A method for predicting milling stability based on limited experimental samples

Abstract

The present application relates to a kind of milling stability prediction method based on limited experimental sample, belong to machining field, with tool tip point main order modal parameter and each direction cutting force coefficient as random variable, the influence law of the effect of spindle speed to each variable is combined, the value of each variable under different speed is repeatedly randomly sampled, generate the multiple value series of all variables in full speed range, the limit cutting depth theoretical value is calculated under different series in combination with traditional milling stability analysis method, design a small amount of cutting chatter experiment to obtain corresponding limit cutting depth, the relative error between a small amount of experimental value and corresponding predicted value of limit cutting depth is calculated under each value series, determine the value series with minimum error value as optimal series, calculate a large number of limit cutting depth theoretical sample, establish neural network model with milling allowance as input, limit cutting depth theoretical value as output, use a small amount of experimental sample to fine-tune, correct and improve milling stability prediction precision.

Description

Technical Field

[0001] This invention belongs to the field of machining and relates to a method for predicting milling stability based on a limited number of experimental samples. Background Technology

[0002] The continuous upgrading of the manufacturing industry has placed higher demands on the high efficiency and high precision of CNC machining equipment. However, chatter caused by regenerative effects during high-speed milling restricts further improvements in machine tool efficiency and precision. Regenerative chatter is the most influential form of chatter in milling, and significant research has been conducted on milling chatter suppression methods based on regenerative chatter models. Among these methods, by establishing a dynamic model of the machining system and predicting milling stability, it is possible to obtain… Figure 1 Stability lobe diagrams distinguish between chatter and non-chatter regions. Given a combination of milling width and feed per tooth, chatter instability will occur during cutting when the selected cutting parameters at a certain spindle speed exceed the corresponding limit depth of cut. Therefore, plotting stability lobe diagrams to guide the rational selection of chatter-free milling parameter combinations is a major research direction for suppressing chatter. Lobe curve prediction methods can be mainly divided into frequency domain methods and time domain methods. Both methods require first obtaining the frequency response function and cutting force coefficient of the tool-workpiece system to establish a dynamic model of the milling process, and then solving the milling stability boundary in the frequency and time domains, respectively.

[0003] The tool tip frequency response function is typically obtained through hammer impact experiments when the tool is stationary. However, changes in the spindle speed during CNC machine tool operation alter the tool tip frequency response function at rest, leading to lower accuracy in stability lobe diagrams plotted based on the stationary frequency response function. Furthermore, the rotational motion of the tool makes it impossible to directly obtain the running tool tip frequency response function using hammer impact experiments. Combining analytical models of milling stability theory and chatter experiments, the main modal parameters of the tool tip frequency response function under spindle operation were identified in reverse. This allowed for the reconstruction of the tool tip frequency response function (FRF) at different spindle speeds, which was then input into the milling dynamics model to predict the corresponding limiting depth of cut. Ma Weizhen et al. further extended this inverse identification method, studying the differentiation characteristics of the tool tip dynamic behavior and proposing that considering the variation of tool tip stiffness with spindle speed could improve the accuracy of milling stability prediction. However, the prediction accuracy of milling stability in this type of method is limited by the accuracy of the tool tip FRF modal parameters, and chatter experiments are required at each spindle speed to construct a complete lobe diagram.

[0004] Furthermore, the tangential and radial cutting force coefficients required for milling stability analysis are usually assumed to be constants and are primarily calculated using the average cutting force method and the bevel cutting force method proposed by Budak and Altinta. Both methods require the collection of cutting force experimental data and the identification of the average cutting force coefficient through regression analysis. However, the inherent identification error will affect the accuracy of stability prediction, and studies have found that the cutting force coefficient varies with milling parameters. Therefore, some scholars have established surrogate models to describe the functional relationship between the cutting force coefficient and various milling variables. Campatelli et al., combining milling force experiments under different process conditions, established a cutting force coefficient response surface model with various milling parameters as variables. However, establishing an accurate regression model requires a large number of cutting experiments.

[0005] Therefore, considering the difficulty in accurately obtaining the tool tip frequency response function and cutting force coefficient, some scholars directly plot stability lobe diagrams using chatter experiments. Quintana et al. used a microphone to pick up noise signals during the machining process and performed chatter identification through Fast Fourier Transform (FFT). They used the axial depth of cut at different spindle speeds when chatter occurred as the critical value to plot the cutting stability lobe diagram. Grossi et al. further improved the chatter experiment method proposed by Quintana et al., proposing a chatter experiment method based on increasing spindle speed to reduce the number of experiments, but it still requires repeated experiments when the cutting width and feed per tooth change.

[0006] In summary, the analytical method for predicting milling stability is difficult to obtain high-precision tool tip frequency response function and cutting force coefficient, and cannot guarantee the prediction accuracy of milling stability lobe diagram. On the other hand, the experimental method for predicting milling stability relies on a lot of machining experiments, which will drastically increase production costs and reduce production efficiency. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a milling stability prediction method based on limited experimental samples. According to the traditional analytical method of milling stability theory, the theoretical value of the limit cutting depth under different combinations of milling parameters is calculated by using the easily obtainable static tool tip frequency response function and the non-precisely calculated cutting force coefficient. Then, a low-reliability milling stability prediction machine learning model is established. Then, a small number of experimental combinations of spindle speed, cutting width, feed per tooth, and limit cutting depth are obtained by using milling chatter experiments. This small number of experimental samples and transfer learning methods are used to correct the previously established low-reliability calculation model, resulting in a milling stability model that is more adapted to real machining scenarios. This effectively improves the milling stability prediction accuracy under small sample conditions, so as to ensure the milling stability prediction accuracy while reducing experimental costs.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A milling stability prediction method based on finite experimental samples includes the following steps:

[0010] S1: The tool tip frequency response function of the CNC machine tool under the stopped state is obtained by hammer impact test, the modal parameters of each major order in the x and y directions are identified, and then different combinations of cutting parameters are designed and corresponding cutting experiments are carried out. The radial and tangential cutting force coefficients are identified by the average cutting force method, and the nominal values ​​of modal parameters and cutting force coefficients are formed.

