An EEMD-BPF-based coupling chatter signal extraction method for industrial robot milling and reaming

Abstract

This invention discloses a method for extracting chatter signals from milling and reaming coupling in industrial robots based on EEMD-BPF, comprising the following steps: preprocessing the original force signal using the EEMD method to decompose it into intrinsic mode components (IMFs). s (N represents the total number of sampling points of the force signal) and residual component RS; intrinsic mode component IMF s The intrinsic modal components (IMFs) with the coupling flutter frequency as the dominant excitation frequency were found. c As the dominant modal component of coupled flutter, the correlation coefficient thresholding method is used to analyze the dominant modal component IMF. c Select n IMFs with coupling flutter correlation s The BPF method was used to analyze IMFs with coupled flutter correlation. s Bandpass filtering is performed to obtain the IMF. s The system contains coupled chatter signal components (m=1,2,...,n); based on the principle of signal superposition, these coupled chatter signal components are superimposed to obtain a reconstructed coupled chatter signal. This invention can improve the accuracy of coupled chatter signal extraction in industrial robot milling and reaming, meeting the hole-making processing requirements in intelligent manufacturing.

Description

Technical Field

[0001] This invention relates to the field of industrial robot machining signal processing technology, specifically to a method for extracting chatter signals from milling and reaming coupling in industrial robots based on EEMD-BPF. Background Technology

[0002] With the emergence of the concept of intelligent manufacturing, machine tool processing can no longer meet the design requirements of personalized and customized industrial chains. Industrial robots, with their high flexibility and large workspace, are destined to become the jewel of the next generation of manufacturing. However, currently, the limited rigidity of the robot body hinders its development in the field of cutting processing. Chatter, as an important manifestation of instability in cutting processing, takes the form of coupled chatter primarily in robot machining. The occurrence of coupled chatter not only affects the processing quality of products but can also severely damage the processing system. Therefore, the effective extraction of coupled chatter signals in industrial robot machining is of great significance for process stability and product accuracy improvement.

[0003] Numerous research findings have been made regarding the effective extraction of coupled flutter signals from industrial robot machining. The mainstream methods include Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), and Variational Mode Decomposition (VMD). While EMD, as a precursor to EEMD, possesses adaptive decomposition capabilities, it cannot prevent mode aliasing from affecting the effective extraction of coupled flutter signals. Although EEMD introduces white noise to suppress mode aliasing to some extent, the suppression primarily targets aliasing in high-frequency modes, offering little effect on aliasing in the low-frequency modes (typically 10-100Hz) where the coupled flutter signal resides. Furthermore, its computational complexity places certain demands on the operating equipment. While VMD outperforms the former two in suppressing mode aliasing, it retains the shortcomings of clustering and segmentation algorithms in terms of the predefined number of modes K, making it difficult to achieve ideal results in practical signal processing.

[0004] While the above methods can produce some effect in the extraction of coupled chatter signals in industrial robot machining, they are difficult to suppress modal aliasing in the results. Furthermore, for finishing processes such as milling and hole reaming, the actual cutting depth is small, and the coupled chatter energy generated by the cutting force is low. This results in modal aliasing in the signal decomposition results having a significant impact on the effective extraction of coupled chatter signals. It is difficult to achieve the desired effect using existing methods. Summary of the Invention

[0005] In view of this, the present invention addresses the modal aliasing problem in the extraction of coupled chatter signals during milling and reaming of industrial robots in the prior art, and provides a method for extracting coupled chatter signals during milling and reaming of industrial robots based on EEMD-BPF.

