selected to fit the geometric error to obtain the geometric error polynomial, whose expression is:

[0100] δ yy (Y) = -0.48119y - 0.01246y 2 +1.36575×10 -4 y 3 -4.99795×10 -7 y 4 +6.19125×10 -10 y 5

[0101] The slope of the established thermal change and the thermal error polynomial at the selected temperature-sensitive point:

[0102] K i =0.00429T1+0.04071T5-1.19986

[0103] Based on the separation modeling method of positioning error, the geometric error polynomial and the thermal error polynomial mentioned above are combined to obtain the comprehensive positioning error, i.e., the CNC machine tool error prediction model:

[0104] δ yy (Y,T)=(0.00429T1+0.04071T5-1.28584)y-0.01246y 2 +1.36575×10 -4 y 3 -4.99795×10 -7 y 4 +6.19125×10 -10 y 5

[0105] The fitted curve of the constructed multiple linear regression thermal error model is as follows: Figure 5 As shown.

[0106] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for predicting thermal errors in CNC machine tools, characterized in that, include: The degree to which the machine tool deviates from the target machine tool position during operation is measured to obtain the positioning error, and the positioning error curve is obtained based on the positioning error. Collect temperature data at several temperature measurement points on a CNC machine tool, including: arranging several temperature measurement points on the CNC machine tool according to a temperature sensor placement strategy; installing a temperature sensor at the location of each temperature measurement point; and continuously sampling the temperature at the temperature measurement points using the temperature sensors at intervals. Based on temperature data, a clustering algorithm is used to divide several temperature measurement points into different groups, including: using the Canopy clustering algorithm to perform coarse clustering of the temperature measurement points to determine the number of clusters K and the initial cluster centers; using the number of clusters K and the initial cluster centers as input to the K-means clustering algorithm to divide the several temperature measurement points into different groups. The temperature measuring point with the largest correlation coefficient with the thermal change slope of the positioning error curve in each group was selected as the temperature sensitive point. A thermal error prediction model is established for predicting thermal errors in CNC machine tools, including: Using the temperature of the temperature-sensitive point as input and the thermal change slope of the positioning error curve as output, a thermal error polynomial is established using polynomial fitting. The geometric error of the measuring machine tool is used as input, and the positioning error is used as output. A polynomial fitting is then used to establish the geometric error polynomial. According to the separation modeling method, the coefficients of the geometric error polynomial are replaced with the thermal error polynomial to obtain the CNC machine tool thermal error prediction model; The temperature data of the temperature-sensitive points measured in real time are input into the CNC machine tool thermal error prediction model to obtain the thermal error of the CNC machine tool.

2. The method for predicting thermal errors in CNC machine tools according to claim 1, characterized in that, The coarse clustering of temperature measurement points using the Canopy clustering algorithm includes: S11. Set the initial distance threshold as... T1, T2 , T1 > T2 ; S1 2. Select any temperature measuring point. P Calculate the temperature at this measuring point. P Determine the distance to all cluster centers, and the closest distance D between the temperature measuring point P and all cluster centers; If no cluster center exists, then the temperature measurement point P is considered a new cluster. S13. If the distance D is less than T1, it means that the temperature measuring point P belongs to the cluster to which the nearest cluster center belongs, and the temperature measuring point P is added to the cluster to which the nearest cluster center belongs. S14. If the distance D Less than T2 This indicates the temperature measuring point. P It not only belongs to the cluster to which its nearest cluster center belongs, but also indicates the temperature measuring point. P Since it is very close to the current cluster center, this temperature measurement point P is excluded. S15. If the distance D Greater than T1 Then the temperature measuring point P A new cluster is formed; S16. Repeat S12-S15 until all temperature measurement points have been classified, then end the loop to obtain the number of clusters K and the initial cluster centers.

3. The method for predicting thermal errors in CNC machine tools according to claim 2, characterized in that, The K-means clustering algorithm is used to divide several temperature measurement points into different groups, including: S21. Determine the number of clusters as K and the initial cluster centers as... a ={ a1 , a2 ,..., aK }; S22. Calculate the distance from each temperature measuring point to the K cluster centers, and assign them to the class corresponding to the cluster center with the smallest distance; S23. For each category, recalculate its cluster centers: in, It is a new cluster center. Cluster The number of temperature measuring points in the middle This indicates the temperature value of the temperature measurement point belonging to this cluster; S24. Repeat S22-S23 until the set termination condition is met, then stop the loop and divide the temperature measurement points into K groups.

4. The method for predicting thermal errors in CNC machine tools according to claim 1, characterized in that, The temperature measuring points with the largest correlation coefficient with the thermal change slope of the positioning error curve in each group are selected as temperature sensitive points, including: Calculate the correlation coefficient between the thermal change slope of each set of temperature measuring points and the positioning error curve: Where X represents the temperature value of each set of temperature measurement points, and Y is the slope of the thermal change curve of the positioning error curve. The correlation coefficient; The temperature measurement point with the highest correlation coefficient in each group was selected as the temperature sensitive point.

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