[0011] S2: Determine the random number variation ranges for the modal natural frequency, modal stiffness, modal damping ratio, and cutting force coefficient, respectively, and generate corresponding random numbers within each range; use the product of the modal natural frequency, modal stiffness, and modal damping ratio corresponding to the previous spindle speed and each random number as the modal natural frequency, modal stiffness, and modal damping ratio at the current speed; use the product of the nominal value of the cutting force coefficient in each direction and each random number as the cutting force coefficient at the current spindle speed; repeat this process until the maximum value of the spindle speed is covered;

[0012] S3: Determine multiple value series of modal parameters and cutting force coefficients within the entire spindle speed range, and combine them with the stability milling theory calculation formula to obtain the limit cutting depth corresponding to different spindle speeds under each value series;

[0013] S4: Using spindle speed, cutting width, and feed per tooth as design variables, a Latin hypercube experimental design is used to plan the chatter test within their variation range to obtain the experimental value of the ultimate cutting depth. Under each scheme, the ultimate cutting depth is predicted based on the modal parameters and cutting force coefficient of each value series. The mean absolute percentage error (MAPE) of each scheme under each series is calculated by comparing the actual value and the predicted value of the ultimate cutting depth. The series with the smallest MAPE value is the optimal series. This series is used to predict the ultimate cutting depth under any combination of spindle speed, cutting width, and feed per tooth, so as to generate a large amount of low-confidence data that is more similar to the target domain as source domain data.

[0014] S5: Within the range of spindle speed, cutting width, and feed per tooth variation, a Latin hypercube experimental design is used to select multiple combinations of spindle speed, cutting width, and feed per tooth. Based on step S7, sufficient source domain data that is closer to the target domain data is generated. Combined with artificial neural network training, a limit cutting depth prediction model with spindle speed, cutting width, and feed per tooth as input is used as the source domain pre-trained model, and its network structure and parameters are transferred to the target domain. On this basis, the network parameters of each pre-trained model are finely adjusted using a small amount of target domain data obtained in step S7, thereby establishing a milling stability prediction model that is suitable for the target domain and has high accuracy.

[0015] Furthermore, step S1 specifically includes:

[0016] S11: A vibration testing system is used to conduct a hammer impact test. The tool tip is excited by a hammer, and the vibration signal is picked up by an acceleration sensor attached to the tool tip. The data is acquired and processed by a dynamic signal acquisition and analysis system to obtain the x and y frequency response functions of the tool tip at the time of shutdown and to identify its modal parameters, including the modal natural frequency ω. nx and ω ny Modal damping ratio ξ x and ξ y and modal stiffness k x and k y ;

[0017] S12: Multiple sets of milling experiments were conducted using spindle speed, depth of cut, width of cut, and feed per tooth as variables;

[0018] S13: A dynamic force measuring instrument is used to collect milling force signals during the machining process, and the radial and tangential cutting force coefficients are obtained by measuring the cutting force;

[0019] S14: Define the modal parameters and cutting force coefficient at a spindle speed of 0 rpm as nominal values ​​{ω nx ,ξ x ,k x ,ω ny ,ξ y ,k y ,K r ,K t}

[0020] Furthermore, step S2 specifically includes:

[0021] S21: Considering the decrease in modal natural frequencies and modal stiffness in each direction as they change with spindle speed, the spindle speed range is discretized at a fixed speed interval. The nominal values ​​of the modal natural frequencies and modal stiffness in the x and y directions, ω, are identified when the machine tool is stopped. nx ,k x ,ω ny ,k y Starting from}, the spindle speed is increased sequentially according to the set speed interval, and {ω} is performed at each spindle speed. nx ,k x ,ω ny ,k y The random sampling is performed with the values ​​of each parameter at the previous spindle speed as a reference. At the same time, a range of variation with a maximum value of 1 is set. Within this range, random numbers corresponding to each parameter are generated. The values ​​of the modal natural frequency and modal stiffness at the current spindle speed are defined as the product of the reference value and the random number. This process is repeated until the maximum value of the spindle speed is covered.

[0022] S22: Since the modal damping ratio in each direction does not exhibit a clear evolution pattern with increasing spindle speed, the nominal values ​​of each parameter {ξ} at 0 rpm are used. x ,ξ y Starting from}, for each discrete spindle speed formed in step S21, the values ​​of each parameter under the previous spindle speed are used as a reference. The upper and lower boundaries are set with 1 as the middle value to form a variation range. Random numbers of each modal damping ratio are generated using this range. The product of each reference value and the random number is defined as the modal damping ratio under the current spindle speed.

[0023] S23: Considering the identification error of the cutting force coefficient and its randomness during the machining process, at each discrete spindle speed formed in step S21, the nominal value of the cutting force coefficient in each direction {K} in step S1 is used. r ,K t Using} as the baseline, and setting the upper and lower boundaries with 1 as the intermediate value, a variation range is formed. Within this range, random numbers corresponding to the cutting force coefficients in each direction are generated. The product of each baseline value and the random number is defined as the cutting force coefficient at the current spindle speed.