[0006] The technical solution of this invention is to provide a method for extracting chatter signals from milling and reaming coupling in industrial robots based on EEMD-BPF, the specific steps of which are as follows:

[0007] Step 1: Use the EEMD method to process the force signal Preprocessing is performed to decompose the intrinsic mode components (IMFs) at different frequencies. s ( N represents the force signal. (Total number of sampling points) and residual signal RS;

[0008] In step one, the EEMD method is used to process the force signal. The preprocessing process includes four steps: (1) setting the overall mean frequency M; (2) converting the standard normal white noise into a standard normal distribution. (j=1,2,...,M, 50) M 100) superimposed on the input signal To generate new signals (j=1,2,...,M); (3) For M signals EMD decomposition yields M IMFs. s Sequence; (4) For M IMFs s The sequence is averaged to obtain the intrinsic mode components (IMFs) at different frequencies. s ;

[0009] Further, the EMD decomposition in step (3) specifically includes the following steps: (1) acquiring the input signal (2) Generate the upper and lower envelopes using cubic polynomial interpolation. , (3) Take the average of the upper and lower envelopes. (4) Determine the difference Whether the IMF conditions are met is determined by the following conditions: the number of local extrema and zero-crossings is equal or differs by one within the sampling time, and the mean of the upper and lower envelopes is 0 at any given time. If these conditions are not met, then... As the input signal, repeat steps (1) to (4) until the condition is met, and finally obtain the result. As the first intrinsic mode component, i.e., IMF j1 (5) Using input signals Subtract IMF j1 Obtain the residual (6) Using residuals As a new input signal, repeat steps (1) to (5) until the residual is a monotonic function or has only one extreme value, which is the residual signal. At this time, the signal It is decomposed into multiple intrinsic mode components and a residual signal, i.e. ( N represents the force signal. (Total number of sampling points)

[0010] Furthermore, in the EMD decomposition, step (1) uses a one-sided trend discrimination method to obtain the maximum and minimum values ​​of the signal. The specific calculation process is as follows:

[0011]

[0012]

[0013]

[0014] in, Indicates the total number of sampling points. The set of sampling points Indicates that the sampling point is in the sampling set The number in the middle, Indicates sampling number The corresponding ordinate, Indicates that the sampling point is in the sampling set or The serial number in Labels for sampling points showing a downward trend With serial number The set constituted The labels for sampling points showing an upward trend. With serial number The set that constitutes; in the set In the middle, the label of the maximum point satisfy ,and The label of the left adjacent minimum point is In the set In the text, the label of the minimum point satisfy ,and The label of the left adjacent maximum point is ;

[0015] Step 2: Intrinsic Mode Components (IMF) s The intrinsic modal components (IMFs) with the coupling flutter frequency as the dominant excitation frequency were found. cAs the dominant modal component of coupled flutter, the correlation coefficient threshold method is used to calculate the IMF. s With the dominant mode component of coupled flutter IMF c Correlation coefficient between ( Selecting those with coupling flutter correlation ( ) IMF s Correlation coefficient in correlation discrimination The criteria for judgment are: (1) no correlation or very weak correlation: (2) Weak correlation: (3) Moderately relevant: (4) Strong correlation: (5) Extremely strong correlation: ;

[0016] The correlation coefficient in step two The calculation formula is:

[0017]

[0018] Step 3: Apply a band-pass filter (BPF) to filter components with coupling flutter correlation. IMF s Filtering is performed to obtain the IMF. s Included flutter signal components (m=1,2,...,n);

[0019] In step three, the BPF method is used to analyze the coupling flutter correlation. IMF s The filtering process is characterized by integrating a Kalman filter method with a fourth-order Butterworth narrowband filter to filter the narrowband output. (m=1,2,...,n) undergoes white noise filtering to obtain the final coupled flutter signal components. The specific calculation process is as follows:

[0020] Fourth-order Butterworth narrowband filter transfer function for:

[0021]

[0022]

[0023] in For quality factors, Indicates the sampling frequency of the input signal. Indicates the low-end cutoff frequency of the passband. Indicates the high-end cutoff frequency of the passband. Indicates the center frequency of the coupled flutter signal. Indicates the low-end cutoff frequency of the passband. The normalized angular frequency, Indicates the high-end cutoff frequency of the passband. The normalized angular frequency, Indicates the frequency of the coupled flutter signal The normalized angular frequency;

[0024] Obtained through bilinear transformation z-transform expression and according to The coefficients of each item are obtained Discretized expression :

[0025]

