Milling chatter diagnosis method based on multi-step differential entropy

Abstract

This invention discloses a milling chatter diagnosis method based on multi-step differential entropy, belonging to the field of mechanical system fault diagnosis technology. The operation steps are as follows: select the sensor type and installation location, determine the chatter diagnosis parameters; acquire synchronous vibration data X; set the differential step number μ = 1, the embedding dimension m, and the time delay τ, and repeat the following calculations until the differential step number μ is greater than the maximum differential step number μ. T Up to; reconstruct the phase space P of the synchronous vibration data X. μ According to the difference rule, the phase space P μ After processing, the phase space P′ is obtained. μ ; Calculate the phase space P′ μ The method calculates the cosine similarity between adjacent rows of data; divides the interval [-1, 1] into ε intervals at equal intervals, and calculates the probability distribution of the obtained cosine similarity in each interval, and calculates the μ-step difference entropy; sets the difference step number μ = μ + 1 and the embedding dimension m = m0 + (μ - 1), and returns to continue calculating the μ-step difference entropy; determines the flutter type according to the flutter diagnosis criteria; the method of this invention can effectively overcome the inherent defects of traditional entropy, significantly improve the accuracy, timeliness and reliability of flutter diagnosis, provide solid technical support for the research and identification of flutter in the machining process, effectively improve machining efficiency, reduce the impact of flutter on machining quality, and reduce production costs. In addition, the method of this invention is highly in line with the trend of intelligent development in the manufacturing industry, has broad application prospects, and is expected to promote technological innovation and progress in the machining industry.

Description

Technical Field

[0001] This invention belongs to the field of mechanical system fault diagnosis technology, specifically relating to a milling chatter diagnosis method based on multi-step difference entropy (MSDE). Background Technology

[0002] Chatter, a self-excited vibration phenomenon caused by the dynamic interaction between the tool and the workpiece during milling, can lead to deterioration of the machined surface quality, shortened tool life, and even equipment damage. Generally, regenerative chatter in milling includes periodic bifurcation chatter and Hopf bifurcation chatter. Research literature indicates that machining parameters that induce periodic bifurcation chatter can improve machining efficiency while meeting machining quality requirements. To improve machining efficiency, some researchers have proposed using machining parameters that induce periodic bifurcation chatter. Therefore, it is necessary to diagnose chatter generated during milling and identify periodic bifurcation chatter. Furthermore, to study the hazards caused by different chatter types, it is necessary to diagnose various chatter types. Therefore, diagnosing chatter occurring during milling is of great significance.

[0003] Flutter diagnosis methods generally include data acquisition, feature extraction, and fault decision-making. The quality of feature extraction significantly affects the accuracy of flutter diagnosis; therefore, feature extraction is considered one of the most important aspects.

[0004] Patent No. 202410194548.8 discloses a high-speed milling chatter diagnosis method based on multi-resolution asynchronous entropy, where the extracted fault features are multi-resolution asynchronous entropy. While this method has achieved significant results in identifying chatter types, it requires a relatively long data sequence. When the data sequence length is relatively short, the method cannot accurately identify the chatter type. For example, when identifying cycle-4 bifurcation chatter, the method requires at least 11 spindle revolutions of data. It is well known that chatter should be identified promptly during milling to prevent unacceptable consequences. The relatively long time delay of this method may make it unsuitable for chatter detection.