[0024] Furthermore, in step S3, the limit depth of cut corresponding to different spindle speeds under each value series is obtained by combining the stability milling theory calculation formula, including:

[0025] At each discrete spindle speed, the tool tip frequency response function is reconstructed using the corresponding modal parameters. This function is then combined with the associated cutting force coefficient and input into formula (1) to obtain the limiting depth of cut a corresponding to the current spindle speed. plim For the spindle speed between two adjacent discrete values, its corresponding modal parameters and cutting force coefficient are set to be consistent with the relevant parameters corresponding to the smaller spindle speed. Therefore, according to the milling stability theory analysis formula (1), the limit cutting depth a corresponding to any spindle speed is calculated. plim :

[0026]

[0027] In the formula, K t Λ is the tangential cutting force coefficient, N is the number of tool teeth, and Λ R and Λ I G represents the real and imaginary parts of the eigenvalue Λ. xx With G yy Let a be the direct frequency response function of the tool tip in the x and y directions. xx a yy a xy a yx It is the average directionality coefficient associated with milling parameters.

[0028] Furthermore, in step S4, the mean absolute percentage error (MAPE) of each group of schemes under each series is calculated using the actual value and the predicted value of the limit cutting depth, as shown in the following formula:

[0029]

[0030] In the formula, N t Let a be the total number of samples. plim_pi and a plim_ri These are the predicted value and the actual value, respectively.

[0031] Furthermore, step S4 specifically includes the following steps:

[0032] S41: Using the Latin hypercube experiment in {n,a e ,f z N is generated within the range of change. t A set of data was used to conduct chatter experiments with progressively increasing depths of cut under each set of conditions. Cutting force signals were captured and their spectrum analyzed during the milling process. The depth of cut at which chatter occurred was calibrated as the limiting depth of cut, and N was then determined. t A set of highly reliable data forms the target domain dataset D. t ={n t a et f z_t a plim_t}, randomly select D t The m sets of experimental data in the sample are used as a small number of samples for fine-tuning the source domain pre-trained model, and the remaining experimental data are only used for subsequent verification of the effectiveness of the proposed method.

[0033] S42: From D t The m sets of experimental data were randomly selected as the benchmark. Based on the modal parameters and cutting force coefficients of multiple series, the average relative error between the predicted and experimental values ​​of the m sets of limit cutting depths in each series was predicted according to formula (1). The series with the smallest MAPE value was the optimal series.

[0034] Furthermore, step S5 specifically includes the following steps:

[0035] S51: Using the Latin hypercube experiment in {a e f z Multiple sets of samples are generated within the variation range, and milling parameters {n} are formed under each set of samples based on the spindle speed. s a e_s f z_s For each set of parameters, the limiting depth of cut is calculated according to formula (1) using the optimal series of modal parameters and cutting force coefficients, thus constructing a total of j sets of source domain datasets D. s ={n s a e_s fz_s a plim_s};

[0036] S52: Randomly select source domain data D s 80% of the data sets were used as the training set, and the remaining 20% ​​were used as the test set.

[0037] S53: A pre-trained model in the source domain is built using a multilayer perceptron (MLP). The MLP input layer consists of three neurons, representing the spindle speed n and the cutting width a, respectively. e and feed per tooth f z The output layer contains one neuron, representing the limiting cutting depth a. plim The number of hidden layers and neurons was selected and adjusted based on the source domain data. After multiple experiments, three hidden layers were finally selected, with 16, 13 and 10 nodes in each hidden layer. The activation functions of the three hidden layers and the output layer were all Tanh functions. A pre-trained model Model_r was built using the training set.

[0038] S54: Retain the 5-layer topology of the source domain pre-trained model, the number of neurons in each layer, and the connection weights of neurons in adjacent layers, and use it as the initial prediction model for milling stability in the target domain.

[0039] S55: Use the m sets of experimental data selected in step S41 as the target domain training data D t_p By globally fine-tuning the connection weights of the pre-trained model Model_r using the mean squared error loss function, a milling stability prediction model Model_t suitable for the target domain is established.

[0040] The beneficial effects of this invention are as follows: This invention focuses on the problems of low accuracy and high cost of traditional milling stability theoretical analysis and experimental analysis. It proposes to introduce a transfer learning method to simultaneously utilize the effective information contained in a large amount of low-cost theoretical data and a small amount of high-cost experimental data. Using easily obtainable modal parameters and inaccurately estimated cutting force coefficients as random variables, it combines traditional milling stability analysis methods to generate theoretical samples that are closer to the experimental samples of the ultimate cutting depth, thus narrowing the difference between the source domain theoretical dataset and the target domain experimental dataset. Then, a neural network prediction model of the ultimate cutting depth is established using this theoretical dataset. This prediction model is fine-tuned and corrected using a small number of experimental samples and the model transfer method, establishing a milling stability prediction model that is more adapted to real machining scenarios. This improves the accuracy of milling stability prediction while reducing experimental costs. The specific innovations are as follows:

[0041] (1) Using easily obtainable static tool tip modal parameters and average cutting force coefficient as random variables, the influence of spindle speed effect on each random variable during CNC machine tool operation is considered. Multiple series of modal parameters and cutting force coefficient values ​​in the full speed range are generated and used as inputs to the traditional milling stability theory model. The limit cutting depth corresponding to different milling parameters is then predicted. The mean absolute percentage error (MAPE) between a small number of limit cutting depth experimental calibration values ​​and corresponding predicted values ​​is calculated. The series with the smallest error value is used as the optimal series of modal parameters and cutting force coefficient. Based on this, the limit cutting depth is calculated by combining the optimal series and the traditional milling stability theory model. This can construct source domain data that is closer to the target domain data.