[0026] In the formula, T represents the sampling interval. , for The coefficients corresponding to the terms in the numerator and denominator, where k represents the number of samples. Indicates signal The corresponding IMF with coupling flutter correlation s Narrowband filter output at the k-th sampling point;

[0027] Filtering out by Kalman filtering method The white noise in the image is used to obtain the final output after BPF processing. :

[0028]

[0029] In the formula express covariance, Indicates the input signal The covariance of the observation noise included. Indicates the input signal The covariance of process noise included;

[0030] Finally, the discretized expression after white noise removal. The final coupled flutter signal components are obtained. ;

[0031] Step 4: Based on the principle of signal superposition, combine the coupled flutter signal components obtained in Step 3. The reconstructed coupled flutter signal is obtained by superposition processing. ;

[0032] In step four The specific calculation formula is as follows:

[0033]

[0034] Where n represents the number of intrinsic mode components with coupled flutter correlation.

[0035] Compared with existing technologies, this invention has the following advantages: By employing the correlation coefficient thresholding method and the BPF method, this invention can avoid the impact of modal coupling in the EEMD results on the effective extraction of coupled chatter signals during milling and reaming in industrial robots. Furthermore, considering the large computational load in the EEMD implementation process, a one-sided trend discrimination method is introduced to simplify the process of determining extreme values. In summary, this invention can improve the accuracy of coupled chatter signal extraction during milling and reaming in industrial robots, meeting the needs of hole processing monitoring and quality improvement in intelligent manufacturing. Attached Figure Description

[0036] Figure 1 This is a flowchart of the method for extracting chatter signals from milling and reaming coupling in industrial robots based on EEMD-BPF according to the present invention.

[0037] Figure 2 This refers to the milling and reaming force sensor signal for an industrial robot, as described in this embodiment of the invention.

[0038] Figure 3 The result of EEMD processing and correlation discrimination of the industrial robot milling and reaming force sensor signal in this embodiment of the invention;

[0039] Figure 4 The logarithmic magnitude-frequency response curve of the transfer function of the fourth-order Butterworth narrowband filter according to an embodiment of the present invention;

[0040] Figure 5 The logarithmic phase frequency response curve of the transfer function of the fourth-order Butterworth narrowband filter according to an embodiment of the present invention;

[0041] Figure 6 The Fourier transform of the dominant modal component IMF5 of the milling and reaming coupling chatter of the industrial robot in this embodiment of the invention;

[0042] Figure 7 The results of extracting the coupled chatter signal of the industrial robot milling and reaming in this embodiment of the invention. Fourier transform. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0044] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, the accompanying drawings are not drawn to scale precisely for illustrative purposes and are intentionally left blank.

[0045] like Figure 1 As shown, the present invention provides a method for extracting chatter signals from milling and reaming coupling in industrial robots based on EEMD-BPF, comprising the following steps:

[0046] Step 1: Use the EEMD method to process the force signal Preprocessing is performed to decompose the intrinsic mode components (IMFs) at different frequencies. s ( N represents the force signal. (Total number of sampling points) and residual signal RS;

[0047] In step one, the EEMD method is used to process the force signal. The preprocessing process includes four steps: (1) setting the overall mean frequency M; (2) converting the standard normal white noise into a standard normal distribution. (j=1,2,...,M, 50) M 100) superimposed on the input signal To generate new signals (j=1,2,...,M); (3) For M signals EMD decomposition yields M IMFs. s Sequence; (4) For M IMFs s The sequence is averaged to obtain the intrinsic mode components (IMFs) at different frequencies. s ;

[0048] Further, the EMD decomposition in step (3) specifically includes the following steps: (1) acquiring the input signal (2) Generate the upper and lower envelopes using cubic polynomial interpolation. , (3) Take the average of the upper and lower envelopes. (4) Determine the difference Whether the IMF conditions are met is determined by the following conditions: the number of local extrema and zero-crossings is equal or differs by one within the sampling time, and the mean of the upper and lower envelopes is 0 at any given time. If these conditions are not met, then... As the input signal, repeat steps (1) to (4) until the condition is met, and finally obtain the result. As the first intrinsic mode component, i.e., IMF j1 (5) Using input signals Subtract IMF j1 Obtain the residual (6) Using residuals As a new input signal, repeat steps (1) to (5) until the residual is a monotonic function or has only one extreme value, which is the residual signal. At this time, the signal It is decomposed into multiple intrinsic mode components and a residual signal, i.e. ( N represents the force signal. (Total number of sampling points)

