Machine tool cutting stability prediction method based on similarity measurement and semi-supervised learning

Abstract

The invention relates to the technical field of machine tool dynamics and machine tool machining, in particular to a machine tool cutting stability prediction method based on similarity measurement and semi-supervised learning. The method comprises the following steps: firstly, selecting machining positions by adopting an orthogonal experimental design method, dividing the selected machining positions into a plurality of clusters, and sorting the machining positions in each cluster; according to the set sample label rate, part of machining positions are selected for a hammering experiment, and the limit cutting depth is calculated. Then, a pseudo label is generated for the unmarked processing position by using a K-nearest neighbor thought; then, a multi-layer perceptron is adopted as a prediction model, and a composite loss function is designed; and finally, training the model by using the true-false mixed sample set, and evaluating the performance of the model. According to the method, the high precision of the prediction model can be ensured while the required hammering test times can be remarkably reduced, so that the experiment cost and the time consumption are greatly reduced.

Description

Technical Field

[0001] This invention relates to the fields of machine tool dynamics and machine tool machining technology, and in particular to a method for predicting machine tool cutting stability based on similarity metric and semi-supervised learning. Background Technology

[0002] During milling, the machining system is susceptible to periodic chatter caused by internal excitation between the tool, workpiece, and machine tool, especially for milling cutters with a large length-to-diameter ratio. This chatter phenomenon not only severely degrades the surface quality of the workpiece and limits the improvement of machining efficiency, but also accelerates tool wear and increases production costs.

[0003] Stability lobe diagrams are tools for predicting and avoiding chatter by optimizing parameters to improve machining quality and efficiency. The tool tip frequency response function (FRF), a key parameter reflecting the tool-workpiece vibration characteristics, is an indispensable input for solving stability lobe diagrams. Currently, the main methods for obtaining the tool tip FRF include finite element simulation and impact testing. However, in actual machining, the positions of various moving parts of the machine tool are time-varying to accommodate the relative motion between the tool and workpiece, causing changes in the machine tool's spatial structure and affecting the distribution of the overall stiffness and damping matrices. This alters the tool tip FRF and further impacts cutting stability. Therefore, to correct the stability lobe diagram at different machining positions, impact testing or finite element simulation is required at each new position, significantly increasing time and economic costs. To address this issue, some researchers have attempted to combine impact testing, finite element simulation, and surrogate modeling techniques to predict the tool tip modal parameters and cutting stability within the machining space. For example, Huang Hua et al. selected key locations as input sample points and used response surface methodology to establish a prediction model for the minimum critical depth of cut; Ye Songtao et al. used a nonlinear least squares weighted superposition method to predict the tool tip FRF at arbitrary machining poses in the workspace. These methods improve prediction efficiency to some extent, but repeated experiments or simulations are still needed at a large number of machining locations to obtain sufficient training samples to ensure prediction accuracy.

[0004] Transfer learning and semi-supervised learning offer new approaches to constructing surrogate models in scenarios with few samples. For example, Chen et al. used the TrAdaBoost.R2 algorithm to predict position-related modal parameters of the tool-holder combination under few samples; Shen Zedong et al. proposed a multi-source transfer learning algorithm based on the transfer kernel function of Gaussian process regression to predict tool tip modal parameters under different poses. However, both of these methods are limited to considering only the angular changes of the spindle head rotation axis, and constructing a source domain model with high accuracy still requires a large amount of labeled data. Therefore, how to achieve high-precision prediction of cutting stability in the machine tool workspace under conditions with few samples has become a core technical problem that urgently needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a machine tool cutting stability prediction method based on similarity measurement and semi-supervised learning. This method can significantly reduce the number of hammer tests required while ensuring high accuracy of the prediction model, thereby greatly reducing experimental costs and time consumption.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A machine tool cutting stability prediction method based on similarity metric and semi-supervised learning includes the following steps: Step 1: Select multiple machining positions from the machine tool workspace, divide the machining positions into multiple clusters based on the K-means clustering algorithm, and sort the machining positions within the clusters based on the distance metric. Step 2: Based on the set sample label rate, select multiple representative machining positions within the cluster and conduct hammer impact experiments on the representative machining positions to obtain the tool tip frequency response function (FRF). Calculate the limiting depth of cut under different combinations of spindle speed and cutting width. Combine the representative machining positions, spindle speed, cutting width, and limiting depth of cut to construct a real sample set. The limiting cutting depth ; In the formula, The tangential cutting force coefficient is... This refers to the number of teeth on the cutting tool. and The real and imaginary parts of the eigenvalue Λ calculated based on the vibration characteristics of the workpiece-tool system; Step 3: Based on the K-nearest neighbor concept, obtain the limit cutting depth of the unselected machining position within each cluster, and construct a pseudo sample set using the predicted limit cutting depth; Step 4: Mix the real sample set and pseudo sample set under each sample label rate to form a real-pseudo sample mixed training set, and use the real sample set of all processing positions as the test set. Use the real-pseudo sample mixed training set to train the semi-supervised prediction model built with multilayer perceptron, and use the test set to test the trained semi-supervised prediction model to obtain the cutting stability prediction model. Input the machining position, spindle speed, and cutting width, predict the ultimate cutting depth based on the cutting stability prediction model, and evaluate the machine tool stability through the ultimate cutting depth.