[0042] (2) By combining a large amount of source domain data and artificial neural network methods, a pre-trained model of the limit cutting depth with spindle speed, milling width and feed per tooth as input is established. Then, this pre-trained model is fine-tuned by a small number of target domain samples collected by chatter experiment to compensate for the measurement error of tool tip dynamic characteristics and cutting force coefficient, and to incorporate the influence of various uncertain factors in the machining process. This can establish a target domain milling stability prediction model that is more in line with the real machining scenario.

[0043] (3) Design different amounts of target domain data, and use the “pre-training-fine-tuning” transfer learning method proposed in this invention to establish a milling stability prediction model under target domain data of different scales. At the same time, use a small amount of target domain data directly to establish a milling stability prediction model. By comparing the prediction accuracy of the two models on the test set, the effectiveness and superiority of the method proposed in this invention under limited experimental samples are demonstrated.

[0044] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0045] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0046] Figure 1 For milling stability lobe diagram;

[0047] Figure 2 The theoretical curve of the leaf-shaped stability diagram for milling and its related experimental values;

[0048] Figure 3 This is a flowchart illustrating a milling stability prediction method based on finite experimental samples in this invention.

[0049] Figure 4 (a) is an analysis diagram of the frequency response function in each direction in an embodiment of the present invention, and (b) is an analysis diagram of the cutting force spectrum. Detailed Implementation

[0050] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0051] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0052] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0053] Figure 2 The paper describes the lobe diagram plotted based on milling stability theory and lists the limiting depths of cut calibrated through chatter experiments at different rotational speeds. It shows a significant difference between the predicted and actual limiting depths of cut. However, although the theoretically predicted lobe diagram is not precise enough, it still reflects the approximate shape and evolution trend of the actual lobe curve. Therefore, the potential similarity between milling stability theory and experimental predictions can be fully utilized, and the prediction accuracy of milling stability theory analysis can be effectively improved by introducing a small number of experimental samples.

[0054] This invention introduces random variables and model transfer learning into milling stability prediction. First, the principal modal parameters at the tool tip and the cutting force coefficients in each direction are used as random variables. Then, considering the influence of spindle speed on these variables, the values ​​of each variable at different speeds are randomly sampled to generate a series of values ​​for all variables across the entire speed range. Multiple value series are generated through repeated random sampling. Traditional milling stability prediction is then performed under different series, while simultaneously designing a small number of chatter experiments to obtain the corresponding limiting depth of cut. The relative error between the experimental values ​​and the corresponding predicted values ​​of the limiting depth of cut is calculated for each value series. This determines the optimal value series and generates a large number of theoretical samples of the limiting depth of cut to reduce the difference between the predicted and experimental values. Machine learning methods and transfer learning are then introduced. A milling stability prediction model is established based on the previously generated large number of samples, and this pre-trained model is fine-tuned again using a small amount of collected experimental data to establish a milling stability prediction model for real-world machining scenarios. In summary, based on the basic concepts and terminology of transfer learning, the milling stability prediction transfer learning problem involved in this invention can be described as follows:

[0055] (1) Both the source and target domain data are composed of the spindle speed n and the cutting width a. e Feed per tooth f z and the corresponding limiting depth of cut a plim Composition, where a in the source domain and the target domain plim The values ​​are taken from theoretical calculations and experimental calibrations, and the number of samples in the source domain is much larger than the number of samples in the target domain.

[0056] (2) Establish a pre-trained model of the ultimate cutting depth in the source domain with spindle speed, cutting width and feed per tooth as inputs, and fine-tune this pre-trained model using a small amount of target domain data, thereby obtaining a milling stability prediction model with high prediction accuracy in the target domain.

[0057] Based on the above methods of reducing data discrepancies and transfer learning, the milling stability prediction based on a small number of experimental samples proposed in this invention can be realized step by step according to steps (1) to (8):

[0058] Step 1: Obtain the tool tip frequency response function of the CNC machine tool in a stopped state using a hammer impact test, and identify the modal parameters of each major order in the x and y directions, i.e., the modal natural frequencies (ω). nx and ω ny ), modal damping ratio (ξ) x and ξ y ) and modal stiffness (k x and k y Then, different combinations of cutting parameters were designed and corresponding cutting experiments were conducted. The radial and tangential cutting force coefficients (i.e., K) were identified using the average cutting force method. r and Kt Based on this, the nominal values ​​of modal parameters and cutting force coefficients {ω} are formed. nx ,ξ x ,k x ,ω ny ,ξ y ,k y ,K r ,K t};

[0059] Step 2: For the modal natural frequencies and modal stiffness in each direction, considering their decreasing characteristic with spindle speed, the spindle speed range is discretized at a fixed speed interval. The nominal values ​​{ω} of the modal natural frequencies and modal stiffness identified in the x and y directions when the machine tool is stopped (i.e., when the spindle speed is 0 rpm) are used. nx ,k x ,ω ny ,k y Starting from}, the spindle speed is increased sequentially according to the set speed interval, and {ω} is performed at each spindle speed. nx ,k x ,ω ny ,k y The random sampling is performed using the values ​​of each parameter at the previous spindle speed as a reference, while setting a variation range with a maximum value of 1. Within this range, random numbers are generated for each parameter. The modal natural frequency and modal stiffness at the current spindle speed are defined as the product of the reference value and the random number. This process is repeated until the maximum value of the spindle speed is covered.

[0060] Step 3: Since the modal damping ratio in each direction does not exhibit a clear evolution pattern with increasing spindle speed, the nominal values ​​of each parameter {ξ} at 0 rpm are used. x ,ξ y Starting from}, for each discrete spindle speed formed in step 2, the values ​​of each parameter under the previous spindle speed are used as a reference. The upper and lower boundaries are set with 1 as the middle value to form a variation range. Random numbers of each modal damping ratio are generated using this range. The product of each reference value and the random number is defined as the modal damping ratio under the current spindle speed.

