Milling chatter detection method based on principal component energy entropy

Abstract

This invention discloses a milling chatter detection method based on principal component energy entropy; belonging to the field of mechanical system fault detection technology, the operation steps are as follows: select sensor type, determine installation location and set chatter detection related parameters; acquire one-dimensional synchronous vibration data; expand the one-dimensional synchronous vibration data into multi-dimensional synchronous data; perform zero-centering processing on the multi-dimensional synchronous data respectively; use principal component analysis to reduce the dimensionality of the zero-centered multi-dimensional synchronous data to obtain principal components; calculate the principal component energy entropy PCEE1 and principal component energy entropy PCEE2; determine whether chatter occurs; the milling chatter detection method based on principal component energy entropy disclosed in this patent can effectively and reliably detect milling chatter; this invention has low computational complexity and low computational cost, and can quickly detect chatter; in addition, this invention is not affected by changes in spindle speed and can be applied to milling chatter detection at different speeds.

Description

Technical Field

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

[0002] In the field of machining, milling is widely used in key industries such as aerospace, automotive manufacturing, and mold processing due to its high efficiency and precision. However, chatter during milling has consistently hindered improvements in machining efficiency and quality. Chatter is a self-excited vibration caused by the dynamic interaction between the tool and the workpiece. Its generation mechanism is complex, involving multiple factors such as the dynamic characteristics of the machine tool-tool-workpiece system, cutting parameter matching, and environmental disturbances. Chatter not only causes deterioration of the machined surface quality (such as chatter marks and burrs), abnormal tool wear, and even chipping, but it can also damage machine tool components, significantly increasing production costs. According to industry statistics, chatter-related machining failures account for more than 30% of precision machining failures. Therefore, chatter detection has significant economic implications.

[0003] In flutter detection, flutter feature extraction is one of the most important aspects. For complex flutter signals, signal decomposition methods are generally used to process them, breaking them down into a series of nonlinear components with clear physical meaning. These decomposed components are then further processed and analyzed to extract flutter-sensitive feature quantities, such as energy entropy.

[0004] Currently, commonly used signal decomposition methods include wavelet packet decomposition, empirical mode decomposition, variable mode decomposition, and their improved algorithms. Therefore, various energy entropies can be obtained based on these decomposition methods. Patent application number 2021110169321 discloses an EEMD energy entropy based on EEMD. This energy entropy can be used to assess the health status of bearings. Patent application number 2022106550476 discloses a CEEMD energy entropy based on CEEMD and proposes a bearing fault diagnosis method based on CEEMD energy entropy. Patent 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 aliasing 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 derive energy entropy based on the energy distribution of these components. While EEMD, CEEMD, and CNCEEMDAN energy entropies can all characterize bearing faults, their computational cost is relatively high. Furthermore, EEMD, CEEMD, and CNCEEMDAN are all improved algorithms developed from empirical mode decomposition. The lack of rigorous mathematical foundations in empirical mode decomposition limits the application of EEMD, CEEMD, and CNCEEMDAN energy entropies.

[0005] Researchers have proposed wavelet packet energy entropy based on wavelet packet decomposition. While wavelet packet decomposition is relatively computationally inexpensive, selecting appropriate wavelet basis functions is crucial. Inappropriate basis functions can lead to erroneous decomposition signals, thereby reducing the ability of wavelet packet energy entropy to characterize faults.

[0006] Furthermore, the energy entropy method described above cannot reliably extract flutter features associated with periodic N-bifurcation.

[0007] To address the aforementioned problems, this invention discloses a milling chatter detection method based on principal component energy entropy. This chatter detection method requires fewer detection parameters, has low dependence on human expert knowledge, and does not require model training based on a large amount of historical data. It can be applied to intelligent milling machining systems. Summary of the Invention

[0008] Purpose of the invention: In order to overcome the shortcomings of existing methods mentioned in the background art, this invention requests the disclosure of a milling chatter detection method based on principal component energy entropy. Two principal component energy entropies are used to extract chatter indicators. This method can detect whether chatter occurs in real time and reliably.