[0005] To address the shortcomings of the aforementioned chatter diagnosis methods, this invention discloses a novel milling chatter diagnosis method based on multi-step differential entropy. This method identifies chatter types by calculating multi-step differential entropy. Multi-step differential entropy effectively overcomes the inherent defects of traditional entropy, significantly improving the accuracy, timeliness, and reliability of chatter diagnosis. It provides solid technical support for chatter research and identification in machining processes, effectively improving machining efficiency, reducing the impact of chatter on machining quality, and lowering production costs. Furthermore, the multi-step differential entropy-based milling chatter diagnosis method aligns perfectly with the trend of intelligent manufacturing, possessing broad application prospects and the potential to drive technological innovation and progress in the machining industry. Summary of the Invention

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

[0007] Technical solution: This 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): Obtain synchronous vibration data X;

[0010] Step (3): Set the difference step number μ, the embedding dimension m, and the time delay to 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, the phase space P′ is obtained. μ ;

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

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

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

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

[0017] Further, the sensors in step (1) are a vibration sensor and a speed sensor; the vibration sensor is installed on the workpiece or spindle to measure the vibration of the workpiece or 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, and the maximum number of differential steps μ. T μ T Threshold The sampling length is kM, where k is the spindle speed; the initial value of the embedding dimension m0 is determined based on 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] Using the spindle speed as a reference signal, vibration data during the milling process is acquired synchronously; the acquired vibration data includes 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 difference step number μ is set to 1; the embedding dimension m is set to the initial embedding dimension 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] Based on 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 is obtained. μ for Where, m-dimensional embedding vector Represented as:

[0025]

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

[0027] For phase space P μ For each m-dimensional vector, the phase space P′ with embedding dimension m-μ is obtained by processing it using the difference rule. μ for The difference rule is as follows:

[0028]

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

[0030] For the phase space P′ after differentiation μ For the data in the i-th row, calculate the cosine similarity D_D between it and the data in the (i+1)-th row. μ (i), as shown in the following formula:

[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 ), with an interval of 2 / ε; calculate the probability that all cosine similarities obtained in step (6) fall within each interval. in Based on the probability of each interval The formula for calculating the μ-step difference entropy is as follows:

[0036]

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

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

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

[0040] The μ obtained from the above steps T The differential entropy is considered as a flutter diagnostic feature, and the flutter type is determined according to the flutter diagnostic criteria; the flutter diagnostic criteria are shown in the table below:

[0041] Table 1 Flutter Diagnostic Criteria

[0042]

[0043] In the table, Y represents the μ-th step differential entropy MSDE. μ Greater than or equal to the flutter threshold rμ N represents the μ-th step differential entropy MSDE μ Less than the flutter threshold r μ X represents the μ-th step difference entropy MSDE μ It needs to be determined based on the difference step number μ and the chatter type. If all μ-th step difference entropies are MSDE... μ All are less than the threshold r μ Then the flutter is a Hopf bifurcation type flutter; when all μ-th step difference entropy MSDE μ All are greater than or equal to the threshold r μ If the condition is met, the milling process is in a chatter-free state; otherwise, the milling process exhibits periodic bifurcation chatter. For periodic bifurcation chatter, the method of this 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 patent mainly includes the following beneficial effects: (1) The milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention patent 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 patent requires less computational cost and can diagnose chatter type more quickly; (3) The milling chatter diagnosis method based on multi-step differential entropy disclosed in the present invention patent requires a relatively short data sequence length, which overcomes the shortcomings of existing methods that cannot handle 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 patent is not affected by the spindle speed and can be applied to the chatter diagnosis of milling processes with different speeds. Attached Figure Description

[0045] Figure 1 This is a flowchart of the milling chatter diagnosis method based on multi-step differential entropy disclosed in this invention;

[0046] Figure 2 This is a diagram of workpiece vibration displacement without chatter in an embodiment of the present invention;

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

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

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

[0050] Figure 6 This is a multi-step differential entropy distribution diagram under different flutter types. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings.

