A Flutter Recognition Method Based on Wavelet Packet Energy Ratio

Abstract

The application discloses a chattering recognition method based on wavelet packet energy proportion. j Acceleration signals in the milling process are collected; the collected acceleration signals are segmented at certain time intervals in the time domain; each segment of the acceleration signals is subjected to j-layer wavelet packet decomposition, and two sub-signals containing different frequency bands are obtained respectively; the energy of each sub-signal after the decomposition of each segment of the acceleration signals is calculated, and the total energy of each segment of the acceleration signals is calculated; the energy proportion of each sub-signal in the corresponding acceleration signal segment is calculated, and the sum S k of the chattering frequency band energy proportions of each segment of the acceleration signals is calculated; and step six is comparing S k with a threshold value to determine the cutting state of the milling system in the time segment. The application can accurately recognize the serious chattering and weak chattering phenomena in the milling process.

Description

Technical Field

[0001] This invention belongs to the field of milling machining condition monitoring technology, and more specifically, it relates to a chatter identification method based on wavelet packet energy ratio. Background Technology

[0002] During machining, the workpiece, tool holder, and other structures vibrate. Furthermore, repeated fluctuations in cutting force cause discontinuous cutting. When both frequencies are the same, it leads to severe vibration in the machining system, resulting in chatter. Chatter is a harmful phenomenon in machining, significantly impacting machining stability. It greatly limits the efficiency of machine tools and the machining accuracy of workpieces. When chatter occurs, the surface finish of the workpiece deteriorates, tool wear is accelerated, harsh noise is generated, and even substantial economic losses can result.

[0003] When chatter occurs, the machining system transitions from a steady state to an unstable state. The energy of the machining system also shifts from being concentrated at the spindle frequency and its multiples to the chatter frequency; this is the principle of energy accumulation in chatter. Wavelet packet decomposition can decompose a signal into multiple sub-signals according to its frequency range. Based on energy distribution, energy entropy is currently the most commonly used method. However, when the machining state is complex and chatter is at an extremely weak stage, the change in entropy value is extremely small, making it difficult to reach the set threshold. Monitoring the energy proportion of sub-signals within the chatter frequency band allows for a more accurate and direct identification of the machining state. Summary of the Invention

[0004] To address the aforementioned issues and accurately identify chatter and weak chatter phenomena occurring during the processing, this invention proposes a chatter identification method based on the energy ratio of wavelet packets, according to the principle of energy accumulation during chatter.

[0005] The objective of this invention is achieved through the following technical solutions.

[0006] This invention relates to a flutter identification method based on wavelet packet energy ratio, comprising the following steps:

[0007] Step 1: Install an accelerometer on the bottom of the milling workpiece to collect acceleration signals during the milling process;

[0008] Step 2: Divide the acquired acceleration signal into segments in the time domain at certain time intervals to obtain the Q-segment acceleration signal;

[0009] Step 3: Perform wavelet packet decomposition at level j on each acceleration signal segment to obtain 2 j Sub-signals containing different frequency bands;

[0010] Step 4: Calculate the energy of each sub-signal after decomposing each acceleration signal segment, as well as the total energy of each acceleration signal segment.

[0011] Step 5: Calculate the energy proportion of each sub-signal in its respective acceleration signal segment, and the sum of the energy proportions of the flutter frequency band of each acceleration signal segment, S. k ;

[0012] Step 6: Sum of the flutter frequency band energy proportions of each acceleration signal segment. k The cutting status of the milling system within the given time period is determined by comparing it with a threshold.

[0013] The wavelet basis function used in step three for wavelet packet decomposition is the Daubechise wavelet. Each segment of the acceleration signal is decomposed into 2... j Each sub-signal represents a different frequency range, and the frequency interval represented by the m-th sub-signal is [(m-1)f s / 2 j ,mf s / 2 j ], f s It uses the Nyquist frequency, which is half the sampling frequency used when acquiring acceleration signals.

[0014] The energy of each sub-signal after decomposition of each acceleration signal segment as described in step four is calculated using the following formula:

[0015] E ki =∫|p ki (t)| 2 dt

[0016] In the formula, E ki p is the energy of the i-th sub-signal after decomposing the k-th segment of the acceleration signal. ki (t) is the i-th sub-signal obtained after wavelet packet decomposition of the k-th acceleration signal, k = 1, 2, ..., Q, i = 1, 2, ..., 2 j ;

[0017] The total energy of each acceleration signal segment is calculated using the following formula:

[0018]

[0019] In the formula, E k It is the total energy of the acceleration signal in the k-th segment.