[0009] Technical solution: The milling chatter detection method based on principal component energy entropy described in this invention specifically includes the following steps:

[0010] Step (1): Select the sensor type, determine the installation location, and set the relevant parameters for flutter 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): Process multidimensional synchronized data separately using zero-centralization;

[0014] Step (5): Use principal component analysis to reduce the dimensionality of the multidimensional synchronous data after zero-centered processing to obtain principal components;

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

[0016] Step (7): Determine if flutter occurs.

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

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

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

[0020] Based on the number of milling cutter teeth k, the number of synchronous sampling points M per tooth cycle, and the milling cutter rotation speed m, the one-dimensional synchronous vibration data Y is expanded into M-dimensional data Y1, as shown below:

[0021]

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

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

[0024] The zero-centering method is used to perform zero-centering on each mk-dimensional vector in the M-dimensional synchronous data Y1. The resulting M-dimensional data Y2 after zero-centering is shown below:

[0025]

[0026] in, Let be the average value of the h-th row of data in the M-dimensional data Y1.

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

[0028] First, the M-dimensional synchronous data Y2 is considered as sample data consisting of M variables and mk samples in each variable. Principal component analysis is used to reduce the dimensionality of this sample data, and the first a principal components X = [x1,x2,x3,...,xi,...,xa] whose cumulative contribution rate is first greater than or equal to the cumulative contribution rate threshold T are selected. Then, the M-dimensional synchronous data Y2 is considered as sample data consisting of mk variables and M samples in each variable. Principal component analysis is used to reduce the dimensionality of this sample data, and the first b principal components Z = [z1,z2,z3,...,zj,...,zb] whose cumulative contribution rate is first greater than or equal to the cumulative contribution rate threshold T are selected.

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

[0030] First, calculate the energy value E for each of the a principal components X = [x1,x2,x3,…,xi,…,xa] and the b principal components Z = [z1,z2,z3,...,zj,...,zb]. 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 ratio of the energy of each of the a principal components X = [x1, x2, x3, ..., xi, ..., xa] and the energy of each of the b principal components Z = [z1, z2, z3, ..., zj, ..., zb] to their total energy, and denote the value 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 They are respectively:

[0032]

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

[0034]

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

[0036] The two principal component energy entropies PCEE1 and PCEE2 obtained in step (6) are regarded as flutter indicators and compared with the flutter thresholds r1 and r2 set in step (1) to determine whether flutter has occurred. If the principal component energy entropies PCEE1 and PCEE2 are less than or equal to the flutter thresholds r1 and r2 respectively, 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 in 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) The milling chatter detection method based on principal component energy entropy disclosed in this patent can effectively and reliably detect milling chatter.

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

[0041] (3) The milling chatter detection method based on principal component energy entropy disclosed in this patent is not affected by the spindle speed change and can be applied to milling chatter detection at different speeds. Attached Figure Description

[0042] Figure 1 This is a flowchart of a milling chatter detection method based on principal component energy entropy disclosed in this invention;

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

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

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

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

[0047] Figure 6 This is a graph showing the flutter detection results of the principal component energy entropy (PCEE1) in an embodiment of the present invention.

[0048] Figure 7 This is a graph showing the flutter detection results of the principal component energy entropy (PCEE2) in an embodiment of the present invention. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings.

[0050] This invention provides a method for detecting milling chatter based on principal component energy entropy, such as... Figure 1 As shown, the specific steps include:

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

[0052] The sensors are vibration sensors and speed sensors. The speed sensor is installed near the milling cutter or spindle to measure the milling cutter speed data. The vibration sensor is installed near the workpiece to be detected or the spindle to measure the vibration data of the workpiece or spindle. The chatter detection parameters include: the number of milling cutter teeth k, the number of synchronous sampling points M per tooth cycle, the milling cutter rotation speed m, the cumulative contribution rate threshold T, and the chatter thresholds r1 and r2. In this embodiment, a single-tooth milling cutter with 1 tooth is selected. The number of synchronous sampling points M per tooth cycle is set to 400, the milling cutter rotation speed m 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] Based on the pre-set number of milling cutter teeth k, the number of synchronous sampling points M per tooth cycle of the milling cutter, and the number of milling cutter revolutions m, synchronous vibration data of the workpiece or spindle is collected synchronously with the milling cutter speed signal as a reference. The collected one-dimensional synchronous vibration data can be expressed as Y=[y(1),y(2),y(3),...,y(mkM)].

