Milling chatter diagnosis method based on multi-step differential entropy

Abstract

The invention discloses a milling chatter diagnosis method based on multi-step differential entropy, and belongs to the technical field of mechanical system fault diagnos.The method comprises the operation steps that the type and the installation position of a sensor are selected, and chatter diagnosis parameters are determined; acquiring synchronous vibration data X; the difference step number mu is set to be equal to 1, the embedded dimension is m, the time delay is tau, and the following calculation is repeated until the difference step number mu is larger than the maximum difference step number mu T; reconstructing a phase space P [mu] of the synchronous vibration data X; processing the phase space P [mu] according to a difference rule to obtain a phase space P '[mu]; calculating the cosine similarity between each two adjacent rows of data in the phase space P 'mu; the interval [-1, 1] is divided into epsilon intervals at equal intervals, probability distribution of the obtained cosine similarity in each interval is counted, and mu step difference entropy is calculated; making the difference step number mu = mu + 1 and the embedded dimension m = m0 + (mu-1), and returning to continue to calculate the mu step difference entropy; determining a flutter type according to a flutter diagnosis criterion; the method can effectively overcome the inherent defects of traditional entropy, remarkably improve the accuracy, timeliness and reliability of flutter diagnosis, provide solid technical support for flutter research and recognition in the machining process, practically improve the machining efficiency, reduce the influence of flutter on the machining quality and reduce the production cost. Besides, the method is highly in line with the trend of intelligent development of the manufacturing industry, has wide application prospects, and is expected to promote technical innovation and progress of the machining industry.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical system fault diagnosis, and in particular relates to a milling chatter diagnosis method based on Multi-Step Difference Entropy (MSDE). Background Art

[0002] During the milling process, chatter is a self-excited vibration phenomenon caused by the dynamic interaction between the tool and the workpiece, which can lead to deterioration of the machined surface quality, shortened tool life, and even equipment damage. Generally speaking, the regenerative chatter of milling includes periodic bifurcation chatter, Hopf bifurcation chatter, etc. Research literature shows that the machining parameters that cause periodic bifurcation chatter can improve the machining efficiency while meeting the requirements of machining quality. In order to improve the machining efficiency, some researchers propose to use machining parameters that cause periodic bifurcation chatter to machine the workpiece. To this end, it is necessary to diagnose the chatter generated during the milling process and identify the periodic bifurcation chatter. In addition, in order to study the hazards caused by different chatter types, it is necessary to diagnose various chatter types. Therefore, it is of great significance to diagnose the chatter that occurs during the milling process.

[0003] Flutter diagnosis methods generally include: data acquisition, feature extraction, fault decision, etc. The quality of feature extraction seriously affects the accuracy of flutter diagnosis, so feature extraction is regarded as one of the most important contents.

[0004] The invention patent with patent number 202410194548.8 discloses a high-speed milling chatter diagnosis method based on multi-resolution asynchronous entropy, and the extracted fault feature is multi-resolution asynchronous entropy. Although this method has achieved remarkable results in identifying chatter types, the data sequence length required by this method is relatively long. When the data sequence length is relatively short, the method cannot accurately identify the chatter type. For example, when identifying period-4 bifurcation type chatter, the method requires at least 11 spindle revolutions of data. It is well known that during the milling process, chatter should be identified in a timely manner to prevent unacceptable consequences. The time delay of this method is relatively long and may not be suitable for chatter detection.

[0005] In view of the shortcomings of the above-mentioned chatter diagnosis method, the patent of this invention discloses a new type of milling chatter diagnosis method based on multi-step differential entropy, which identifies the chatter type by calculating multi-step differential entropy. Multi-step differential entropy can effectively overcome the inherent defects of traditional entropy, significantly improve the accuracy, timeliness and reliability of chatter diagnosis, provide solid technical support for chatter research and identification in mechanical processing, effectively improve processing efficiency, reduce the impact of chatter on processing quality, and reduce production costs. In addition, the milling chatter diagnosis method based on multi-step differential entropy is highly consistent with the trend of manufacturing industry towards intelligent development, has broad application prospects, and is expected to promote technological innovation and progress in the mechanical processing industry. Summary of the invention

[0006] Purpose of the invention: The present invention discloses a milling chatter diagnosis method based on multi-step differential entropy, which can diagnose the chatter type in real time and reliably through multi-step differential entropy.