[0007] Furthermore, selecting multiple machining positions from the machine tool workspace refers to selecting multiple machining positions from the machine tool workspace based on the orthogonal experimental design method, with the displacement of each motion axis of the machine tool as the design variable.

[0008] Furthermore, the processing locations within the clusters are sorted based on distance metrics, including: maximizing the similarity within clusters and the separation between clusters, calculating the Euclidean distance between each pair of processing locations within each cluster, obtaining the sum of the distances between each processing location and the remaining processing locations within the cluster, and sorting the processing locations within the clusters in descending order of the sum value.

[0009] Furthermore, the processing location is divided into multiple clusters based on the K-means clustering algorithm, and the number of clusters is determined by the silhouette coefficient method.

[0010] Furthermore, based on the sample label rate, multiple representative processing positions are selected within each cluster, including: multiplying the sample label rate and the number of processing positions within each cluster and taking the integer part to obtain the number of representative processing positions, with the processing positions ranked first within the cluster being the representative processing positions.

[0011] Furthermore, based on the K-nearest neighbor concept, the limit cutting depth of the unselected machining position within each cluster is obtained, including: setting a nearest neighbor screening coefficient, multiplying the nearest neighbor screening coefficient by the number of representative machining positions within the cluster and rounding down to determine the number of nearest neighbor machining positions, calculating the Euclidean distance between the unselected machining position and the representative machining position, sorting the Euclidean distance values ​​in descending order, selecting the representative machining position with the highest number of nearest neighbor machining positions as the nearest neighbor machining position of the unselected machining position, and using the average limit cutting depth of multiple nearest neighbor machining positions under the same spindle speed and cutting width combination as the predicted limit cutting depth of the unselected machining position.

[0012] Furthermore, the loss function of the semi-supervised prediction model during training , For the loss of the real sample set, For pseudo-sample set loss, The pseudo-sample loss weight coefficient is used. Both the real sample set loss and the pseudo-sample set loss are obtained through mean squared error (SSE).

[0013] Furthermore, the semi-supervised prediction model uses the mean absolute percentage error (MAPE) to evaluate the model's prediction accuracy during testing.

[0014] The beneficial effects of this invention are as follows: by using a semi-supervised learning framework based on similarity metrics, the required number of hammer tests is significantly reduced while ensuring the high accuracy of the prediction model, thereby greatly reducing experimental costs and time consumption.

[0015] Representative sample intelligent selection mechanism: Through clustering and similarity assessment, the most representative small number of processing locations are actively selected for hammering tests to maximize the value of limited experimental information and reduce the amount of labeled data required from the source.

[0016] A method for generating pseudo-labels for unlabeled data: Based on the strategy of proximity similarity, pseudo-labels for the ultimate cutting depth are generated for a large number of unlabeled machining locations using a small amount of labeled data, effectively expanding the training dataset.

[0017] A composite semi-supervised prediction model fusing real and pseudo labels: The construction of a semi-supervised prediction model and the training of a model based on a composite loss function fuse real and pseudo labels, which improves prediction accuracy under the condition of scarce labeled data and enhances the generalization ability of the model. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0019] 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. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0020] This embodiment discloses a machine tool cutting stability prediction method based on similarity measurement and semi-supervised learning, which includes the following steps: Step 1: Select multiple machining positions from the machine tool workspace based on the orthogonal experimental design method, divide the selected machining positions into multiple clusters based on the K-means clustering algorithm, and sort the machining positions within each cluster based on the distance metric.