[0055] In this implementation, based on the number of milling cutter teeth k=1, the number of synchronous sampling points M=400 per spindle revolution, and the number of milling cutter revolutions 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 workpieces under the following conditions are displayed: no chatter, Hopf bifurcation chatter, period-2 bifurcation chatter, and period-3 bifurcation chatter.

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

[0057] Based on the number of milling cutter teeth k, the number of synchronous sampling points M = 400 per tooth cycle, and the milling cutter rotation speed m = 20, the one-dimensional synchronous vibration data Y is expanded into M-dimensional data Y1, as shown below:

[0058]

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

[0060] Step (4): Process multidimensional synchronized data separately using zero-centralization;

[0061] The zero-centering method is used to perform zero-centering on each mk-dimensional vector in the M-dimensional synchronous data Y1. The resulting M-dimensional data Y2 after zero-centering is shown below:

[0062]

[0063] in, Let be the average value of the h-th row of data in the M-dimensional data Y1.

[0064] Step (5): Use principal component analysis to reduce the dimensionality of the multidimensional synchronous data after zero-centered processing to obtain principal components;

[0065] First, the M-dimensional synchronous data Y2 is considered as sample data consisting of M variables and mk samples in each variable. Principal component analysis is used to reduce the dimensionality of this sample data, and the first a principal components X = [x1,x2,x3,...,xi,...,xa] whose cumulative contribution rate is first greater than or equal to the cumulative contribution rate threshold T are selected. Then, the M-dimensional synchronous data Y2 is considered as sample data consisting of mk variables and M samples in each variable. Principal component analysis is used to reduce the dimensionality of this sample data, and the first b principal components Z = [z1,z2,z3,...,zj,...,zb] whose cumulative contribution rate is first greater than or equal to the cumulative contribution rate threshold T are selected.

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

[0067] First, calculate the energy value E for each of the a principal components X = [x1,x2,x3,...,xi,...,xa] and the b principal components Z = [z1,z2,z3,...,zj,...,zb]. x =[E x1 E x2 E x3 ,...,E xi ,...,E xa ] and E z =[E z1 E z2 E z3 ,...,E zj ,...,E zb ];

[0068] Then, calculate the ratio of the energy of each of the a principal components X = [x1, x2, x3, ..., xi, ..., xa] and the energy of each of the b principal components Z = [z1, z2, z3, ..., zj, ..., zb] to the total energy, respectively, 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 They are respectively:

[0069]

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

[0071]

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

[0073] The two principal component energy entropies PCEE1 and PCEE2 obtained in step (6) are regarded as flutter indicators and compared with the flutter thresholds r1 and r2 set in step (1) to determine whether flutter has occurred. If the principal component energy entropies PCEE1 and PCEE2 are less than or equal to the flutter thresholds r1 and r2 respectively, 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 in the next time window until flutter is detected or the detection process ends.

[0074] Figure 6 and Figure 7 The flutter detection results of principal component energy entropy (PCEE1) and principal component energy entropy (PCEE2) using the method of this invention are shown respectively. It can be seen from the figures that the principal component energy entropy without flutter is significantly different from the principal component energy entropy under the other three flutter conditions. In this example, we set the two flutter thresholds to r1 = 4.00 and r2 = 4.00, respectively. Figure 6 and Figure 7 It can be seen that when there is no chatter, both the principal component energy entropy PCEE1 and PCEE2 are greater than the set chatter thresholds r1 = 4.00 and r2 = 4.00, indicating that the milling process is in a chatter-free state. When there is chatter in all three states, the principal component energy entropy PCEE1 and PCEE2 are less than the set thresholds r1 = 4.00 and r2 = 4.00, indicating that chatter has occurred during milling.