[0007] Technical solution: The invention patent discloses a milling chatter diagnosis method based on multi-step differential entropy, which specifically includes the following steps:

[0008] Step (1): Select the sensor type and installation location, and determine the diagnostic parameters;

[0009] Step (2): obtaining synchronous vibration data X;

[0010] Step (3): Set the difference step number μ, embedding dimension m, and time delay τ;

[0011] Step (4): Reconstruct the phase space P of the synchronous vibration data X μ ;

[0012] Step (5): According to the difference rule, the phase space P μ After processing, we get the phase space P′ μ ;

[0013] Step (6): Calculate the phase space P μ The cosine similarity between each two adjacent rows of data;

[0014] Step (7): Divide the interval [-1, 1] into ε equally spaced intervals, and count the probability distribution of the cosine similarity obtained in step (6) in each interval, and calculate the μ-step differential entropy;

[0015] Step (8): Let the number of differential steps μ = μ + 1 and the embedding dimension m = m0 + (μ - 1), return to step (4) and continue to calculate the μ-step differential entropy until the number of differential steps μ is greater than the maximum number of differential steps μ T until;

[0016] Step (9): Determine the flutter type according to the flutter diagnosis criteria.

[0017] Furthermore, the sensors in step (1) are vibration sensors and speed sensors; the vibration sensor is installed on the workpiece or the spindle to measure the vibration of the workpiece or the spindle; the speed sensor is installed near the spindle to measure the spindle speed; the diagnostic parameters include: the number of synchronous sampling points M per spindle revolution, the sampling length, the initial value of the embedding dimension m0, the number of intervals ε, the maximum number of differential steps μ T , μ T Threshold The sampling length is kM, where k is the number of spindle revolutions; the initial value of the embedding dimension m0 is determined according to the milling chatter characteristics; the μ T Threshold Determined according to the 3σ criterion.

[0018] Furthermore, the implementation process of step (2) is as follows:

[0019] The spindle speed is used as a reference signal to synchronously obtain vibration data during the milling process; the vibration data obtained is vibration displacement data, vibration velocity data or vibration acceleration data; the synchronous vibration data can be expressed as:

[0020] X={x(1),x(2),…,x(i),…,x(kM)}.

[0021] Furthermore, the implementation process of step (3) is as follows:

[0022] The differential step number μ is set to 1; the embedding dimension m is set to the embedding dimension initial value m0; and the time delay τ is set to the rotation period of the main axis.

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

[0024] According to the embedding dimension m and time delay τ set in step (3), the phase space of the synchronous vibration data X is reconstructed. The reconstructed phase space P μ for Among them, the m-dimensional embedding vector It is expressed as:

[0025]

[0026] Furthermore, the implementation process of step (5) is as follows:

[0027] For the phase space P μ Each m-dimensional vector in is processed by the difference rule to obtain the phase space P′ with an embedding dimension of m-μ. μ for The difference rule is

[0028]

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

[0030] For the phase space P′ after difference μ Calculate the cosine similarity D_D between the i-th row of data and the i+1-th row of data μ (i), as shown below:

[0031]

[0032] in,

[0033]

[0034] Furthermore, the implementation process of step (7) is as follows:

[0035] Divide the interval [-1,1] into ε equally spaced intervals (I1,I2,I3,…,I ε ), the interval is 2 / ε; the probability of all cosine similarities obtained in step (6) being in each interval in According to the probability of each interval Calculate μ-step differential entropy, the calculation formula is as follows:

[0036]

[0037] Furthermore, the implementation process of step (8) is as follows:

[0038] The setting of the differential step number μ = μ + 1 means adding 1 to the original differential step number μ; then setting the embedding dimension m = m0 + (μ - 1), and repeating the calculation steps (4) to (8) until the differential step number μ is greater than the maximum differential step number μ T So far, we have obtained μ T The difference entropy.

