Milling chatter detection method based on principal component energy entropy

Abstract

The invention discloses a milling chatter detection method based on principal component energy entropy. The method belongs to the technical field of mechanical system fault detection, and comprises the following operation steps: selecting a sensor type, determining an installation position and setting flutter detection related parameters; obtaining one-dimensional synchronous vibration data; expanding the one-dimensional synchronous vibration data into multi-dimensional synchronous data; performing zero-centralization processing on the multi-dimensional synchronous data; performing dimension reduction processing on the multi-dimensional synchronous data after zero centralization processing by utilizing principal component analysis to obtain principal components; a principal component energy entropy PCEE1 and a principal component energy entropy PCEE2 are calculated; judging whether flutter occurs or not; according to the milling chatter detection method based on the principal component energy entropy disclosed by the invention, milling chatter can be effectively and reliably detected; the method has the advantages that the calculation complexity is low, the calculation cost is low, and the flutter can be quickly detected; in addition, the method is not influenced by the rotation speed change of the main shaft, and can be applied to milling chatter detection work at different rotation speeds.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical system fault detection, and relates to a milling chatter detection method based on principal component energy entropy. Background Art

[0002] In the field of machining, the milling process has been widely used in key industries such as aerospace, automotive manufacturing, and mold processing due to its high efficiency and high precision. However, the chatter phenomenon generated during the milling process has always restricted the improvement of machining efficiency and quality. Chatter is a self-excited vibration caused by the dynamic interaction between the tool and the workpiece, and its generation mechanism is complex, involving various factors such as the dynamic characteristics of the machine tool-tool-workpiece system, the matching of cutting parameters, and the disturbance of the machining environment. Chatter will not only cause the deterioration of the machining surface quality (such as vibration marks, burrs), abnormal tool wear or even chipping, but may also cause damage to machine tool components, greatly increasing the production cost. According to industry statistics, machining failure cases caused by chatter account for more than 30% of precision machining failures. Therefore, detecting chatter has important economic significance.

[0003] In the work of chatter detection, chatter feature extraction is one of the most important contents. For complex chatter signals, it is generally necessary to use signal decomposition methods to process them, decompose them into a series of non-linear components with clear physical meanings, and then further process and analyze the decomposed components to extract feature quantities sensitive to chatter, such as energy entropy.

[0004] Currently, common signal decomposition methods include: wavelet packet decomposition, empirical mode decomposition, variational mode decomposition and their improved algorithms, etc. Therefore, multiple energy entropies can be obtained based on the above decomposition methods. A patent for invention (application number: 2021110169321) discloses an EEMD energy entropy based on EEMD. This energy entropy can be used to evaluate the health state of bearings. A patent for invention (application number: 2022106550476) discloses a CEEMD energy entropy based on CEEMD, and proposes a bearing fault diagnosis method based on CEEMD energy entropy. A patent for invention (application number: 2024100625942) discloses a CNCEEMDAN energy entropy based on CNCEEMDAN, and uses this energy entropy as a fault feature for fault diagnosis. EEMD, CEEMD, and CNCEEMDAN are all improved versions of empirical mode decomposition, which can overcome the mode mixing effect of empirical mode decomposition and improve the quality of signal decomposition. EEMD, CEEMD, and CNCEEMDAN all decompose signals into multiple modal components, and then obtain energy entropy according to the energy distribution of multiple modal components. Although EEMD energy entropy, CEEMD energy entropy, and CNCEEMDAN energy entropy can all characterize bearing faults, the calculation cost of the above energy entropies is relatively high. In addition, EEMD, CEEMD, and CNCEEMDAN are all improved algorithms developed based on empirical mode decomposition. Due to the lack of a strict mathematical basis for empirical mode decomposition, this limits the application of EEMD energy entropy, CEEMD energy entropy, and CNCEEMDAN energy entropy.

[0005] Researchers proposed wavelet packet energy entropy based on the wavelet packet decomposition method. Although the calculation cost of the wavelet packet decomposition method is relatively low, it is necessary to select an appropriate wavelet basis function. An inappropriate wavelet basis function may cause incorrect decomposition of signals, thereby reducing the ability of wavelet packet energy entropy to characterize faults.

[0006] In addition, the above energy entropy method cannot reliably extract flutter characteristics related to periodic N bifurcation.