[0020] The energy percentage of each sub-signal in its respective acceleration signal segment, as described in step five, is calculated using the following formula:

[0021]

[0022] In the formula, σki It is the energy percentage of the i-th sub-signal in the k-th segment of the acceleration signal;

[0023] The sum of the flutter frequency band energy proportions of each acceleration signal segment S k Calculate using the following formula:

[0024] S k =σ k2 +σ k3

[0025] In the formula, S k It is the sum of the flutter frequency band energy proportions of the k-th segment of the acceleration signal.

[0026] In step six, the sum of the energy proportions of the flutter frequency bands of each acceleration signal segment, S, is used. k The cutting state of the milling system within the given time period is determined by comparing it with a threshold, as follows:

[0027] ①S k ≤0.3 indicates that the acceleration signal of the k-th segment is in a stable cutting state, representing that the milling system is in a stable cutting state within the corresponding time period;

[0028] ②0.3<S k ≤0.65 indicates that the acceleration signal in the k-th segment is in a weak chatter cutting state, representing that the milling system is in a weak chatter cutting state in the corresponding time period.

[0029] ③0.65<S k , represents the signal when the acceleration signal of the kth segment is in a state of severe chatter cutting, indicating that the milling system is in a state of severe chatter cutting within the corresponding time period.

[0030] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0031] This invention proposes a milling chatter identification method based on wavelet packet energy proportion. First, the acquired vibration signal is decomposed into sub-signals containing information from different frequency bands using wavelet packet decomposition. By monitoring the change in the energy proportion of the sub-signals located in the chatter frequency band and comparing it with a threshold, the stability of the machining process can be identified. The advantages of this method are that it allows for online measurement and real-time monitoring of the machining status, enabling timely identification of chatter occurrences to avoid greater economic losses. Furthermore, it is convenient and low-cost. Attached Figure Description

[0032] Figure 1 This is a flowchart of the flutter identification method based on wavelet packet energy ratio of the present invention.

[0033] Figure 2This is a diagram of the milling experimental working device in this invention.

[0034] Figure 3 The following are time-domain plots of the three sets of acceleration signals;

[0035] Among them, (a) stable cutting, (b) weak chatter cutting, and (c) severe chatter cutting.

[0036] Figure 4 This is a schematic diagram of acceleration signal data segmentation.

[0037] Figure 5 For data 11 Wavelet packet decomposition and the spectrum of its sub-signals.

[0038] Figure 6 The frequency domain plots of the three sets of acceleration signals are shown.

[0039] Among them, (a) stable cutting, (b) weak chatter cutting, and (c) severe chatter cutting.

[0040] Figure 7 The graph shows the energy percentage of the three acceleration signals in the flutter band as a function of time.

[0041] Among them, (a) stable cutting, (b) weak chatter cutting, and (c) severe chatter cutting. Detailed Implementation

[0042] The present invention will now be further described with reference to the accompanying drawings.

[0043] This invention relates to a flutter identification method based on wavelet packet energy ratio, such as... Figure 1 As shown, it includes the following steps:

[0044] Step 1: Install an accelerometer on the bottom of the milling workpiece to collect acceleration signals during the milling process.

[0045] Step 2: Divide the acquired acceleration signal into segments in the time domain at certain time intervals to obtain the Q-segment acceleration signal.

[0046] Step 3: Perform wavelet packet decomposition at level j on each acceleration signal segment to obtain 2 j There are 3 sub-signals containing different frequency bands, where j is a positive integer greater than or equal to 2.

[0047] The wavelet basis function used in the wavelet packet decomposition is the Daubechise wavelet, i.e., the dbN wavelet, where N is the order. Each segment of the acceleration signal is decomposed into 2-1 waves. j Each sub-signal represents a different frequency range, and the frequency interval represented by the m-th sub-signal is [(m-1)f s / 2 j ,mfs / 2 j ], f s It uses the Nyquist frequency, which is half the sampling frequency used when acquiring acceleration signals.

[0048] Step 4: Calculate the energy of each sub-signal after decomposing each acceleration signal segment, as well as the total energy of each acceleration signal segment.

[0049] Calculate the energy of each sub-signal after decomposing each segment of the acceleration signal using the following formula:

[0050] E ki =∫|p ki (t)| 2 dt (1)

[0051] In the formula, E ki p is the energy of the i-th sub-signal after decomposing the k-th segment of the acceleration signal. ki (t) is the i-th sub-signal obtained after wavelet packet decomposition of the k-th acceleration signal, k = 1, 2, ..., Q, i = 1, 2, ..., 2 j .

[0052] Calculate the total energy of each acceleration signal segment using the following formula:

[0053]

[0054] In the formula, E k It is the total energy of the acceleration signal in the k-th segment.