[0039] Furthermore, the implementation process of step (9) is as follows:

[0040] The μ obtained in the above steps T The differential entropy is regarded as a flutter diagnosis feature, and the flutter type is determined according to the flutter diagnosis criterion; the flutter diagnosis criterion is shown in the following table:

[0041] Table 1 Flutter diagnosis criteria

[0042]

[0043] In the table, Y represents the μ-th step differential entropy MSDE μ Greater than or equal to the chatter threshold rμ , N represents the μ-th step differential entropy MSDE μ Less than the chatter threshold r μ , and X represents the μ-th step differential entropy MSDE μ It needs to be determined according to the number of difference steps μ and the type of dither. If all μ-th step difference entropy MSDE μ are all less than the threshold r μ , then the chatter is a Hopf bifurcation type chatter; when all μ-th step difference entropy MSDE μ are greater than or equal to the threshold r μ , the milling process is in a non-chatter state; otherwise, the milling process is a periodic bifurcation type chatter. For the periodic bifurcation type chatter, the method of the present invention can be further classified, and the specific judgment criteria are shown in Table 1.

[0044] Beneficial effects: Compared with the prior art, the present invention mainly includes the following beneficial effects: (1) The milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention can reliably diagnose the type of milling chatter; (2) Compared with the invention method with patent number 202410194548.8, the milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention requires less computational cost and can diagnose the chatter type more quickly; (3) The data sequence length required for the milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention is relatively short, which overcomes the disadvantage that the existing method cannot process short data sequences and shortens the time delay of chatter diagnosis; (4) The milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention is not affected by the spindle speed and can be applied to the chatter diagnosis of milling processing at different speeds. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flowchart of the milling chatter diagnosis method based on multi-step differential entropy disclosed by the present invention;

[0046] Figure 2 is a vibration displacement diagram of a workpiece when there is no chatter in an embodiment of the present invention;

[0047] Figure 3 is a vibration displacement diagram of a workpiece during period-2 bifurcation type chatter in an embodiment of the present invention;

[0048] Figure 4 is a vibration displacement diagram of a workpiece during period-3 bifurcation type chatter in an embodiment of the present invention;

[0049] Figure 5 is a vibration displacement diagram of a workpiece during Hopf bifurcation type chatter in an embodiment of the present invention;

[0050] Figure 6 It is the multi-step differential entropy distribution diagram under different chatter types. DETAILED DESCRIPTION

[0051] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0052] The calculation process of the milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention is as follows: Figure 1 As shown, the specific steps include:

[0053] Step (1): Select the sensor type and installation location, and determine the diagnostic parameters.

[0054] The selected sensors are vibration sensors and speed sensors; the vibration sensor is installed on the workpiece or the spindle to measure the vibration of the workpiece or the spindle; the speed sensor is installed near the spindle to measure the spindle speed; the diagnostic parameters include: the number of synchronous sampling points M per spindle revolution, the sampling length, the initial value of the embedding dimension m0, the number of intervals ε, the maximum number of differential steps μ T , μ T Threshold The sampling length is kM, where k is the number of spindle revolutions; the initial value of the embedding dimension m0 is determined according to the milling chatter characteristics; the μ T Threshold Determined according to the 3σ criterion. In this embodiment, the initial value m0 of the embedding dimension is set to 4.

[0055] Step (2): Obtain synchronous vibration data X.

[0056] The obtained milling synchronous vibration data X can be expressed as

[0057] X={x(1),x(2),…,x(i),…,x(kM)}

[0058] Step (3): Set the difference step number μ = 1, the embedding dimension m = 4, and the time delay τ as the rotation period of the main axis.

[0059] Step (4): Reconstruct the phase space P of the synchronous vibration data X μ .

[0060] According to the embedding dimension m and time delay τ set in step (3), the phase space of the synchronous vibration data X is reconstructed, and the reconstructed phase space P μ for Among them, the i-th embedding vector is an m-dimensional vector represented by:

[0061]

[0062] Step (5): According to the difference rule, the phase space P v After processing, we get the phase space P′ μ .