[0052] The calculation flow of the milling chatter diagnosis method based on multi-step differential entropy disclosed in this 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 a vibration sensor and a speed sensor; the vibration sensor is installed on the workpiece or spindle to measure the vibration of the workpiece or 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, and the maximum number of difference steps μ. T μ T Threshold The sampling length is kM, where k is the spindle speed; the initial value of the embedding dimension m0 is determined based on the milling chatter characteristics; the μ T Threshold The embedding dimension is 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 acquired synchronous vibration data X from milling can be represented 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] Based on 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 is obtained. μ for Wherein, the i-th embedding vector An m-dimensional vector is represented as:

[0061]

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

[0063] For phase space P μ For each m-dimensional vector, the phase space P′ with embedding dimension m-μ is obtained by processing it using the difference rule. μ for The difference rule is as follows:

[0064]

[0065] Step (6): Calculate the phase space P μ Cosine similarity between each pair of adjacent rows of data

[0066] For the phase space P′ after differentiation μ For the data in the i-th row, calculate the cosine similarity D_D between it and the data in the (i+1)-th row. μ (i), as shown in the following formula:

[0067]

[0068] in,

[0069]

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

[0071] Divide the interval [-1, 1] into ε equal intervals (I1, I2, I3, ..., I...). ε ), with an interval of 2 / ε; calculate the probability that all cosine similarities obtained in step (6) fall within each interval. in Based on the probability of each interval The formula for calculating the μ-step difference entropy is as follows:

[0072]

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

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

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

[0076] The μ obtained from the above steps T The differential entropy is considered as a flutter diagnostic feature, and then the flutter type is determined according to the flutter diagnostic criteria; the flutter diagnostic criteria are shown in the table below:

[0077] Table 1 Flutter Diagnostic Criteria

[0078]

[0079]

[0080] In the table, Y represents the μ-th step differential entropy MSDE. μ Greater than or equal to the flutter threshold r μ N represents the μ-th step differential entropy MSDE μ Less than the flutter threshold r μ X represents the μ-th step difference entropy MSDE μ It needs to be determined based on the difference step number μ and the chatter type. If all μ-th step difference entropies are MSDE... μ All are less than the threshold r μ Then the flutter is a Hopf bifurcation type flutter; when all μ-th step difference entropy MSDE μ All are greater than or equal to the threshold r μ If the condition is met, the milling process is in a chatter-free state; otherwise, the milling process exhibits periodic bifurcation chatter. For periodic bifurcation chatter, the method of this invention can be further classified, and the specific judgment criteria are shown in Table 1.

[0081] In this embodiment, the differential method is used to process the synchronously sampled data. It should be noted that the differential method here does not directly process the synchronously sampled data, but rather processes each dimension of the data after phase space reconstruction. Furthermore, the number of differential steps and the embedding dimension need to be updated each time the μ-step differential entropy is calculated. When the milling process is chatter-free, the synchronously sampled vibration signal of the workpiece is as follows: Figure 2 As shown. When the milling process involves periodic -2 bifurcation chatter, the synchronously sampled vibration signal of the workpiece is as follows. Figure 3 As shown. Figure 4 and 5 The synchronously sampled vibration signals during milling processes, specifically for periodic -3 bifurcation chatter and Hopf chatter, are presented respectively. The synchronous vibration signals are processed using the method of this invention to obtain μ. T A multi-step difference entropy value. Figure 6 This is a multi-step differential entropy distribution diagram for different flutter types. Based on the obtained μ... T Multistep differential entropy values ​​and flutter diagnostic criteria can be used to diagnose the type of flutter.