[0061] Step 4, considering the identification error of the cutting force coefficient and its randomness during the machining process, at each discrete spindle speed formed in Step 2, the nominal value of the cutting force coefficient in each direction in Step 1, {K}, is used. r ,K t Using} as the baseline, and setting the upper and lower boundaries with 1 as the intermediate value, a variation range is formed. Within this range, random numbers corresponding to the cutting force coefficients in each direction are generated. The product of each baseline value and the random number is defined as the cutting force coefficient at the current spindle speed.

[0062] Step 5: Based on steps 2 to 4, a series of modal parameters and cutting force coefficients within the spindle speed variation range can be obtained. For each discrete spindle speed formed in step 2, the tool tip frequency response function is reconstructed using the corresponding modal parameters. This function is then combined with the associated cutting force coefficient and used as the input to formula (1) to obtain the limit cutting depth a corresponding to the current spindle speed. plim For the spindle speed between two adjacent discrete values, its corresponding modal parameters and cutting force coefficient are set to be consistent with the relevant parameters corresponding to the smaller spindle speed. Therefore, according to the milling stability theory analysis formula (1), the limit cutting depth a corresponding to any spindle speed can be calculated. plim .

[0063]

[0064] In the formula, K t Λ is the tangential cutting force coefficient, N is the number of tool teeth, and Λ R and Λ I G represents the real and imaginary parts of the eigenvalue Λ. xx With G yy Let a be the direct frequency response function of the tool tip in the x and y directions. xx a yy a xy a yx It is the average directionality coefficient associated with milling parameters.

[0065] Step 6: Repeating steps 2 to 4 allows for repeated random sampling of the modal parameters and cutting force coefficients at each spindle speed. This yields multiple value series of modal parameters and cutting force coefficients across the entire spindle speed range. Then, combining this with step 5, the limiting cutting depth 'a' corresponding to different spindle speeds in each value series can be obtained using formula (1). plim .

[0066] Step 7: Using milling parameters such as spindle speed n and cutting width a... e Feed per tooth f z To design the variables, N was selected using a Latin hypercube experiment within its range of variation. t A small number of experimental schemes were conducted, and chatter experiments were performed under each scheme to obtain experimental values ​​of the limiting depth of cut. Furthermore, the milling parameters from each scheme were substituted into steps 5 and 6, and the modal parameters and cutting force coefficients for each scheme were used to predict 'a'. plim And then through a plim The actual and predicted values ​​are calculated according to formula (2) for each series N. tThe mean absolute percentage error (MAPE) of the proposed schemes is used to determine the optimal series, which has the smallest MAPE value. This indicates that the modal parameters and cutting force coefficients in this series are likely closer to the actual values. Therefore, this series is used to predict any {n,a} e ,f z} Combination of a plim This is done by generating a large amount of low-confidence data that is more similar to the target domain as source domain data.

[0067]

[0068] In the formula, N t Let a be the total number of samples. plim_pi and a plim_ri These are the predicted value and the actual value, respectively.

[0069] Step 8: In the milling parameters n, a e and f z Within the range of variation, a Latin hypercube experimental design was used to select multiple n and a values. e and f z The combination of n and a is then used to generate sufficient source domain data that is closer to the target domain data according to step 7, thereby combining artificial neural network training with n and a e and f z For the input a plim The prediction model is used as the source domain pre-trained model, and its network structure and parameters are transferred to the target domain. Based on this, the network parameters of the pre-trained model are finely adjusted using a small amount of target domain data obtained in step 7, thereby establishing a milling stability prediction model that is suitable for the target domain and has high accuracy.

[0070] Specific examples:

[0071] like Figure 3 As shown, a 4-tooth carbide cutting tool with a diameter of 20mm is used to mill an aluminum workpiece measuring 120mm × 100mm × 80mm. The variation ranges of various milling parameters are as follows: spindle speed n = [3000rpm, 8000rpm], milling width a e =[2mm, 20mm], feed per tooth f z = [0.03mm / z, 0.3mm / z], the specific implementation steps are as follows:

[0072] Step 1: First, a hammer impact test is conducted using a vibration testing system. A hammer excites the tool tip, and an accelerometer attached to the tool tip picks up the vibration signal. The data is then acquired and processed by a dynamic signal acquisition and analysis system to obtain the X and Y frequency response functions of the tool tip at the time of shutdown and to identify its modal parameters. Then, a spindle speed of n = 6000 rpm and a cutting width a are selected. e=10mm, feed per tooth f z Five sets of milling experiments were conducted with milling force values ​​of [0.03, 0.06, 0.09, 0.12, 0.15] mm / z. A dynamic force gauge was used to collect the milling force signals during the machining process. The tangential and normal cutting force coefficients K were identified by the obtained average cutting force. t =607MPa, K r =238MPa. Table 1 lists detailed information on modal parameters and average cutting force coefficients for each order.

[0073] The Latin hypercube experiment was used to analyze n and a. e and f z 2000 sets of milling parameters were randomly sampled within the variation range. Then, based on the nominal values ​​of each parameter in Table 1, 2000 sets of a were calculated using formula (1). plim As a standard set, eight single-factor experiments were designed to consider the absence of each mode. Under each experiment, the FRF of the reconstructed knife tip was used to calculate 2000 new a values. plim The relative error between the current order mode and the standard set is calculated to evaluate the influence of the current order mode on milling stability. As can be seen from Table 2, the second order in the X direction and the first to third orders in the Y direction have high relative error values. Therefore, the fourth order is taken as the main order mode and the changes in its modal parameters are considered.