[0007] To address the above problems, the present invention discloses a milling flutter detection method based on principal component energy entropy. This flutter detection method requires fewer detection parameters to be set, has a low dependence on artificial expert knowledge, and does not require relying on a large amount of historical data for model training, and can be applied to intelligent milling processing systems. Summary of the Invention

[0008] Object of the Invention: In order to overcome the deficiencies of the existing methods mentioned in the background art, the present invention requests to disclose a milling flutter detection method based on principal component energy entropy. Two principal component energy entropies are used to extract flutter indicators, and this method can detect the occurrence of flutter in real time and reliably.

[0009] Technical solution: A milling chatter detection method based on principal component energy entropy according to the present invention specifically includes the following steps:

[0010] Step (1): Select the sensor type, determine the installation position, and set the parameters related to chatter detection;

[0011] Step (2): Obtain one-dimensional synchronous vibration data;

[0012] Step (3): Expand the one-dimensional synchronous vibration data into multi-dimensional synchronous data;

[0013] Step (4): Perform zero-centralization processing on the multi-dimensional synchronous data respectively;

[0014] Step (5): Use principal component analysis to reduce the dimension of the multi-dimensional synchronous data after zero-centralization processing to obtain the principal components;

[0015] Step (6): Calculate the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2;

[0016] Step (7): Determine whether chatter occurs.

[0017] Further, in the step (1), the sensor types are vibration sensors and rotational speed sensors; the rotational speed sensor is installed near the milling cutter or the spindle and is used to measure the rotational speed data of the milling cutter; the vibration sensor is installed near the workpiece to be detected or the spindle and measures the vibration data of the workpiece or the spindle; the parameters related to chatter detection include: the number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, the rotational speed m of the milling cutter, the cumulative contribution rate threshold T, and the chatter thresholds r1 and r2.

[0018] Further, in the step (2), according to the preset number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, and the rotational speed m of the milling cutter, with the milling cutter rotational speed signal as a reference, the synchronous vibration data of the workpiece or the spindle is synchronously collected, and the collected one-dimensional synchronous vibration data can be expressed as Y = [y(1), y(2), y(3),..., y(mkM)].

[0019] Further, the implementation process of the step (3) is as follows:

[0020] According to the number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, and the rotational speed m of the milling cutter, the one-dimensional synchronous vibration data Y is expanded into M-dimensional data Y1, and the expanded M-dimensional data Y1 is as follows:

[0021]

[0022] where h = 1, 2,..., M.

[0023] Further, the implementation process of the step (4) is as follows:

[0024] The zero-centralization processing method is used to perform zero-centralization processing on each mk-dimensional vector in the M-dimensional synchronous data Y1. The M-dimensional data Y2 after zero-centralization processing is as follows:

[0025]

[0026] where is the average value of the h-th row data in the M-dimensional data Y1.

[0027] Furthermore, the implementation process of the step (5) is as follows:

[0028] First, regard the M-dimensional synchronous data Y2 as sample data composed of M variables and each variable containing mk samples, and use principal component analysis to perform dimensionality reduction processing on this sample data, and select the first a principal components X = [x1, x2, x3,..., xi,..., xa] whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold T for the first time; then regard the M-dimensional synchronous data Y2 as sample data composed of mk variables and each variable containing M samples, and use principal component analysis to perform dimensionality reduction processing on this sample data, and select the first b principal components Z = [z1, z2, z3,..., zj,..., zb] whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold T for the first time.

[0029] Furthermore, the implementation process of the step (6) is as follows:

[0030] First, calculate the energy values of the a principal components X = [x1, x2, x3,…, xi,…, xa] and the b principal components Z = [z1, z2, z3,..., zj,..., zb] respectively as E x =[E x1 ,E x2 ,E x3 ,...,E xi ,...,E xa and E z =[E z1 ,E z2 ,E z3 ,...,E zj ,...,E zb ;

[0031] Then, calculate the ratios of the energy of the a principal components X = [x1, x2, x3,..., xi,..., xa] and the b principal components Z = [z1, z2, z3,…, zj,..., zb] to their total energy as P x =[P x1 ,P x2 ,P x3 ,…,P xi,...,P xa and P z = [P z1 , P z2 , P z3 ,…, P zj ,..., P zb , where P xi and P zj are respectively:

[0032]

[0033] Finally, calculate the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2 respectively. The calculation process is as follows:

[0034]

[0035] Furthermore, the implementation process of step (7) is as follows:

[0036] Regard the two principal component energy entropies PCEE1 and PCEE2 obtained in step (6) as flutter indicators, and compare them with the flutter thresholds r1 and r2 set in step (1) respectively to determine whether flutter occurs; if the principal component energy entropies PCEE1 and PCEE2 are respectively less than or equal to the flutter threshold r1 and the flutter threshold r2, it is considered that flutter has occurred, otherwise flutter has not occurred. At this time, return to step (2) and continue to perform flutter detection for the next time window until flutter is detected or the detection process ends.