Claims

1. A milling chatter diagnosis method based on multi-step differential entropy, characterized in that, The operating steps are as follows: Step (1): Select the sensor type and installation location, and determine the flutter diagnostic parameters; Step (2): Obtain synchronous vibration data X; Step (3): Set the difference step number μ, embedding dimension m, and time delay as follows: ; Step (4): Reconstruct the phase space of the synchronous vibration data X The specific process of reconstructing the phase space of the synchronous vibration data X is as follows: based on the embedding dimension m and time delay set in step (3) Phase space reconstruction is performed on the synchronous vibration data X. The reconstructed phase space... for , where m-dimensional embedding vector Represented as: ； Step (5): Perform phase space according to the difference rule Processing is performed to obtain the phase space. The phase space The specific processing implementation is as follows: For the phase space... For each m-dimensional vector, the embedding dimension is obtained by processing it using the difference rule. phase space for The difference rule is as follows: ； Step (6): Calculate the phase space Cosine similarity between any two adjacent rows of data; for the phase space after difference. For the data in the i-th row, calculate the cosine similarity between the i-th row and the (i+1)-th row. As shown in the following formula: ， wherein , , ; Step (7): Divide the interval [-1,1] into ε equally spaced intervals, and calculate the probability distribution of the cosine similarity obtained in step (6) in each interval, and calculate the μ-step difference entropy; Step (8): Let the difference step number μ = μ + 1 and the embedding dimension m = m0 + (μ - 1), return to step (4) and continue to calculate the μ-step difference entropy until the difference step number μ is greater than the maximum difference step number. until; Step (9): Determine the type of flutter according to the flutter diagnosis criteria.

2. The multi-step differential entropy based milling chatter diagnosis method of claim 1, wherein, In step (1): The sensors are a vibration sensor and a speed sensor; the vibration sensor is installed on the workpiece or spindle to measure the vibration of the workpiece or 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, and the maximum number of difference steps. , Threshold The sampling length is kM, where k is the spindle speed; the initial value of the embedding dimension m0 is determined based on the milling chatter characteristics; Threshold Determined according to the 3σ criterion.

3. The multi-step differential entropy based milling chatter diagnosis method of claim 1, wherein, In step (2): The specific process for acquiring synchronous vibration data X is as follows: using the spindle speed as a reference signal, vibration data during the milling process is acquired synchronously; the acquired vibration data includes vibration displacement data, vibration velocity data, or vibration acceleration data; the acquired synchronous vibration data is represented as follows: 。 4. The multi-step differential entropy based milling chatter diagnosis method of claim 1, wherein, In step (3): the difference step number μ is set to 1; the embedding dimension m is set to the initial value m0; the time delay is... The rotation period set as the main axis.

5. The multi-step differential entropy based milling chatter diagnosis method of claim 1, wherein, The implementation process of step (7) is as follows: Divide the interval [−1,1] into ε equally spaced intervals. The interval is 2 / ε; the probability of all cosine similarities obtained in step (6) falling within each interval is calculated. ,in Based on the probability of each interval The formula for calculating the μ-step difference entropy is as follows: 。 6. The multi-step differential entropy based cutter chatter diagnostic method of claim 1, wherein, The implementation process of step (8) is as follows: The setting of the difference step number μ = μ + 1 means adding 1 to the original difference step number μ; then setting the embedding dimension m = m0 + (μ - 1), and repeating steps (4) to (8) until the difference step number μ is greater than the maximum difference step number. So far, a total of One difference entropy.

7. The multi-step differential entropy based cutter chatter diagnostic method of claim 1, wherein, The implementation process of step (9) is as follows: The step of calculating the differential entropy of the vibration signal is as follows: The differential entropy is taken as a chattering diagnosis feature, and then the chattering type is determined according to a chattering diagnosis criterion as shown in the following table: Table 1. Flutter Diagnostic Criteria In the table, Y represents the μ-th step differential entropy MSDE. μ Greater than or equal to the flutter threshold N represents the μ-th step differential entropy MSDE μ Less than the flutter threshold X represents the μ-th step difference entropy MSDE μ It needs to be based on the number of difference steps And flutter type to determine; if all μ-th step differential entropy MSDE μ If all values ​​are less than the threshold #imgpt43#, then the flutter is a Hopf bifurcation type flutter; when all μ-th step differential entropy MSDE μ If all values ​​are greater than or equal to the threshold #imgpt44#, then the milling process is in a chatter-free state; otherwise, the milling process is a periodic bifurcation chatter. For periodic bifurcation chatter, it can be further classified, and the specific judgment criteria are shown in Table 1.

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