[0021] Using the displacement of each motion axis of the machine tool as the design variable, an orthogonal experimental design method is used to plan the experimental scheme, and N machining positions are selected from the entire workspace of the machine tool.

[0022] The K-means clustering algorithm is used to divide the N processing locations into C clusters, and the number of clusters C is determined by the silhouette coefficient method.

[0023] To maximize intra-class similarity and inter-class separation, the Euclidean distance between each pair of processing positions is calculated within each cluster. The sum of the distances between each processing position and the remaining processing positions within the same cluster is obtained, and the processing positions within the cluster are sorted in descending order of the sum.

[0024] Step 2: Based on the set sample label rate, select multiple representative machining positions within each cluster and conduct hammer impact experiments on the representative machining positions to obtain the tool tip frequency response function (FRF) and calculate the limiting depth of cut under different combinations of spindle speed and cutting width; combine the representative machining positions, spindle speed, cutting width, and limiting depth of cut to construct a real sample set.

[0025] The sample labeling rate R ranges from 0 to 1. The closer R is to 0, the fewer samples are available for training, and vice versa.

[0026] The number of representative machining positions S (S<M) is obtained by multiplying the sample label rate R and the number of machining positions M (M<N) in each cluster and taking the integer part. The first S machining positions after sorting in each cluster are selected as representative machining positions, and a hammer impact experiment is performed on the representative machining positions to obtain the tool tip frequency response function FRF. The limit cutting depth under different spindle speed and cutting width combinations is calculated based on the stability theory analytical method.

[0027] The limiting cutting depth ; In the formula, The tangential cutting force coefficient is... This refers to the number of teeth on the cutting tool. and Let G(iω) be the real and imaginary parts of the eigenvalue Λ calculated based on the vibration characteristics of the workpiece-tool system. If the workpiece stiffness is significantly higher than that of the tool, the vibration characteristics of the workpiece-tool system G(iω) are... c It can be simplified to the knife-tip frequency response function FRF.

[0028] By marking the limiting depth of cut and corresponding machining positions under different combinations of spindle speed and cutting width, a real-world sample is constructed. ,in, For a representative machining location, n is the spindle speed. For cutting width, This represents the ultimate cutting depth.

[0029] Step 3: Based on the K-nearest neighbor concept, obtain the limit cutting depth of the unselected machining position within each cluster, and construct a pseudo sample set using the predicted limit cutting depth.

[0030] A nearest neighbor selection coefficient is set. The number of nearest neighbor machining positions J is determined by multiplying the nearest neighbor selection coefficient by the number of representative machining positions S in each cluster and rounding down. The Euclidean distance between the unselected machining positions and the selected machining positions is calculated. The positions are sorted in descending order of Euclidean distance values. The top J representative machining positions after sorting are taken as the nearest neighbor machining positions of the unselected machining positions. The average of the limiting cutting depths of the J nearest neighbor machining positions under the same spindle speed and cutting width combination is taken as the predicted limiting cutting depth of the unselected machining positions. Using this predicted limit cutting depth The spindle speed and cutting width markers were not selected for the construction of pseudo-samples at the machining location.

[0031] Step 4: Mix the real sample set and pseudo sample set under each sample label rate to form a real-pseudo sample mixed training set, and use the real sample set of all processing positions as the test set. Use the real-pseudo sample mixed training set to train the semi-supervised prediction model established by multilayer perceptron, and use the test set to test the trained semi-supervised prediction model to obtain the cutting stability prediction model.

[0032] The composite loss function , For the loss of the real sample set, For pseudo-sample set loss, The pseudo-sample loss weight coefficient is used. Both the real sample set loss and the pseudo-sample set loss are obtained through mean squared error (SSE).

[0033] Design the number of hidden layers and neurons in a multilayer perceptron, define hyperparameters such as learning rate, activation function, and optimizer, and train the multilayer perceptron using a real-sham mixed sample set until the model loss function converges.

[0034] Using the mean absolute percentage error (MAPE) as the evaluation index, the performance of the established limit cutting depth prediction model is evaluated using a test set. The validated multilayer perceptron model can then be used to predict the cutting stability of new machining positions and obtain the corresponding limit cutting depth values.

