Milling chatter detection method based on contribution entropy and cumulative contribution entropy

Abstract

The invention discloses a flutter detection method based on contribution entropy and cumulative contribution entropy, which comprises the following steps: selecting a sensor and an installation position thereof, and determining sampling parameters and threshold values; acquiring m groups of periodic synchronous single-point sampling data X; zero centralization processing is carried out on the m groups of periodic synchronous single-point sampling data X; performing dimension reduction processing on the m groups of periodic synchronous single-point sampling data after zero centralization processing by adopting PCA (Principal Component Analysis) to obtain a plurality of principal components, contribution rates C of the principal components and an accumulated contribution rate S of the principal components; calculating a contribution entropy E and a cumulative contribution entropy U; and judging whether flutter occurs or not. According to the method, the contribution entropy and the accumulated contribution entropy serve as flutter indexes, the influence of working conditions, rotating speed changes and disturbance noise on the flutter detection result is reduced, the method can be applied to milling flutter detection of different rotating speeds, flutter can be reliably detected, the flutter detection accuracy is high, the calculation cost is relatively low, and the method is suitable for popularization and application. And the flutter detection efficiency is improved, so that the flutter detection cost is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical processing state detection, and particularly relates to a milling chatter detection method based on Contribution Entropy and Cumulative Contribution Entropy. Background Art

[0002] Milling chatter is a self-excited vibration phenomenon that occurs during the milling process and has become the main factor restricting the improvement of production efficiency and part processing quality, especially during the milling of thin-walled workpieces. Due to the low stiffness of thin-walled workpieces, it is difficult to fundamentally eliminate chatter solely by selecting process parameters. To improve processing efficiency and quality, it is necessary to implement online detection of milling chatter.

[0003] Chatter signals are characterized by non-linearity, non-stationarity, and multiple components. In the research of milling chatter detection, traditional time-domain and frequency-domain analysis methods often struggle to effectively capture the non-linear and non-stationary characteristics of chatter signals. Therefore, in recent years, entropy-based signal processing methods have gradually become a research hotspot in the field of chatter detection.

[0004] Entropy, as an index to measure the complexity and uncertainty of a signal, can effectively reflect the inherent characteristics of chatter signals. When chatter occurs, chatter components appear in the machine tool vibration signal, changing the original signal complexity. Therefore, using entropy as a chatter index can be used to identify the occurrence of chatter.

[0005] Currently, researchers have proposed various concepts of entropy and applied them to fault detection. For example, Sample Entropy can effectively distinguish between steady-state cutting and chatter states by measuring the regularity of signal sequences; Fuzzy Entropy further improves the ability to characterize signal complexity by introducing a fuzzy membership function; Approximate Entropy provides a simple and effective method for chatter detection by comparing the similarity of signal sequences. In addition, Dispersion Entropy can better capture the non-linear characteristics of chatter signals by quantifying the probability distribution differences of signals.

[0006] Although the above entropy methods can be used for fault detection, they may not be able to identify periodic bifurcation chatter. In addition, the above entropy methods have high computational complexity and relatively high computational costs, and are not suitable for high-speed milling chatter detection.

[0007] In order to reliably and quickly identify chatter occurring in the milling process, this invention patent discloses a milling chatter detection method based on contribution entropy and cumulative contribution entropy. The milling chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by this invention can reliably identify various types of chatter, and has relatively low computational cost, and can be applied to the chatter detection of high-speed milling. Summary of the Invention

[0008] Object of the Invention: Aiming at the defects existing in the existing methods in the background art, this invention discloses a chatter detection method based on contribution entropy and cumulative contribution entropy. This inventive method uses Principal Component Analysis (PCA) to perform dimensionality reduction processing on multiple groups of periodically synchronized single-point sampling data collected, and then obtains contribution entropy and cumulative contribution entropy and uses them as chatter indicators for chatter detection. The contribution entropy and cumulative contribution entropy disclosed by this invention are highly sensitive to chatter and can better characterize milling chatter. In addition, the chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by this invention has relatively low computational cost and can be used for chatter detection in high-speed milling.