[0075] This invention can reliably and in real-time detect milling chatter. The method of this invention not only has high detection accuracy and reliability, but also low computational complexity and cost. In this embodiment, the computational cost of the method of this invention was tested using a desktop computer with an Intel Core i5-8300H 2.30GHz CPU. The computational cost of calculating 1000 principal component energy entropies (PCEE1) or PCEE2 using the method of this invention is approximately 1.042 seconds, which meets the requirements for real-time detection of milling chatter.

[0076] In addition, the milling chatter detection method based on principal component energy entropy disclosed in this invention requires fewer parameters. Implementing this method requires less expert knowledge and does not require a large amount of historical data to train the model.

Claims

1. A method for detecting milling chatter based on principal component energy entropy, specifically including the following steps: Step (1): Select the sensor type, determine the installation location, and set the relevant parameters for flutter 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): Process multidimensional synchronized data separately using zero-centralization; Step (5): Use principal component analysis to reduce the dimensionality of the multidimensional synchronous data after zero-centered processing to obtain principal components; Step (6): Calculate the principal component energy entropy PCEE1 and principal component energy entropy PCEE2; Step (7): Determine if flutter 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 sensor and speed sensor; the speed sensor is installed near the milling cutter or spindle to measure the milling cutter speed data; the vibration sensor is installed near the workpiece to be detected or the spindle to measure the vibration data of the workpiece or spindle. The chatter detection parameters include: the number of milling cutter teeth k, the number of synchronous sampling points M per tooth cycle of the milling cutter, the number of milling cutter revolutions m, the cumulative contribution rate threshold T, and the chatter thresholds r1 and r2.

3. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that, In step (2), based on the preset number of milling cutter teeth k, the number of synchronous sampling points M per tooth cycle of the milling cutter and the number of milling cutter rotations m, the synchronous vibration data of the workpiece or spindle is synchronously collected with reference to the milling cutter rotation speed signal. 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), based on the number of milling cutter teeth k, the number of synchronous sampling points M per tooth cycle, and the milling cutter rotation speed m, the one-dimensional synchronous vibration data Y is expanded into M-dimensional data Y1. The expanded M-dimensional data Y1 is shown below: Where h = 1, 2, ..., M.

5. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that, In step (4), each mk-dimensional vector in the M-dimensional data Y1 is zero-centered using the zero-centering method. The mk-dimensional data Y2 after zero-centering is shown below: in, Let be the average value of the h-th row of data in the M-dimensional data Y1.

6. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that, In step (5), the M-dimensional synchronous data Y2 is first regarded as sample data consisting of M variables and mk samples in each variable. Principal component analysis is used to reduce the dimensionality of the data, and the first a principal components X = [x1,x2,x3,...,xi,...,xa] whose cumulative contribution rate is first greater than or equal to the cumulative contribution rate threshold T are selected. Then, the M-dimensional synchronous data Y2 is regarded as sample data consisting of mk variables and M samples in each variable. Principal component analysis is used to reduce the dimensionality of the data, and the first b principal components Z = [z1,z2,z3,...,zj,...,zb] whose cumulative contribution rate is first greater than or equal to the cumulative contribution rate threshold T are selected.

7. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that, In step (6), firstly, the energy values ​​E of the a principal components X = [x1,x2,x3,...,xi,...,xa] and the b principal components Z = [z1,z2,z3,...,zj,...,zb] are calculated respectively. 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 ratio of the energy of each of the a principal components X = [x1, x2, x3, ..., xi, ..., xa] and the energy of each of the b principal components Z = [z1, z2, z3, ..., zj, ..., zb] to the total energy, respectively, 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 They are respectively: Finally, the principal component energy entropy PCEE1 and principal component energy entropy PCEE2 are calculated separately. The calculation process is as follows:

8. The milling chatter detection method based on principal component energy entropy according to claim 1, characterized in that, The two principal component energy entropies PCEE1 and PCEE2 obtained in step (6) are regarded as flutter indicators and compared with the flutter thresholds r1 and r2 set in step (1) to determine whether flutter has occurred. If the principal component energy entropies PCEE1 and PCEE2 are less than or equal to the flutter thresholds r1 and r2 respectively, 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 in the next time window until flutter is detected or the detection process ends.

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