[0035] Taking a vertical machining center as an example, the displacement strokes of its moving parts in the x, y, and z directions are 0~750mm, 0~460mm, and 0~460mm, respectively, to verify the method described in this embodiment.

[0036] (1) Sixty-four processing positions were selected using the orthogonal experimental design method, and eight levels were selected for displacement in each direction. The three-factor eight-level table shown in Table 1 was planned.

[0037] Table 1. Processing positions selected based on orthogonal experimental design method

[0038] (2) The K-means clustering algorithm was used to analyze the clusters of the 64 processing locations. The number of clusters varied between 4 and 10. When the number of clusters was equal to 6, the silhouette coefficient had a maximum value of 0.48. Therefore, in this embodiment, the 64 processing locations were divided into 6 clusters. Then, the Euclidean distance between any processing location and all the remaining processing locations was calculated in each cluster. The processing locations were sorted according to the sum of the distances, as shown in Table 2. Table 2 lists the processing location numbers contained in each cluster, and their values ​​correspond to the orthogonal experimental scheme numbers in Table 1.

[0039] Table 2 shows the processing positions of each cluster after sorting.

[0040] (3) With the sample labeling rate R set to 0.5, the number of processing positions selected for each cluster are 5, 6, 5, 6, 6, and 6 respectively. The specific processing positions are shown in bold in Table 2. The frequency response function (FRF) of the tool tip is obtained by hammer impact test for the selected processing positions, and its limit cutting depth is calculated.

[0041] The spindle speed is set to a range of 2000~8000 rpm based on the machine tool power, combined with the tool cutting width. The variation range is 3~12mm. Using 200rpm as the interval for discrete spindle speed variation, and selecting 10 cutting widths through Latin hypercube experimental design, 33×10=330 {n,} are obtained for each machining position. The combined limit of cutting depth Based on the sample labeling rate, 34 processing locations were selected (5+6+5+6+6+6), resulting in a total of 34×330=11220 known real sample sets.

[0042] (4) For each unselected processing position in each cluster (not bolded in Table 2), calculate its Euclidean distance to all marked processing positions within the cluster and sort them. Set the nearest neighbor selection coefficient of the K-nearest neighbor idea to 0.5. Multiply this coefficient by the total number of currently marked positions and round down to obtain the number of nearest neighbors. Select the corresponding nearest neighbor processing positions according to the sorting and mark them with the same {n, a e Combined Limiting Depth of Cut The average value is used as the pseudo-label for the currently unmarked processing location. This results in a pseudo-sample set of (64-34)×330=9900 sets of data.

[0043] (5) Use 11220+9900=21120 sets of real-pseudo sample mixes of real sample sets and pseudo sample sets of 64 processing positions as the training set, and use 11220 sets of real sample sets calculated from 34 processing positions as the test set.

[0044] The semi-supervised prediction model uses a five-layer perceptron. The network architecture includes five input units, three sequentially connected hidden layers (each with 40 neurons and ReLU activation function), and one output unit (ReLU activation).

[0045] The model was trained using the Adam algorithm with an initial learning rate of 0.01, and loss weights α=0.8 were assigned to the spurious samples in the training set. The model's predictive performance was quantified by its mean absolute percentage error (MAPE) on the test set. At R=0.5, the MAPE reached a relatively small value of 7.82%, indicating that the established predictive model can predict the limit depth of cut at any machining position quite well.

[0046] To verify the effectiveness of the proposed method under limited sample conditions, a multilayer perceptron model was established as Model_1, and three additional comparative models, Model_1, Model_3, and Model_4, were designed.

[0047] Model_2 is a multilayer perceptron prediction model trained using labeled real samples; Model_3 involves randomly selecting the machining location to be marked in the machine tool workspace, and then using the proposed method to construct a true-false mixed sample set to train the multilayer perceptron prediction model. Model_4 uses XGBoost, an extreme gradient boosting tree suitable for small sample problems, as the regression learner, and trains the prediction model using a mixture of true and false samples, consistent with this embodiment.