[0074] Table 1

[0075]

[0076] Table 2

[0077]

[0078] Step 2: For the modal natural frequencies and modal stiffness in each direction, considering their decreasing characteristics with the change of spindle speed, the spindle speed range [3000rpm, 8000rpm] is discretized at 200rpm. Random sampling of each changing parameter determined in Step 1 is performed at each spindle speed. During sampling, the value of each parameter at the previous spindle speed is used as a reference. Random numbers corresponding to each parameter are generated in the interval [0.99, 1]. The value of the modal natural frequency and modal stiffness at the current spindle speed is defined as the product of the reference value and the random number, ensuring that the random sampling covers every discrete value in the spindle speed range [3000rpm, 8000rpm].

[0079] Step 3: For the modal damping ratio in each direction, considering that it does not show a clear evolution law with the change of spindle speed, for each discrete spindle speed formed in Step 2, the values ​​of each parameter under the previous spindle speed are used as a reference, and random numbers of each modal damping ratio are generated in the interval [0.95, 1.05]. The product of each reference value and the random number is defined as the modal damping ratio under the current spindle speed.

[0080] Step 4, considering the identification error of the cutting force coefficient and its randomness during the machining process, at each discrete spindle speed formed in step (2), the nominal values ​​of the radial and tangential cutting force coefficients {K} are used. r ,K t Using the reference value (as shown in Table 1) as a baseline, random numbers corresponding to the cutting force coefficients in each direction are generated in the interval [0.8, 1.2]. The product of each reference value and the random number is defined as the cutting force coefficient in each direction at the current spindle speed.

[0081] Step 5: By repeating steps 2 to 4, 5000 different value series of main order modal parameters and cutting force coefficients are randomly generated across the entire speed range. Then, at different speeds in each value series, the main order and non-main order modal parameters are used to reconstruct the tool tip frequency response function according to the modal superposition method. Based on this, combined with the randomly generated cutting force coefficient at that speed, the theoretical value of the associated limit cutting depth is calculated according to formula (1).

[0082]

[0083] In the formula, K t Λ is the tangential cutting force coefficient, N is the number of tool teeth, and Λ R and Λ I G represents the real and imaginary parts of the eigenvalue Λ. xx With G yy Let a be the direct frequency response function of the tool tip in the x and y directions. xx a yy a xy a yx It is the average directionality coefficient associated with milling parameters.

[0084] Step 6, as follows Figure 4 As shown in (a) and (b), the Latin hypercube experiment is used in {n,a} e ,f z 300 sets of data were generated within the variation range. Chatter experiments were conducted by progressively increasing the cutting depth under each set of conditions. Cutting force signals were captured and their spectrum analyzed during the milling process. Figure 4In (b), besides the spindle rotation frequency and the cutting tooth frequency and their harmonics, the newly emerging frequency of 775.1 Hz is close to the weakest mode frequencies of 750.70 Hz and 717.8 Hz in the X and Y directions, respectively. This indicates that chatter occurred during the machining process of this set of milling parameters. The current cutting depth is calibrated as the limit cutting depth, and then 300 sets of high-confidence data are used to form the target domain dataset D. t ={n t a et f z_t a plim_t}, randomly select D t The 40 sets of experimental data were used as a small sample for fine-tuning the source domain pre-trained model, while the remaining 260 sets of experimental data were used only for subsequent verification of the effectiveness of the proposed method.

[0085] Step 7, from step 6 from D t Using 40 randomly selected sets of experimental data as a baseline, and based on the modal parameters and cutting force coefficients under 5000 series, the 40 sets of {n} under each series are predicted according to step 5 and formula (1). t a e_t f z_t The corresponding limit cutting depth is calculated according to formula (2) to obtain the average relative error between the predicted and experimental values ​​of the limit cutting depth in 40 sets. A total of 5000 series of average relative error values ​​are obtained, among which the optimal series corresponds to the smallest average relative error of 16.63%.

[0086] Based on this, the Latin hypercube experiment was used in {a e f z Within the variation range, 100 sets of samples are generated. Within each set of samples, the spindle speed range [3000 rpm, 8000 rpm] is discretized at 200 rpm, resulting in a total of 100 × 26 = 2600 sets of milling parameters {n}. s a e_s f z_s For each set of parameters, the optimal series of modal parameters and cutting force coefficients are used to calculate the corresponding limiting cutting depth according to equation (1), ultimately forming 2600 sets of source domain datasets D. s ={n s a e_s f z_s a plim_s}

[0087] Step 8, randomly select source domain data D s2600 × 0.8 = 2080 sets of data are used as the training set, and the remaining 2600 × 0.2 = 520 sets of data are used as the test set. Considering that the Multi-layer Perceptron (MLP) is a typical machine learning method that has been well applied in CNC milling, this embodiment uses a Multi-layer Perceptron (MLP) to build a pre-trained model in the source domain. The MLP input layer consists of three neurons, representing the spindle speed n and the cutting width a, respectively. e and feed per tooth f z The output layer contains one neuron, representing the limiting cutting depth a. plim The number of hidden layers and neurons was selected and adjusted based on the source domain data. After multiple experiments, three hidden layers were finally selected, with 16, 13, and 10 nodes in each hidden layer, respectively. At this time, the multilayer perceptron can be represented as a 5-layer topology of 3×16×13×10×1. The activation functions of the three hidden layers and the output layer are all Tanh functions. The learning rate is defined as 0.01, and the model is trained using a loss function. Finally, a source domain pre-trained model Model_r is established using 2080 training sets. The effectiveness of the pre-trained model Model_r is evaluated using the average relative error of formula (2). Its average relative error on 520 test sets is 1.22%, indicating that the multilayer perceptron established on the source domain has high prediction accuracy and can be used for subsequent transfer learning in the target domain.