[0037] Beneficial effects

[0038] Compared with the prior art, the method of the present invention mainly has the following beneficial effects:

[0039] (1) A milling flutter detection method based on principal component energy entropy disclosed in this invention patent can effectively and reliably detect milling flutter.

[0040] (2) A milling flutter detection method based on principal component energy entropy disclosed in this invention patent has a relatively low computational complexity, low computational cost, and can quickly detect flutter.

[0041] (3) A milling flutter detection method based on principal component energy entropy disclosed in this invention patent is not affected by the change of spindle speed and can be applied to the milling flutter detection work with different speeds. Description of the drawings

[0042] Figure 1 is a flow chart of a milling flutter detection method based on principal component energy entropy disclosed in the present invention;

[0043] Figure 2This is the synchronous vibration displacement diagram of the workpiece without chatter in the embodiment of the present invention;

[0044] Figure 3 This is the synchronous vibration displacement diagram of the workpiece during Hopf bifurcation type chatter in the embodiment of the present invention;

[0045] Figure 4 This is the synchronous vibration displacement diagram of the workpiece during period-2 bifurcation type chatter in the embodiment of the present invention;

[0046] Figure 5 This is the synchronous vibration displacement diagram of the workpiece during period-3 bifurcation type chatter in the embodiment of the present invention;

[0047] Figure 6 This is the chatter detection result diagram of the principal component energy entropy PCEE1 in the embodiment of the present invention;

[0048] Figure 7 This is the chatter detection result diagram of the principal component energy entropy PCEE2 in the embodiment of the present invention. Detailed implementation manners

[0049] The following further elaborates on the present invention patent in conjunction with the attached drawings.

[0050] The present invention provides a milling chatter detection method based on principal component energy entropy, as Figure 1 shown, which specifically includes the following steps:

[0051] Step (1): Select the sensor type, determine the installation position, and set the relevant parameters for chatter detection;

[0052] The sensor types are vibration sensors and rotational speed sensors; the rotational speed sensor is installed near the milling cutter or the spindle, and is used to measure the rotational speed data of the milling cutter; the vibration sensor is installed near the workpiece to be detected or the spindle, and measures the vibration data of the workpiece or the spindle; the relevant parameters for chatter detection include: the number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, the rotational speed m of the milling cutter, the cumulative contribution rate threshold T, the chatter thresholds r1 and r2. In this embodiment, the selected milling cutter is a single-tooth milling cutter with the number of teeth being 1, the number of synchronous sampling points M within each tooth cycle of the milling cutter is set to 400, the rotational speed m of the milling cutter is set to 20, the cumulative contribution rate threshold T = 99%, and the chatter thresholds r1 and r2 are both 4.00.

[0053] Step (2): Collect one-dimensional synchronous vibration data;

[0054] According to the preset number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, and the rotational speed m of the milling cutter, with the rotational speed signal of the milling cutter as a reference, synchronously collect the synchronous vibration data of the workpiece or the spindle. The collected one-dimensional synchronous vibration data can be expressed as Y = [y(1), y(2), y(3),..., y(mkM)].

[0055] In this embodiment, according to the number of milling cutter teeth k = 1, the number of synchronous sampling points M = 400 per revolution period of the spindle, and the number of revolutions of the milling cutter m = 20, the one-dimensional synchronous vibration data Y can be expressed as Y = [y(1), y(2), y(3),..., y(8000)]. Figures 2 - 5 The synchronous vibration displacement data of the workpiece under chatter-free, Hopf bifurcation chatter, period-2 bifurcation chatter, and period-3 bifurcation chatter are respectively shown.

[0056] Step (3): Expand the one-dimensional synchronous vibration data into multi-dimensional synchronous data;

[0057] According to the number of milling cutter teeth k, the number of synchronous sampling points M = 400 per tooth period of the milling cutter, and the number of revolutions of the milling cutter m = 20, the one-dimensional synchronous vibration data Y is expanded into M-dimensional data Y1. The expanded M-dimensional data Y1 is as follows:

[0058]

[0059] where h = 1, 2,..., 400.