[0055] Step 5: Calculate the energy proportion of each sub-signal in its respective acceleration signal segment, and the sum of the energy proportions of the flutter frequency band of each acceleration signal segment, S. k .

[0056] The energy percentage of each sub-signal in its respective acceleration signal segment is calculated using the following formula:

[0057]

[0058] In the formula, σ ki It represents the energy percentage of the i-th sub-signal within its corresponding k-th segment of the acceleration signal.

[0059] Calculate the sum of the flutter frequency band energy proportions S of each segment of the acceleration signal using the following formula. k :

[0060] S k =σ k2 +σ k3 (4)

[0061] In the formula, S kIt is the sum of the energy proportions of the flutter frequency band of the k-th acceleration signal, which is equal to the sum of the energy proportions of the 2nd and 3rd sub-signals in the k-th acceleration signal, or the sum of the energy proportions of frequency band 2 and frequency band 3.

[0062] Step 6: Sum of the flutter frequency band energy proportions of each acceleration signal segment k The cutting state of the milling system within the given time period is determined by comparing the data with a threshold. Specifically:

[0063] ①S k ≤0.3 indicates that the acceleration signal of the k-th segment is in a stable cutting state, representing that the milling system is in a stable cutting state within the corresponding time period;

[0064] ②0.3<S k ≤0.65 indicates that the acceleration signal in the k-th segment is in a weak chatter cutting state, representing that the milling system is in a weak chatter cutting state in the corresponding time period.

[0065] ③0.65<S k , represents the signal when the acceleration signal of the kth segment is in a state of severe chatter cutting, indicating that the milling system is in a state of severe chatter cutting within the corresponding time period.

[0066] To verify the method of the present invention, three sets of milling experiments can be conducted, respectively under stable cutting, weak chatter cutting, and severe chatter cutting conditions. Figure 2 As shown, an accelerometer is used to collect acceleration signals during the milling process, and the sampling frequency is set to 10000Hz.

[0067] In this embodiment, the milling experiment was conducted on a five-axis CNC machining center. The cutting tool was a carbide end mill with two flutes, and the workpiece was AISI 1040. The end mill diameter was 0.6 mm, the rake angle was approximately 10°, and the helix angle was approximately 30°. The milling experiment was conducted under dry cutting conditions. The milling parameters for the three sets of experiments are shown in Table 1.

[0068] Table 1 Milling parameters

[0069]

[0070] The time-domain plots of the three sets of acceleration signals are as follows: Figure 3 As shown, the acceleration amplitude range under stable processing conditions is [-5, 5], the acceleration amplitude under weak chatter conditions is in the range [-15, 15], and the acceleration amplitude under severe chatter conditions is in the range [-25, 25]. As chatter intensifies, the time-domain amplitude of the vibration signal increases rapidly.

[0071] In this embodiment, as Figure 4As shown, the collected vibration signal data Data (with a data length of L) is divided into Q data arrays at 0.1s time intervals. (The data length of each array is L / Q). Each small data segment represents the vibration situation within a different time range.

[0072] In this embodiment, combined with Figure 5 The three segments of acceleration signal data were decomposed into three levels of wavelet packets using the db10 wavelet, yielding eight sub-signals containing different frequency ranges. Only the data is shown here. 11 The result after decomposition. Since the sampling frequency is 10000Hz, the signal frequency range is [0, 5000Hz]. The bandwidth represented by the 8 sub-signals obtained by decomposition is 625Hz, and the frequency range represented by the m-th sub-signal is [625(m-1), 625m].

[0073] Then, calculate the energy of each sub-signal after decomposition of each acceleration signal segment according to formula (1), and calculate the total energy of each acceleration signal segment according to formula (2). Calculate the energy proportion of each sub-signal in its respective acceleration signal segment according to formula (3), and calculate the sum S of the flutter frequency band energy proportions of each acceleration signal segment according to formula (4). k .

[0074] In this embodiment, data 11 For example, the energy of the obtained 8 sub-signals is The total energy of the acceleration signal is E1 = 34.44, and the energy proportions of the 8 sub-signals are: The sum of the energy proportions of frequency band 2 and frequency band 3 is: S1 = σ 12 +σ 13 =0.0119.