[0088] Step 9: Retain the 5-layer topology, the number of neurons in each layer, and the connection weights of neurons in adjacent layers of the source domain pre-trained model, and use it as the initial prediction model for milling stability in the target domain. Then, use the 40 sets of data selected in Step 6 as the target domain training data D. t_p A milling stability prediction model, Model_t, suitable for the target domain, is established by globally fine-tuning the connection weights of the pre-trained model Model_r using the mean squared error loss function. This is based on 300 sets of high-confidence data D. t As a test set, Model_t has an average relative error of 6.33%, indicating that Model_t can reflect the milling stability information of the target domain well, and is higher than the average relative error of 13.67% obtained by directly using Model_r on 300 test sets.

[0089] Furthermore, Model_3, a milling stability prediction model built directly using 40 sets of target domain training data, has an average relative error of only 38.33% on 300 test sets, which is much higher than the average relative error of Model_t (6.33%). This further demonstrates that transfer learning can assist in modeling milling stability in the target domain under small sample conditions.

[0090] Meanwhile, a large amount of milling stability data was generated directly using the nominal values ​​of modal parameters and cutting force coefficients in Table 1. This data was used as the source domain data to establish a multilayer perceptron prediction model for milling stability. This model was then directly transferred to the target domain and globally fine-tuned using 40 sets of data to obtain the target domain milling stability prediction model Model_4. The average relative error of this model on 300 test sets was 15.95%, which is much larger than the average relative error of 6.33% obtained using Model_t. This indicates that the source domain data construction method proposed in this invention can further improve the prediction accuracy of the transfer learning model.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A milling stability prediction method based on finite experimental samples, characterized in that: Includes the following steps: S1: The tool tip frequency response function of the CNC machine tool under the stopped state is obtained by hammer impact test, the modal parameters of each major order in the x and y directions are identified, and then different combinations of cutting parameters are designed and corresponding cutting experiments are carried out. The radial and tangential cutting force coefficients are identified by the average cutting force method, and the nominal values ​​of modal parameters and cutting force coefficients are formed. S2: Determine the random number variation ranges for the modal natural frequency, modal stiffness, modal damping ratio, and cutting force coefficient, respectively, and generate corresponding random numbers within each range; use the product of the modal natural frequency, modal stiffness, and modal damping ratio corresponding to the previous spindle speed and each random number as the modal natural frequency, modal stiffness, and modal damping ratio at the current speed; use the product of the nominal value of the cutting force coefficient in each direction and each random number as the cutting force coefficient at the current spindle speed; repeat this process until the maximum value of the spindle speed is covered; S3: Determine multiple value series of modal parameters and cutting force coefficients within the entire spindle speed range, and combine them with the calculation formula of traditional stability milling theory to obtain the limit cutting depth corresponding to different spindle speeds under each value series; S4: Using spindle speed, cutting width, and feed per tooth as design variables, a Latin hypercube experimental design is used to plan the chatter test within their variation range to obtain the experimental value of the ultimate cutting depth. Under each scheme, the ultimate cutting depth is predicted based on the modal parameters and cutting force coefficient of each value series. The mean absolute percentage error (MAPE) of each scheme under each series is calculated by comparing the actual value and the predicted value of the ultimate cutting depth. The series with the smallest MAPE value is the optimal series. This series is used to predict the ultimate cutting depth under any combination of spindle speed, cutting width, and feed per tooth, so as to generate a large amount of low-confidence data that is more similar to the target domain as source domain data. S5: Within the range of spindle speed, cutting width, and feed per tooth variation, a Latin hypercube experimental design is used to select multiple combinations of spindle speed, cutting width, and feed per tooth. Based on step S7, sufficient source domain data that is closer to the target domain data is generated. Combined with artificial neural network training, a limit cutting depth prediction model with spindle speed, cutting width, and feed per tooth as input is used as the source domain pre-trained model, and its network structure and parameters are transferred to the target domain. On this basis, the network parameters of each pre-trained model are finely adjusted using a small amount of target domain data obtained in step S7, thereby establishing a milling stability prediction model that is suitable for the target domain and has high accuracy.

2. The milling stability prediction method based on finite experimental samples according to claim 1, characterized in that: Step S1 specifically includes: S11: A vibration testing system is used to conduct a hammer impact test. The tool tip is excited by a hammer, and the vibration signal is picked up by an acceleration sensor attached to the tool tip. The data is acquired and processed by a dynamic signal acquisition and analysis system to obtain the x and y frequency response functions of the tool tip at the time of shutdown and to identify its modal parameters, including the modal natural frequency ω. nx and ω ny Modal damping ratio ξ x and ξ y and modal stiffness k x and k y ; S12: Multiple sets of milling experiments were conducted using spindle speed, depth of cut, width of cut, and feed per tooth as variables; S13: A dynamic force measuring instrument is used to collect milling force signals during the machining process, and the radial and tangential cutting force coefficients are obtained by measuring the cutting force; S14: Define the main modal parameters and cutting force coefficients at a spindle speed of 0 rpm as nominal values ​​{ω nx ,ξ x ,k x ,ω ny ,ξ y ,k y ,K r ,K t } 3. The milling stability prediction method based on finite experimental samples according to claim 1, characterized in that: Step S2 specifically includes: S21: Considering the decrease in modal natural frequencies and modal stiffness in each direction as they change with spindle speed, the spindle speed range is discretized at a fixed speed interval. The nominal values ​​of the modal natural frequencies and modal stiffness in the x and y directions, ω, are identified when the machine tool is stopped. nx ,k x ,ω ny ,k y Starting from}, the spindle speed is increased sequentially according to the set speed interval, and {ω} is performed at each spindle speed. nx ,k x ,ω ny ,k y The random sampling is performed with the values ​​of each parameter at the previous spindle speed as a reference. At the same time, a range of variation with a maximum value of 1 is set. Within this range, random numbers corresponding to each parameter are generated. The values ​​of the modal natural frequency and modal stiffness at the current spindle speed are defined as the product of the reference value and the random number. This process is repeated until the maximum value of the spindle speed is covered. S22: Since the modal damping ratio in each direction does not exhibit a clear evolution pattern with increasing spindle speed, the nominal values ​​of each parameter {ξ} at 0 rpm are used. x ,ξ y Starting from}, for each discrete spindle speed formed in step S21, the values ​​of each parameter under the previous spindle speed are used as a reference. The upper and lower boundaries are set with 1 as the middle value to form a variation range. Random numbers of each modal damping ratio are generated using this range. The product of each reference value and the random number is defined as the modal damping ratio under the current spindle speed. S23: Considering the identification error of the cutting force coefficient and its randomness during the machining process, at each discrete spindle speed formed in step S21, the nominal value of the cutting force coefficient in each direction {K} in step S1 is used. r ,K t Using} as the baseline, and setting the upper and lower boundaries with 1 as the intermediate value, a variation range is formed. Within this range, random numbers corresponding to the cutting force coefficients in each direction are generated. The product of each baseline value and the random number is defined as the cutting force coefficient at the current spindle speed.