[0009] Technical Solution: The chatter detection method based on contribution entropy and cumulative contribution entropy described in this invention specifically includes the following steps:

[0010] S1. Select sensors and their installation positions, and determine sampling parameters and thresholds;

[0011] S2. Obtain m groups of periodically synchronized single-point sampling data X;

[0012] S3. Perform zero-centralization processing on each of the m groups of periodically synchronized single-point sampling data X;

[0013] S4. Use PCA to perform dimensionality reduction processing on the m groups of periodically synchronized single-point sampling data after zero-centralization processing to obtain multiple principal components and their contribution rates C and cumulative contribution rates S;

[0014] S5. Calculate contribution entropy E and cumulative contribution entropy U;

[0015] S6. Determine whether chatter occurs.

[0016] Further, the sensors described in S1 are vibration sensors and rotational speed sensors; the vibration sensors can be vibration displacement sensors, vibration velocity sensors or vibration acceleration sensors; the vibration sensors are installed on the spindle housing and are used to measure the spindle vibration signal; the rotational speed sensors are installed at the milling cutter or the spindle and are used to measure the rotational speed signal of the milling cutter or the spindle.

[0017] Further, the sampling parameters and thresholds in S1 include the number of cutter teeth k, the number of synchronous sampling points m per tooth cycle of the cutter, the data length, the cumulative contribution rate threshold S0, and the chatter thresholds T1 and T2; the data length is kLm, where k is the number of cutter teeth and L is the rotational speed of the cutter or the spindle; the thresholds T1 and T2 are both preset critical values of chatter indicators.

[0018] Further, the periodic synchronous single-point sampling data in S2 refers to a set of data obtained by synchronously collecting a single data within each tooth cycle of the cutter; if the number of synchronous sampling points per tooth cycle of the cutter is set to m, then m groups of periodic synchronous single-point sampling data X = [X1, X2, X3,..., X i ,..., X m T ,

[0019]

[0020] Further, the implementation process of S3 is as follows: For the m groups of periodic synchronous single-point sampling data X, zero-centering processing is respectively performed, and the m groups of periodic synchronous single-point sampling data after zero-centering processing are denoted as Y,

[0021]

[0022] where x i is the mean value of the i-th row data in the m groups of periodic synchronous single-point sampling data X, that is, the mean value of the data X i .

[0023] Further, the implementation process of S4 is as follows: Regarding the m groups of periodic synchronous single-point sampling data Y after zero-centering processing as sample data composed of m variables and each variable containing kL samples, PCA is used to perform dimensionality reduction processing on the m groups of periodic synchronous single-point sampling data Y after zero-centering processing, obtaining multiple eigenvalues and eigenvectors; the eigenvalues are sorted in descending order according to the magnitude of the eigenvalues to obtain the corresponding principal components; the contribution rate and cumulative contribution rate of the principal components are respectively calculated; the first n principal components whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold S0 for the first time are selected, and their contribution rates C and cumulative contribution rates S are selected,

[0024] C = [C1 C2 C3 … C n

[0025] S = [S1 S2 S3 … S n

[0026] Further, the implementation process of S5 is as follows: First, calculate the ratio PC of each contribution rate in the contribution rate C to all n contribution rates:

[0027] ​​​PC = [PC1 PC2 PC3 … PC n ,

[0028] where PC n is the ratio of the contribution rate of the nth principal component to the contribution rates of all n principal components,

[0029]

[0030] Then calculate the ratio PS of each cumulative contribution rate to the cumulative contribution rates of all n cumulative contribution rates

[0031] PS = [PS1 PS2 PS3…PS n

[0032] where PS n is the ratio of the cumulative contribution rate of the nth principal component to the cumulative contribution rates of all n principal components,

[0033]

[0034] Finally, calculate the contribution entropy E and the cumulative contribution entropy U,

[0035]

[0036] Furthermore, the implementation process of S6 is as follows: Consider the calculated contribution entropy E and cumulative contribution entropy U as flutter indicators and compare them with the preset thresholds T1 and T2; If the contribution entropy E is less than or equal to the preset threshold T1 and the cumulative contribution entropy U is greater than or equal to the preset threshold T2, it is considered that chatter has occurred in the milling process, otherwise it is considered that chatter has not occurred, and return to step (2) to continue chatter detection.