[0063] For the phase space P μ Each m-dimensional vector in is processed by the difference rule to obtain the phase space P′ with an embedding dimension of m-μ. μ for The difference rule is

[0064]

[0065] Step (6): Calculate the phase space P μ The cosine similarity between two adjacent rows of data

[0066] For the phase space P′ after difference μ Calculate the cosine similarity D_D between the i-th row of data and the i+1-th row of data μ (i), as shown below:

[0067]

[0068] in,

[0069]

[0070] Step (7): Divide the interval [-1, 1] into ε equally spaced intervals, and count the probability distribution of the cosine similarity obtained in step (6) in each interval, and calculate the μ-step differential entropy.

[0071] Divide the interval [-1,1] into ε intervals (I1,I2,I3,…,I ε ), the interval is 2 / ε; the probability of all cosine similarities obtained in step (6) being in each interval in According to the probability of each interval Calculate μ-step differential entropy, the calculation formula is as follows:

[0072]

[0073] Step (8): Let the number of differential steps μ = μ + 1 and the embedding dimension m = m0 + (μ - 1), return to step (4) and continue to calculate the μ-step differential entropy until the number of differential steps μ is greater than the maximum number of differential steps μ T until.

[0074] The setting of the differential step number μ = μ + 1 means adding 1 to the original differential step number μ; then setting the embedding dimension m = m0 + (μ - 1), and repeating the calculation steps (4) to (8) until the differential step number μ is greater than the maximum differential step number μ T So far, we have obtained μ T The difference entropy.

[0075] Step (9): Determine the flutter type according to the flutter diagnosis criteria.

[0076] The μ obtained in the above steps T The differential entropy is regarded as a flutter diagnosis feature, and then the flutter type is determined according to the flutter diagnosis criterion; the flutter diagnosis criterion is shown in the following table:

[0077] Table 1 Flutter diagnosis criteria

[0078]

[0079]

[0080] In the table, Y represents the μ-th step differential entropy MSDE μ Greater than or equal to the chatter threshold r μ , N represents the μ-th step differential entropy MSDE μ Less than the chatter threshold r μ , and X represents the μ-th step differential entropy MSDE μ It needs to be determined according to the number of difference steps μ and the type of dither. If all μ-th step difference entropy MSDE μ are all less than the threshold r μ , then the chatter is a Hopf bifurcation type chatter; when all μ-th step difference entropy MSDE μ are greater than or equal to the threshold r μ , the milling process is in a non-chatter state; otherwise, the milling process is a periodic bifurcation type chatter. For the periodic bifurcation type chatter, the method of the present invention can be further classified, and the specific judgment criteria are shown in Table 1.

[0081] In this embodiment, the synchronous sampling data is processed by the differential method. It should be pointed out that the differential method here does not directly process the synchronous sampling data, but processes each dimension of the data after the phase space reconstruction. In addition, each time the μ-step differential entropy is calculated, the differential step number and the embedding dimension need to be updated. When the milling process is chatter-free, the synchronous sampling vibration signal of the workpiece is as follows: Figure 2 When the milling process is a period-2 bifurcation type chatter, the synchronous sampling vibration signal of the workpiece is as follows: Figure 3 shown. Figure 4 and 5 The synchronous sampling vibration signals of the milling process are respectively shown when the milling process is period-3 bifurcation type chatter and Hopf type chatter. The synchronous vibration signal is processed by the method of the present invention to obtain μ T Multi-step differential entropy values. Figure 6 is the multi-step differential entropy distribution diagram under different chatter types. According to the obtained μ T The multi-step differential entropy value and chatter diagnosis criteria can diagnose the chatter type.

Claims

1. A milling chatter diagnosis method based on multi-step differential entropy, characterized in that: The operation steps are as follows: Step (1): Select the sensor type and installation location, and determine the vibration diagnosis parameters; Step (2): obtaining synchronous vibration data X; Step (3): Set the difference step number μ, embedding dimension m, and time delay τ; Step (4): Reconstruct the phase space P of the synchronous vibration data X μ ; Step (5): According to the difference rule, the phase space P μ After processing, we get the phase space P′ μ ; Step (6): Calculate the phase space P′ μ The cosine similarity between each two adjacent rows of data; Step (7): Divide the interval [-1, 1] into ε equally spaced intervals, and count the probability distribution of the cosine similarity obtained in step (6) in each interval, and calculate the μ-step differential entropy; Step (8): Let the number of differential steps μ = μ + 1 and the embedding dimension m = m0 + (μ - 1), return to step (4) and continue to calculate the μ-step differential entropy until the number of differential steps μ is greater than the maximum number of differential steps μ T until; Step (9): Determine the flutter type according to the flutter diagnosis criteria.

2. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1 is characterized in that: In step (1): The sensors are vibration sensors and speed sensors; the vibration sensor is installed on the workpiece or the spindle to measure the vibration of the workpiece or the spindle; the speed sensor is installed near the spindle to measure the spindle speed; the diagnostic parameters include: the number of synchronous sampling points M per spindle revolution, the sampling length, the initial value of the embedding dimension m0, the number of intervals ε, the maximum number of differential steps μ T , μ T Threshold The sampling length is kM, where k is the number of spindle revolutions; the initial value of the embedding dimension m0 is determined according to the milling chatter characteristics; the μ T Threshold Determined according to the 3σ criterion.

3. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1 is characterized in that: In step (2): The specific implementation process of obtaining the synchronous vibration data X is: taking the spindle speed as a reference signal, synchronously obtaining the vibration data during the milling process; the vibration data obtained is vibration displacement data, vibration velocity data or vibration acceleration data; the obtained synchronous vibration data is expressed as: X={x(1),x(2),…,x(i),…,x(kM)}.

4. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1, characterized in that: In step (3): the differential step number μ is set to 1; the embedding dimension m is set to the initial value m0; and the time delay τ is set to the rotation period of the main axis.

5. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1, characterized in that: In step (4): The phase space realization process of reconstructing the synchronous vibration data X is specifically as follows: according to the embedding dimension m and the time delay τ set in step (3), the phase space of the synchronous vibration data X is reconstructed, and the reconstructed phase space P μ for Among them, the m-dimensional embedding vector It is expressed as:

6. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1, characterized in that: In step (5): For the phase space P μ Each m-dimensional vector in is processed by the difference rule to obtain the phase space P′ with an embedding dimension of m-μ. μ for The difference rule is:

7. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1 is characterized in that: In step (6): For the phase space P′ after difference μ Calculate the cosine similarity D_D between the i-th row of data and the i+1-th row of data μ (i), as shown below: in, 8. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1, characterized in that: The implementation process of step (7) is as follows: Divide the interval [-1,1] into ε equally spaced intervals (I1,I2,I3,…,I ε ), the interval is 2 / ε; the probability of all cosine similarities obtained in step (6) being in each interval in According to the probability of each interval Calculate μ-step differential entropy, the calculation formula is as follows:

9. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1, characterized in that: The implementation process of step (8) is as follows: The setting of the differential step number μ = μ + 1 means adding 1 to the original differential step number μ; then setting the embedding dimension m = m0 + (μ - 1), and repeating the calculation steps (4) to (8) until the differential step number μ is greater than the maximum differential step number μ T So far, we have obtained μ T The difference entropy.

10. The milling chatter diagnosis method based on multi-step differential entropy according to claim 1, characterized in that: The implementation process of step (9) is as follows: The μ obtained in the above steps T The differential entropy is regarded as a flutter diagnosis feature, and then the flutter type is determined according to the flutter diagnosis criterion; the flutter diagnosis criterion is shown in the following table: Table 1 Flutter diagnosis criteria In the table, Y represents the μ-th step differential entropy MSDE μ Greater than or equal to the chatter threshold r μ , N represents the μ-th step differential entropy MSDE μ Less than the chatter threshold r μ , and X represents the μ-th step differential entropy MSDE μ It needs to be determined according to the number of difference steps μ and the type of dither. If all μ-th step difference entropy MSDE μ are all less than the threshold r μ , then the chatter is a Hopf bifurcation type chatter; when all μ-th step difference entropy MSDE μ are greater than or equal to the threshold r μ , the milling process is in a non-chatter state; otherwise, the milling process is a periodic bifurcation type chatter. For the periodic bifurcation type chatter, the method of the present invention can be further classified, and the specific judgment criteria are shown in Table 1.

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