[0049] Furthermore, in the EMD decomposition, step (1) uses a one-sided trend discrimination method to obtain the maximum and minimum values ​​of the signal. The specific calculation process is as follows:

[0050]

[0051]

[0052]

[0053] in, Indicates the total number of sampling points. The set of sampling points Indicates that the sampling point is in the sampling set The number in the middle, Indicates sampling number The corresponding ordinate, Indicates that the sampling point is in the sampling set or The serial number in Labels for sampling points showing a downward trend With serial number The set constituted The labels for sampling points showing an upward trend. With serial number The set that constitutes; in the set In the middle, the label of the maximum point satisfy ,and The label of the left adjacent minimum point is In the set In the text, the label of the minimum point satisfy ,and The label of the left adjacent maximum point is ;

[0054] According to the process in step one, for Figure 2 The milling and reaming force signal (taken for 10-20 seconds, with a signal sampling frequency of 2kHz) was decomposed using EEMD, and the decomposition result was: 12 IMFs. s 1 Res;

[0055] Step 2: Intrinsic Mode Components (IMF) s The intrinsic modal components (IMFs) with the coupling flutter frequency as the dominant excitation frequency were found. c As the dominant modal component of coupled flutter, the correlation coefficient threshold method is used to calculate the IMF. s With the dominant mode component of coupled flutter IMF c Correlation coefficient between ( Selecting those with coupling flutter correlation ( ) IMF s Correlation coefficient in correlation discrimination The criteria for judgment are: (1) no correlation or very weak correlation: (2) Weak correlation: (3) Moderately relevant: (4) Strong correlation: (5) Extremely strong correlation: ;

[0056] The correlation coefficient in step two The calculation formula is:

[0057]

[0058] According to the process in step two, based on the frequency of modal coupling flutter in robot machining (typically between 10-100Hz) and IMF... s The frequency domain transformation results determined that the dominant mode component of the coupled flutter was IMF5. The IMF5 and IMF were then calculated. s The correlation coefficients between them are shown in Table 1:

[0059] Table 1: IMF5 and other IMFs s Correlation coefficient between

[0060] <![CDATA[IMF s ]]> <![CDATA[IMF1]]> <![CDATA[IMF2]]> <![CDATA[IMF3]]> <![CDATA[IMF4]]> <![CDATA[IMF5]]> <![CDATA[IMF6]]> Rs 0.0037 0.0042 0.0438 0.3388 1 0.4391 <![CDATA[IMF s ]]> <![CDATA[IMF7]]> <![CDATA[IMF8]]> <![CDATA[IMF9]]> <![CDATA[IMF 10 ]]> <![CDATA[IMF 11 ]]> <![CDATA[IMF 12 ]]> Rs 0.0109 0.0186 0.0066 0.0062 0.0043 0.0010

[0061] Based on the correlation discrimination criteria in step two and the results in Table 1, the IMFs with coupled flutter correlations were determined. s The result is Figure 3 They are: IMF4, IMF5, and IMF6;

[0062] Step 3: Apply a band-pass filter (BPF) to filter components with coupling flutter correlation. IMF s Filtering is performed to obtain the IMF. s Included flutter signal components (m=1,2,...,n);

[0063] In step three, the BPF method is used to analyze the coupling flutter correlation. IMF s The filtering process is characterized by integrating a Kalman filter method with a fourth-order Butterworth narrowband filter to filter the narrowband output. (m=1,2,...,n) undergoes white noise filtering to obtain the final coupled flutter signal components. The specific calculation process is as follows:

[0064] Fourth-order Butterworth narrowband filter transfer function for:

[0065]

[0066]