[0037] Advantageous effects:

[0038] (1) The chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by the method of the present invention can reduce the influence of working conditions and disturbance noise on the chatter detection result, and the calculation cost is relatively low, improving the efficiency of chatter detection, thereby reducing the chatter detection cost.

[0039] (2) The chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by the method of the present invention takes the contribution entropy and cumulative contribution entropy as chatter indicators, can reliably detect chatter, and increases the accuracy of chatter detection.

[0040] (3) The chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by the method of the present invention is not affected by the change of rotational speed and can be applied to the chatter detection of milling at different rotational speeds. Description of the drawings

[0041] Figure 1 ​Flowchart of the flutter detection method based on contribution entropy and cumulative contribution entropy disclosed in the present invention;

[0042] Figure 2 m groups of periodic synchronous single-point sampling data during milling without flutter;

[0043] Figure 3 m groups of periodic synchronous single-point sampling data during milling with Hopf bifurcation type flutter;

[0044] Figure 4 m groups of periodic synchronous single-point sampling data during milling with period-2 bifurcation type flutter;

[0045] Figure 5 m groups of periodic synchronous single-point sampling data during milling with period-3 bifurcation type flutter;

[0046] Figure 6 Contribution entropy E during non-flutter and flutter;

[0047] Figure 7 Cumulative contribution entropy U during non-flutter and flutter; Detailed implementation method

[0048] The implementation process of the method of the present invention will be described below in conjunction with the accompanying drawings and specific embodiments.

[0049] The present invention provides a flutter detection method based on contribution entropy and cumulative contribution entropy, and its process is as Figure 1 shown, including the following steps:

[0050] S1. Select a sensor and its installation position, and determine the sampling parameters and thresholds;

[0051] S2. Obtain m groups of periodic synchronous single-point sampling data X;

[0052] S3. Perform zero-centralization processing on the m groups of periodic synchronous single-point sampling data X respectively;

[0053] S4. Use PCA to perform dimensionality reduction processing on the m groups of periodic synchronous single-point sampling data after zero-centralization processing to obtain multiple principal components and their contribution rates C and cumulative contribution rates S;

[0054] S5. Calculate the contribution entropy E and the cumulative contribution entropy U;

[0055] S6. Determine whether flutter occurs.

[0056] Further, the sensors described in S1 are vibration sensors and rotational speed sensors; the vibration sensors can be vibration displacement sensors, vibration velocity sensors or vibration acceleration sensors; the vibration sensors are installed on the spindle housing for measuring spindle vibration signals; the rotational speed sensors are installed at the milling cutter or the spindle for measuring the rotational speed signals of the milling cutter or the spindle.

[0057] Further, the sampling parameters and thresholds described in S1 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 data length kLm, the cumulative contribution rate threshold S0, the chatter thresholds T1 and T2. In this embodiment, the data length kLm is 8000, the number of teeth k of the milling cutter is 1, the rotational speed L of the spindle is 20, and the number of synchronous sampling points m within each tooth cycle of the milling cutter is 400; the cumulative contribution rate threshold S0 = 0.99, and the cumulative contribution rate threshold S0 is used as the main component selection index; the thresholds T1 = 3.5 and T2 = 4.05 are both preset chatter index critical values.

[0058] Further, the periodic synchronous single-point sampling data described in S2 refers to a set of data obtained by synchronously collecting a single data within each tooth cycle of the milling cutter; setting the number of synchronous sampling points m within each tooth cycle of the milling cutter to 400, 400 sets of periodic synchronous single-point sampling data X = [X1, X2, X3,..., X i ,..., X 400 T ,

[0059]

[0060] Figures 2 - 5 show 400 sets of periodic synchronous single-point sampling data under the conditions of no chatter and three different chatter conditions respectively.

[0061] Further, the implementation process of S3 is as follows: For the 400 sets of periodic synchronous single-point sampling data X, zero-centralization processing is respectively performed, and the 400 sets of periodic synchronous single-point sampling data after zero-centralization processing are denoted as Y,

[0062]

[0063] where x i is the mean value of the i-th row data in the 400 sets of periodic synchronous single-point sampling data X, that is, the mean value of the data X i .