[0060] Step (4): Perform zero-centralization processing on the multi-dimensional synchronous data respectively;

[0061] Using the zero-centralization processing method, perform zero-centralization processing on each mk-dimensional vector in the M-dimensional synchronous data Y1. The zero-centralized M-dimensional data Y2 is as follows:

[0062]

[0063] where is the average value of the h-th row data in the M-dimensional data Y1.

[0064] Step (5): Use principal component analysis to reduce the dimension of the zero-centralized multi-dimensional synchronous data to obtain the principal components;

[0065] First, regard the M-dimensional synchronous data Y2 as sample data composed of M variables and each variable containing mk samples. Use principal component analysis to reduce the dimension of this sample data, and select the first a principal components X = [x1, x2, x3,..., xi,..., xa] whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold T for the first time; then regard the M-dimensional synchronous data Y2 as sample data composed of mk variables and each variable containing M samples. Use principal component analysis to reduce the dimension of this sample data, and select the first b principal components Z = [z1, z2, z3,..., zj,..., zb] whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold T for the first time.

[0066] Step (6): Calculate the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2;

[0067] First, calculate the energy values of a principal components \(X = [x_1, x_2, x_3, \ldots, x_i, \ldots, x_a]\) and b principal components \(Z = [z_1, z_2, z_3, \ldots, z_j, \ldots, z_b]\) as \(E\) x = [E x1 , E x2 , E x3 , \ldots, E xi , \ldots, E xa and \(E\) z = [E z1 , E z2 , E z3 , \ldots, E zj , \ldots, E zb ;

[0068] Then, calculate the ratios of the energy of a principal components \(X = [x_1, x_2, x_3, \ldots, x_i, \ldots, x_a]\) and b principal components \(Z = [z_1, z_2, z_3, \ldots, z_j, \ldots, z_b]\) to their total energy as \(P\) x = [P x1 , P x2 , P x3 , \ldots, P xi , \ldots, P xa and \(P\) z = [P z1 , P z2 , P z3 , \ldots, P zj , \ldots, P zb , where \(P\) xi and \(P\) zj are respectively:

[0069]

[0070] Finally, calculate the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2 respectively. The calculation process is as follows:

[0071]

[0072] Step (7): Determine whether flutter occurs.

[0073] Regarding the two principal component energy entropies PCEE1 and PCEE2 obtained in step (6) as flutter indicators, compare them with the flutter thresholds r1 and r2 set in step (1) respectively to determine whether flutter occurs. If the principal component energy entropies PCEE1 and PCEE2 are respectively less than or equal to the flutter thresholds r1 and r2, it is considered that flutter has occurred; otherwise, flutter has not occurred. At this time, return to step (2) and continue with the flutter detection for the next time window until flutter is detected or the detection process ends.

[0074] Figure 6 and Figure 7 respectively show the flutter detection results of the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2 of the method of the present invention. It can be seen from the figure that there are obvious differences between the principal component energy entropy without flutter and the principal component energy entropies in the other three flutter states. In this example, we set the two flutter thresholds to r1 = 4.00 and r2 = 4.00 respectively. From Figure 6 and Figure 7 it can be seen that the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2 without flutter are both greater than the set flutter thresholds r1 = 4.00 and r2 = 4.00, and it can be determined that the milling process is in a non-flutter machining state. The principal component energy entropies PCEE1 and PCEE2 in the three flutter states are both less than the set thresholds r1 = 4.00 and r2 = 4.00, so it can be determined that flutter has occurred in the milling process.

[0075] The present invention can detect milling flutter reliably and in real time. The method of the present invention not only has high detection accuracy and reliability, but also has a small computational complexity and low computational cost. In this embodiment, the computational cost of the method of the present invention was tested on a desktop computer with an Intel Core i5-8300H 2.30GHz CPU. The computational cost of calculating the principal component energy entropy PCEE1 or the principal component energy entropy PCEE2 1000 times by the method of the present invention is approximately 1.042 seconds, meeting the requirements of real-time detection of milling flutter.

[0076] In addition, for a milling flutter detection method based on principal component energy entropy disclosed by the present invention, fewer parameters are required. During the implementation of the method of the present invention, less expert knowledge is needed, and no large amount of historical data is required to train the model.