4. The milling stability prediction method based on finite experimental samples according to claim 1, characterized in that: In step S3, the limiting depth of cut corresponding to different spindle speeds under each value series is obtained by combining the calculation formula of the stability milling theory, including: At each discrete spindle speed, the tool tip frequency response function is reconstructed using the corresponding modal parameters. This function is then combined with the associated cutting force coefficient and used together as formula (1) to obtain the limiting cutting depth a corresponding to the current spindle speed. plim For the spindle speed between two adjacent discrete values, its corresponding modal parameters and cutting force coefficient are set to be consistent with the relevant parameters corresponding to the smaller spindle speed. Therefore, according to the milling stability theory analysis formula (1), the limit cutting depth a corresponding to any spindle speed is calculated. plim : In the formula, K t Λ is the tangential cutting force coefficient, N is the number of tool teeth, and Λ R and Λ I G represents the real and imaginary parts of the eigenvalue Λ. xx With G yy Let a be the direct frequency response function of the tool tip in the x and y directions. xx a yy a xy a yx It is the average directionality coefficient associated with milling parameters.

5. The milling stability prediction method based on finite experimental samples according to claim 4, characterized in that: Step S4 involves calculating the mean absolute percentage error (MAPE) for each group of schemes in each series using the actual and predicted values ​​of the limit cutting depth. The formula is as follows: In the formula, N t Let a be the total number of samples. plim_pi and a plim_ri These are the predicted value and the actual value, respectively.

6. The milling stability prediction method based on finite experimental samples according to claim 5, characterized in that: Step S4 Specifically, the following steps are included: S41: Using the Latin hypercube experiment on milling parameters {n,a} e ,f z N is generated within the range of change. t A set of data was used to conduct chatter experiments with progressively increasing depths of cut under each set of conditions. Cutting force signals were captured and their spectrum analyzed during the milling process. The depth of cut at which chatter occurred was calibrated as the limiting depth of cut, and N was then determined. t A set of highly reliable data forms the target domain dataset D. t ={n t a et f z_t a plim_t }, randomly select D t The m sets of experimental data in the sample are used as a small number of samples for fine-tuning the source domain pre-trained model, and the remaining experimental data are only used for subsequent verification of the effectiveness of the proposed method. S42: From D t The m sets of experimental data are randomly selected as the benchmark. Based on the modal parameters and cutting force coefficients of multiple series, the theoretical values ​​of the limit cutting depth of each series are calculated according to formula (1). Then, the average relative error (MAPE) between the theoretical value and the experimental value is calculated according to formula (2). The series with the smallest MAPE value is the optimal series.

7. The milling stability prediction method based on finite experimental samples according to claim 6, characterized in that: Step S5 specifically includes the following steps: S51: Using the Latin hypercube experiment in {a e f z Multiple sets of samples are generated within the variation range, and milling parameters {n} are formed under each set of samples based on the spindle speed. s a e_s f z_s For each set of parameters, the limiting depth of cut is calculated according to formula (1) using the optimal series of modal parameters and cutting force coefficients, thus constructing a total of j sets of source domain datasets D. s ={n s a e_s f z_s , a plim_s}； S52: Randomly select source domain data D s 80% of the data sets were used as the training set, and the remaining 20% ​​were used as the test set. S53: A pre-trained model in the source domain is built using a multilayer perceptron (MLP). The MLP input layer consists of three neurons, representing the spindle speed n and the cutting width a, respectively. e and feed per tooth f z The output layer contains one neuron, representing the limiting cutting depth a. plim The number of hidden layers and neurons was selected and adjusted based on the source domain data. After multiple experiments, three hidden layers were finally selected, with 16, 13 and 10 nodes in each hidden layer. The activation functions of the three hidden layers and the output layer were all Tanh functions. A pre-trained model Model_r was built using the training set. S54: Retain the 5-layer topology of the source domain pre-trained model, the number of neurons in each layer, and the connection weights of neurons in adjacent layers, and use it as the initial prediction model for milling stability in the target domain. S55: Use the m sets of experimental data selected in step S41 as the target domain training data D t_p By globally fine-tuning the connection weights of the pre-trained model Model_r using the mean squared error loss function, a milling stability prediction model Model_t suitable for the target domain is established.

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