[0064] ​Further, the implementation process of S4 is as follows: Consider the 400 groups of cycle-synchronized single-point sampling data Y after zero-centralization processing as data consisting of 400 variables with 20 samples for each variable. Apply dimensionality reduction to the 400 groups of cycle-synchronized single-point sampling data Y after zero-centralization processing using PCA to obtain multiple eigenvalues and eigenvectors; Sort the eigenvalues in descending order according to their magnitudes and obtain the corresponding principal components; Calculate the contribution rate and cumulative contribution rate of the principal components respectively; Select the first n principal components whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold S0 for the first time, and select their contribution rate C and cumulative contribution rate S.

[0065] C = [C1 C2 C3 … C n ,

[0066] S = [S1 S2 S3 … S n .

[0067] Further, the implementation process of S5 is as follows: First, calculate the ratio PC of each contribution rate in the contribution rate C to the sum of all n contribution rates:

[0068] PC = [PC1 PC2 PC3 … PC n ,

[0069] where PC n is the ratio of the contribution rate of the nth principal component to the sum of the contribution rates of all n principal components.

[0070]

[0071] Then, calculate the ratio PS of each cumulative contribution rate to the sum of all n cumulative contribution rates

[0072] PS = [PS1 PS2 PS3 … PS n

[0073] where PS n is the ratio of the cumulative contribution rate of the nth principal component to the sum of the cumulative contribution rates of all n principal components.

[0074]

[0075] Finally, calculate the contribution entropy E and cumulative contribution entropy U.

[0076]

[0077] ​Further, the implementation process of S6 is as follows: Consider the calculated contribution entropy E and cumulative contribution entropy U as chatter indicators and compare them with the preset thresholds T1 = 3.5 and T2 = 4.05; If the contribution entropy E is less than or equal to the preset threshold T1 and the cumulative contribution entropy U is greater than or equal to the preset threshold T2, it is considered that chatter has occurred in the milling process, otherwise it is considered that no chatter has occurred, and return to step (2) to continue chatter detection.

[0078] In this embodiment, the vibration data during milling without chatter and with chatter is used to verify the method of the present invention. Figure 2 shows 400 groups of periodic synchronous single-point sampling data without chatter, while Figure 3 、 Figure 4 and Figure 5 respectively show 400 groups of periodic synchronous single-point sampling data with three different types of chatter.

[0079] For the 400 groups of periodic synchronous single-point sampling data without chatter and with three different types of chatter, the contribution entropy C and cumulative contribution entropy S calculated by using the method of the present invention are shown in the following table.

[0080] Table 1 Contribution entropy C and cumulative contribution entropy S

[0081]

[0082] It can be clearly seen from the table that for the 400 groups of periodic synchronous single-point sampling data without chatter, the calculated contribution entropy C is greater than the predetermined threshold T1 and the cumulative contribution entropy S is less than the predetermined threshold T2, and it is judged that no chatter has occurred in the milling process; while for the 400 groups of periodic synchronous single-point sampling data with three types of chatter, the calculated contribution entropy C is less than the predetermined threshold T1 and the cumulative contribution entropy S is greater than the predetermined threshold T2, then it is determined that chatter has occurred in the milling process.

[0083] In summary, the chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by the method of the present invention overcomes the problem of high calculation cost of traditional methods such as EEMD energy entropy. This method has relatively low calculation cost and can be used for chatter detection in high-speed milling. In addition, the chatter detection method based on contribution entropy and cumulative contribution entropy disclosed by the method of the present invention can identify chatter by using contribution entropy and cumulative contribution entropy, can characterize different types of chatter, and improves the chatter detection accuracy.

[0084] The above are only examples of the present invention and are not used to limit the present invention. All equivalent replacements made within the principle of the present invention shall be included in the protection scope of the present invention. The content not elaborated in detail in the present invention belongs to the known prior art of those skilled in the art.