[0067] in For quality factors, Indicates the sampling frequency of the input signal. Indicates the low-end cutoff frequency of the passband. Indicates the high-end cutoff frequency of the passband. Indicates the center frequency of the coupled flutter signal. Indicates the low-end cutoff frequency of the passband. The normalized angular frequency, Indicates the high-end cutoff frequency of the passband. The normalized angular frequency, Indicates the frequency of the coupled flutter signal The normalized angular frequency;

[0068] Obtained through bilinear transformation z-transform expression and according to The coefficients of each item are obtained Discretized expression :

[0069]

[0070] In the formula, T represents the sampling interval. , for The coefficients corresponding to the terms in the numerator and denominator, where k represents the number of samples. Indicates signal The corresponding IMF with coupling flutter correlation s Narrowband filter output at the k-th sampling point;

[0071] Filtering out by Kalman filtering method The white noise in the image is used to obtain the final output after BPF processing. :

[0072]

[0073] In the formula express covariance, Indicates the input signal The covariance of the observation noise included. Indicates the input signal The covariance of process noise included;

[0074] Finally, the discretized expression after white noise removal. The final coupled flutter signal components are obtained. ;

[0075] According to the frequency domain transformation of the coupled flutter dominant mode component IMF5 in the embodiment, the result is: Figure 6 The coupling flutter frequency was determined to be 16.5Hz, therefore the BPF parameters were set as follows: sampling rate The center frequency is 2kHz. It is 16.5Hz. =0, =0, It is 0.01. =0;

[0076] The BPF parameter settings described above can be used to determine the following: and Constraints:

[0077]

[0078] Calculate the quality factor The range of values ​​is You might as well take It is 1.5;

[0079] when When the value is 1.5, the transfer function of the fourth-order Butterworth narrowband filter is:

[0080]

[0081] The corresponding logarithmic magnitude frequency response curve is Figure 4 The logarithmic phase frequency response curve is Figure 5 , Figure 4 As can be seen, the amplitude attenuation corresponding to the flutter frequency is almost zero, fully preserving the flutter information in the dominant mode component of flutter. Furthermore, thanks to the advantages of narrowband filtering, a large amplitude attenuation can be quickly achieved near the center frequency of the flutter. Therefore, narrowband filtering has a good resolution effect on the center frequency of the flutter. Figure 5 The phase margin corresponding to the coupled flutter frequency can be seen from this. This indicates that the narrowband filtering process has a good stability margin and the filtering results do not exhibit divergence.

[0082] Furthermore, the Kalman filter equation can be expressed as:

[0083]

[0084] The narrowband filtering fusion Kalman filtering method achieves the filtering of white noise introduced in EEMD decomposition and white noise generated during signal acquisition.

[0085] The aforementioned narrowband filter fusion Kalman filter method is used to filter the intrinsic mode components IMF4, IMF5, and IMF6 with coupling flutter correlation extracted in step two, thereby obtaining the coupling flutter signal components contained therein. (m=1,2,3);

[0086] Step 4: Based on the principle of signal superposition, combine the coupled flutter signal components obtained in Step 3. The reconstructed coupled flutter signal is obtained by superposition processing. ;

[0087] In step four The specific calculation formula is as follows:

[0088]

[0089] Where n represents the number of intrinsic mode components with coupled flutter correlation;

[0090] According to the processing flow in step four, the reconstructed coupled flutter signal is obtained, and the result is: Figure 7 .

[0091] contrast Figure 6 , Figure 7It can be seen that the reconstructed coupled chatter signal is more complete than the coupled chatter signal contained in the IMF5 dominant mode component of coupled chatter obtained after EEMD processing. It effectively avoids the mode aliasing phenomenon in the decomposition results, and is therefore more conducive to monitoring the milling and reaming process of industrial robots, and further improves the quality of hole making.