[0048] Table 3 lists the MAPE values ​​calculated on the test set for each comparative model under different sample label rates R, from which we can conclude: 1. The MAPE value of Model_1 is lower than that of Model_2 at the same scale, indicating that the pseudo-sample construction method and the true-pseudo hybrid training mechanism proposed in this invention effectively improve the model accuracy. 2. The MAPE values ​​of Model_1 are all lower than those of Model_3 at the same ratio, which verifies that the sample labeling strategy proposed in this invention is more advantageous than the completely random point selection strategy under the true-false hybrid training framework. 3. The MAPE values ​​of Model_1 are all lower than those of Model_4, indicating that compared with the extreme gradient boosting tree XGBoost, the multilayer perceptron can better learn the complex mapping relationship between machining position and limit cutting depth.

[0049] Table 3 Comparison of prediction performance of different models under different labeling rates

[0050] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A machine tool cutting stability prediction method based on similarity measure and semi-supervised learning, characterized by, The method comprises the following steps: Step 1: selecting a plurality of machining positions from a machine tool workspace, dividing the machining positions into a plurality of cluster groups based on a K-means clustering algorithm, and sorting the machining positions in the cluster groups based on a distance metric; Step 2: setting a sample label rate, selecting a plurality of representative machining positions in the cluster groups based on the sample label rate, and performing a hammering experiment on the representative machining positions to obtain a tool tip point frequency response function FRF and calculate a limit cutting depth under different spindle speed and cutting width combinations; and combining the representative machining positions, spindle speed, cutting width and limit cutting depth to construct a real sample set; the limit cutting depth ; wherein is the tangential cutting force coefficient, is the number of tool teeth, and are the real and imaginary parts of the eigenvalue Λ calculated from the workpiece-tool system vibration characteristics; Step 3: obtaining the limit cutting depth of unselected machining positions in each cluster group based on the K-nearest neighbor idea, and constructing a pseudo sample set using the predicted limit cutting depth; Step 4: mixing the real sample set and the pseudo sample set under each sample label rate into a real-pseudo sample mixed training set, using the real sample set of all machining positions as a test set, training a semi-supervised prediction model established by using a multilayer perceptron using the real-pseudo sample mixed training set, testing the trained semi-supervised prediction model using the test set, and obtaining a cutting stability prediction model; Inputting a machining position, a spindle speed and a cutting width, predicting a limit cutting depth based on the cutting stability prediction model, and evaluating the stability of the machine tool through the limit cutting depth.

2. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 1, characterized in that, Selecting a plurality of machining positions from a machine tool workspace refers to selecting a plurality of machining positions from a machine tool workspace based on orthogonal experimental design method with machine tool motion axis displacement as design variable.

3. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 2, characterized in that, Sorting the machining positions in the cluster groups based on a distance metric includes maximizing the similarity within the cluster group and the separation between the cluster groups, calculating the Euclidean distance between each pair of machining positions within each cluster group, obtaining the sum of the distances between each machining position and the remaining machining positions in the cluster group, and arranging the machining positions in the cluster group in descending order according to the sum value.

4. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 1, characterized in that, The machining positions are divided into a plurality of cluster groups based on the K-means clustering algorithm, and the number of cluster groups is determined by the silhouette coefficient method.

5. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 3, characterized in that, Selecting a plurality of representative machining positions in each cluster group based on a sample label rate includes multiplying the sample label rate by the number of machining positions in each cluster group to obtain the number of representative machining positions, and selecting the machining positions in the front of the cluster group as the representative machining positions.

6. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 1, characterized in that, Based on the K-nearest neighbor idea, the limit cutting depth of unselected machining positions in each cluster group is obtained, including setting a neighbor screening coefficient, multiplying the neighbor screening coefficient by the number of representative machining positions in the cluster group to determine the number of neighbor machining positions, calculating the Euclidean distance between the unselected machining positions and the representative machining positions, sorting the Euclidean distance values in descending order, selecting the representative machining positions in the front as the neighbor machining positions of the unselected machining positions, and averaging the limit cutting depths of the plurality of neighbor machining positions under the same spindle speed and cutting width combination to obtain the predicted limit cutting depth of the unselected machining position.

7. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 1, characterized in that, The loss function of the semi-supervised prediction model during training is , is the real sample set loss, is the pseudo sample set loss, is a pseudo sample loss weight coefficient, and the real sample set loss and the pseudo sample set loss are obtained by a sum of squared errors (SSE).

8. The machine tool cutting stability prediction method based on similarity measure and semi-supervised learning according to claim 1, characterized in that, The semi-supervised prediction model uses the mean absolute percentage error MAPE to evaluate the prediction accuracy of the model when testing.

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