Claims

1. A flutter detection method based on contribution entropy and cumulative contribution entropy, characterized in that It includes the following steps: Step (1): Select sensors and their installation positions, and determine sampling parameters and thresholds; Step (2): Obtain m sets of periodically synchronized single-point sampling data X; Step (3): Perform zero-centralization processing on the m sets of periodically synchronized single-point sampling data X respectively; Step (4): Use PCA to perform dimensionality reduction processing on the m sets of periodically synchronized single-point sampling data after zero-centralization processing to obtain multiple principal components and their contribution rates C and cumulative contribution rates S; Step (5): Calculate the contribution entropy E and the cumulative contribution entropy U; Step (6): Determine whether chatter occurs.

2. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, wherein In step (1), the sensors are vibration sensors and rotational speed sensors; the vibration sensors can be vibration displacement sensors, vibration velocity sensors, or vibration acceleration sensors; the vibration sensors are installed on the spindle housing and are used to measure the spindle vibration signal; the rotational speed sensors are installed at the milling cutter or the spindle and are used to measure the rotational speed signal of the milling cutter or the spindle.

3. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, wherein In step (1), the sampling parameters and thresholds include the number of teeth k of the milling cutter, the number of synchronously sampled points m within each tooth cycle of the milling cutter, the data length, the cumulative contribution rate threshold S0, the chatter thresholds T1 and T2; the data length is kLm, where k is the number of teeth of the milling cutter and L is the number of revolutions of the milling cutter or the spindle; the thresholds T1 and T2 are both preset critical values of the chatter index.

4. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, characterized in that In step (2), the periodic synchronous single-point sampling data refers to a set of data obtained by synchronously collecting a single data within each tooth cycle of the milling cutter. If the number of synchronous sampling points within each tooth cycle of the milling cutter is set to m, then m sets of periodic synchronous single-point sampling data X = [X1, X2, X3,..., X i ,..., X m T ,​ 5. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, characterized in that In step (3), the implementation process is as follows: For the m sets of periodically synchronized single-point sampling data X, perform zero-centralization processing respectively. The m sets of periodically synchronized single-point sampling data after zero-centralization processing are denoted as Y. where x i is the mean value of the data in the i-th row of the m groups of periodically synchronized single-point sampling data X, that is, the mean value of the data X i .

6. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, characterized in that In step (4), the implementation process is as follows: Regard the m sets of periodically synchronized single-point sampling data Y after zero-centralization processing as sample data composed of m variables and each variable containing kL samples. Use PCA to perform dimensionality reduction processing on the m sets of periodically synchronized single-point sampling data Y after zero-centralization processing to obtain multiple eigenvalues and eigenvectors; Sort the eigenvalues in descending order according to the magnitude of the eigenvalues and obtain the corresponding principal components; Calculate the contribution rate and cumulative contribution rate of the principal components respectively; Select the first n principal components whose cumulative contribution rate is greater than or equal to the cumulative contribution rate threshold S0 for the first time, and select their contribution rates C and cumulative contribution rates S. C = [C1 C2 C3 … C n ​ S = [S1 S2 S3 … S n .

7. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, characterized in that In step (5), the implementation process is as follows: First, calculate the ratio PC of each contribution rate in the contribution rate C to all n contribution rates: PC = [PC1 PC2 PC3 … PC n ​ where PC n is the contribution rate C of the nth principal component n as the ratio of the contribution rates of all n principal components Then calculate the ratio PS of each cumulative contribution rate to all n cumulative contribution rates PS = [PS1 PS2 PS3…PS n ​ where PS n is the cumulative contribution rate S of the nth principal component n and is the ratio of the cumulative contribution rate of all n principal components, Finally, calculate the contribution entropy E and the cumulative contribution entropy U.

8. The flutter detection method based on contribution entropy and cumulative contribution entropy according to claim 1, characterized in that In step (6), the implementation process is as follows: Compare the calculated contribution entropy E and cumulative contribution entropy U with the preset thresholds T1 and T2 as chatter indices; If the contribution entropy E is less than or equal to the preset threshold T1 and the cumulative contribution entropy U is greater than or equal to the preset threshold T2, it is considered that chatter has occurred in the milling process, otherwise it is considered that chatter has not occurred, and return to step (2) to continue chatter detection.

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