[0092] 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 the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for extracting chatter signals from milling and reaming coupling in industrial robots based on EEMD-BPF, characterized in that, Includes the following steps: Step 1: Use the EEMD method to process the force signal Preprocessing is performed to decompose the intrinsic mode components (IMFs) at different frequencies. s With residual signal in N represents the force signal. The total number of sampling points; Step 2: Intrinsic Mode Components (IMF) s The intrinsic modal components (IMFs) with the coupling flutter frequency as the dominant excitation frequency were found. c As the dominant modal component of coupled flutter, the correlation coefficient threshold method is used to calculate the IMF. s With the dominant mode component of coupled flutter IMF c Correlation coefficient between ,in Selecting those with coupling flutter correlation IMF s ,in Correlation coefficient in correlation discrimination The criteria for judgment are: (1) no correlation or very weak correlation: (2) Weak correlation: (3) Moderately relevant: (4) Strong correlation: (5) Extremely strong correlation: ; Step 3: Employ the BPF method, which combines a fourth-order Butterworth narrowband filter with a Kalman filter, to address the coupling flutter correlation. IMF s Bandpass filtering, which involves narrowband filtering and white noise removal, is performed sequentially to obtain the IMF. s Included flutter signal components Where m = 1, 2, ..., n; Step 4: Based on the principle of signal superposition, combine the coupled flutter signal components obtained in Step 3. The reconstructed coupled flutter signal is obtained by superposition processing. ; The specific calculation process of the BPF method based on fourth-order Butterworth narrowband filter fused with Kalman filter in step three is as follows: the n IMFs with coupling flutter correlation are filtered by a fourth-order Butterworth narrowband filter to obtain the narrowband filtered output. Where m = 1, 2, ..., n, then the Kalman filter method is used to... After white noise filtering, the coupled flutter signal component is finally obtained. The specific calculation process is as follows: Fourth-order Butterworth narrowband filter transfer function for: in For quality factors, Indicates the sampling frequency of the input signal. Indicates the low-end cutoff frequency of the passband. Indicates the high-end cutoff frequency of the passband. Indicates the center frequency of the coupled flutter signal. Indicates the low-end cutoff frequency of the passband. The normalized angular frequency, Indicates the high-end cutoff frequency of the passband. The normalized angular frequency, Indicates the frequency of the coupled flutter signal The normalized angular frequency; Obtained through bilinear transformation z-transform expression and according to The coefficients of each item are obtained Discretized expression : In the formula, T represents the sampling interval. , for The coefficients corresponding to the terms in the numerator and denominator, where k represents the number of samples. Indicates signal The corresponding IMF with coupling flutter correlation s Narrowband filter output at the k-th sampling point; Filtering out by Kalman filtering method The white noise in the image is used to obtain the final output after BPF processing. : In the formula express covariance, Indicates the input signal The covariance of the observation noise included. Indicates the input signal The covariance of process noise included; Finally, the discretized expression after white noise removal. The final coupled flutter signal components are obtained. .

2. The method for extracting coupled chatter signals in milling and reaming of industrial robots based on EEMD-BPF according to claim 1, wherein the EEMD method is used to extract force signals in step one. The preprocessing process includes four steps: (1) setting the overall mean frequency M; (2) converting the standard normal white noise into a standard normal distribution. Superimposed on the input signal To generate new signals , where j=1,2,...,M, 50 M 100; (3) For M signals EMD decomposition yields M IMFs. s Sequence; (4) For M IMFs s The sequence is averaged to obtain the intrinsic mode components (IMFs) at different frequencies. s .

3. The method for extracting coupled chatter signals in milling and reaming of industrial robots based on EEMD-BPF according to claim 2, characterized in that, The EMD decomposition in step (3) uses a one-sided trend discrimination method to obtain the maximum and minimum values ​​of the signal. The specific calculation process is as follows: in, Indicates the total number of sampling points. The set of sampling points Indicates that the sampling point is in the sampling set The number in the middle, Indicates sampling number The corresponding ordinate, Indicates that the sampling point is in the sampling set or The serial number in Labels for sampling points showing a downward trend With serial number The set constituted The labels for sampling points showing an upward trend. With serial number The set that constitutes; in the set In the diagram, the label of the maximum point satisfy ,and The label of the left adjacent minimum point is In the set In the middle, the label of the minimum point satisfy ,and The label of the left adjacent maximum point is .

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