Claims

1. A milling chatter detection method based on principal component energy entropy according to the present invention specifically includes the following steps: Step (1): Select the sensor type, determine the installation position, and set the relevant parameters for chatter detection; Step (2): Obtain one-dimensional synchronous vibration data; Step (3): Expand the one-dimensional synchronous vibration data into multi-dimensional synchronous data; Step (4): Perform zero-centralization processing on the multi-dimensional synchronous data respectively; Step (5): Use principal component analysis to reduce the dimension of the multi-dimensional synchronous data after zero-centralization processing to obtain the principal components; Step (6): Calculate the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2; Step (7): Determine whether chatter occurs.

2. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that In step (1), the sensor types are vibration sensors and rotational speed sensors; the rotational speed sensor is installed near the milling cutter or the spindle and is used to measure the rotational speed data of the milling cutter; the vibration sensor is installed near the workpiece to be detected or the spindle and measures the vibration data of the workpiece or the spindle; The relevant parameters for chatter detection include: the number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, the rotational speed m of the milling cutter, the cumulative contribution rate threshold T, the chatter thresholds r1 and r2.

3. The milling chatter detection method based on principal component energy entropy according to claim 1, wherein In step (2), according to the preset number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, and the rotational speed m of the milling cutter, with the milling cutter rotational speed signal as a reference, synchronously collect the synchronous vibration data of the workpiece or the spindle. The collected one-dimensional synchronous vibration data can be expressed as Y = [y(1), y(2), y(3),..., y(mkM)].

4. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that In step (3), according to the number of teeth k of the milling cutter, the number of synchronous sampling points M within each tooth cycle of the milling cutter, and the rotational speed m of the milling cutter, expand the one-dimensional synchronous vibration data Y into M-dimensional data Y1. The expanded M-dimensional data Y1 is as follows: where h = 1, 2,..., M.

5. The milling chatter detection method based on principal component energy entropy according to claim 1, wherein In step (4), use the zero-centralization processing method to perform zero-centralization processing on each mk-dimensional vector in the M-dimensional data Y1. The mk-dimensional data Y2 after zero-centralization processing is as follows: Among them, is the average value of the h-th row data in the M-dimensional data Y1.

6. The milling chatter detection method based on principal component energy entropy according to claim 1, wherein In step (5), first regard the M-dimensional synchronous data Y2 as sample data composed of M variables and each variable containing mk samples, use principal component analysis to reduce the dimension of this data, and select the first a principal components X = [x1, x2, x3,..., xi,..., xa] whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold T for the first time; then regard the M-dimensional synchronous data Y2 as sample data composed of mk variables and each variable containing M samples, use principal component analysis to reduce the dimension of this data, and select the first b principal components Z = [z1, z2, z3,..., zj,..., zb] whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold T for the first time.

7. The milling chatter detection method based on principal component energy entropy according to claim 1, wherein In step (6), first, calculate the energy values of a principal components X = [x1, x2, x3,..., xi,..., xa] and b principal components Z = [z1, z2, z3,..., zj,..., zb] as E x = [E x1 , E x2 , E x3 ,..., E xi ,..., E xa and E z = [E z1 , E z2 , E z3 ,..., E zj ,..., E zb ; Then, calculate the ratios of the energies of a principal components \(X = [x_1, x_2, x_3, \cdots, x_i, \cdots, x_a]\) and b principal components \(Z = [z_1, z_2, z_3, \cdots, z_j, \cdots, z_b]\) to their total energies as \(P\) x = [P x1 , P x2 , P x3 , \cdots, P xi , \cdots, P xa and \(P\) z = [P z1 , P z2 , P z3 , \cdots, P zj , \cdots, P zb , where \(P\) xi and \(P\) zj are respectively: Finally, calculate the principal component energy entropy PCEE1 and the principal component energy entropy PCEE2 respectively. The calculation process is as follows:

8. The milling chatter detection method based on principal component energy entropy according to claim 1, wherein Regarding the two principal component energy entropies PCEE1 and PCEE2 obtained in step (6) as flutter indicators, compare them with the flutter thresholds r1 and r2 set in step (1) respectively to determine whether flutter occurs. If the principal component energy entropies PCEE1 and PCEE2 are respectively less than or equal to the flutter threshold r1 and the flutter threshold r2, it is considered that flutter has occurred; otherwise, flutter has not occurred. At this time, return to step (2) and continue with the flutter detection for the next time window until flutter is detected or the detection process ends.

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