[0075] In this embodiment, the sum of the energy proportions of frequency band 2 and frequency band 3 is selected as the sum of the flutter frequency band energy proportions for the following reasons: [Combined with...] Figure 6In the diagram, the vertical lines represent the spindle rotation frequency and its multiples. Taking the spectrum under steady-state conditions as an example, the spindle speed is n = 14000 rpm, and the spindle frequency is SF = n / 60 = 233.3 Hz. During steady milling, the vibration frequency of the milling system is mainly distributed at the spindle frequency and its multiples. When chatter occurs, some dominant frequencies that do not belong to the spindle frequency and its multiples appear in the acceleration signal spectrum. From the acceleration signal spectrum under severe chatter conditions, it can be clearly seen that the chatter frequency is mainly concentrated in [1000 Hz, 2000 Hz]. For the second group of experiments (weak chatter), in addition to the chatter frequency between [1000 Hz, 2000 Hz], there are also some frequencies that do not belong to the spindle frequency and its multiples between [4000 Hz, 5000 Hz]. However, compared to the chatter frequency within [1000 Hz, 2000 Hz], their amplitudes are smaller. Therefore, [1000 Hz, 2000 Hz] is the frequency band where the chatter frequency is mainly concentrated. Based on the wavelet packet decomposition characteristics described above, the flutter frequency band [1000Hz, 2000Hz] is contained within frequency bands 2 and 3. Therefore, the energy proportions of frequency bands 2 and 3 are chosen as the sum of the energy proportions of the flutter frequency bands.

[0076] like Figure 7 As shown, the energy percentage is obtained from each small segment of the array. Expressed in the form of a curve, and through S k By comparing with a threshold, the machining system is determined to be in a stable machining, weak chatter machining, or severe chatter machining state.

[0077] ①S k ≤0.3 indicates that the acceleration signal of the k-th segment is in a stable cutting state, representing that the milling system is in a stable cutting state within the corresponding time period;

[0078] ②0.3<S k ≤0.65 indicates that the acceleration signal in the k-th segment is in a weak chatter cutting state, representing that the milling system is in a weak chatter cutting state in the corresponding time period.

[0079] ③0.65<S k , represents the signal when the acceleration signal of the kth segment is in a state of severe chatter cutting, indicating that the milling system is in a state of severe chatter cutting within the corresponding time period.

[0080] Although the functions and working processes of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific functions and working processes described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these are within the protection scope of the present invention.

Claims

1.A chattering recognition method based on wavelet packet energy proportion, characterized in that, The method comprises the following steps: Step one, install an acceleration sensor at the bottom of the workpiece during milling, and collect acceleration signals during the milling process; Step two, segment the collected acceleration signals in the time domain at certain time intervals to obtain Q segments of acceleration signals; Step three, the j-layer wavelet packet decomposition is made to each acceleration signal respectively, and two j sub-signals containing different frequency bands are obtained respectively; Wherein, the wavelet base function used by the wavelet packet decomposition is Daubechise wavelet, 2 j sub-signals after decomposition of each acceleration signal represent different frequency ranges, and the frequency interval represented by the mth sub-signal is , f s is the Nyquist frequency, which is half of the sampling frequency when the acceleration signal is collected. Step four, calculate the energy of each sub-signal after decomposition of each segment of acceleration signals, and the total energy of each segment of acceleration signals; Step five, calculate the energy proportion of each sub-signal in the acceleration signal segment, and the sum of the energy proportion of the jitter frequency band of each acceleration signal segment S k ; The energy proportion of each sub-signal in the corresponding segment of acceleration signals is calculated according to the following formula: ， In the formula, is the energy proportion of the i-th sub-signal in the k-th segment of acceleration signal to which it belongs; The sum S of the jitter band energy proportions of the acceleration signals of the segments k is calculated as follows: ， In the formula, S k is the sum of the jitter band energy ratios of the kth segment of acceleration signals; Step six, the sum S of the energy proportion of the chatter frequency band of each acceleration signal k The cutting state of the milling system in the time period is determined by comparing the threshold value, and the specific process is as follows: k ≤0.3, indicates the kth segment of the acceleration signal is in a stable cutting state, representing that the milling system is in a stable cutting state in the corresponding time period.​ ii) 0.3 < S < 0.7 k ≤0.65, indicates that the kth segment of the acceleration signal is in a weak chatter cutting state, representing that the milling system is in a weak chatter cutting state in the corresponding time period. k , indicates the kth segment of the acceleration signal is a severe chatter cutting state signal, which represents that the milling system is in a severe chatter cutting state in the corresponding time period.​ 2. The wavelet packet energy ratio-based flutter identification method according to claim 1, characterized in that, The energy of each sub-signal after decomposition of each segment of acceleration signals in step four is calculated according to the following formula: ; In the formula, E ki is the energy of the i-th sub-signal after the k-th segment of acceleration signal decomposition, p ki (t) is the i-th sub-signal obtained after wavelet packet decomposition of the k-th segment of acceleration signal, k = 1, 2,..., Q, i = 1, 2,..., 2 j ; The total energy of each segment of acceleration signals is calculated according to the following formula: ; In the formula, E k is the total energy of the kth segment of acceleration signal.

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