Milling chatter detection method based on difference entropy

Abstract

The invention discloses a milling chatter detection method based on differential entropy. Belongs to the technical field of mechanical system fault detection. Acquiring synchronous vibration data X; reconstructing a phase space P of the synchronous vibration data X; subtracting two adjacent columns of data in the phase space P according to a difference rule to obtain a phase space P1; calculating the cosine similarity between each two adjacent rows of data in the phase space P1; dividing the interval [-1, 1] into epsilon intervals at equal intervals, and counting the probability distribution of the obtained cosine similarity in each interval; calculating a difference entropy and taking the difference entropy as a flutter index; judging whether flutter occurs or not; according to the invention, the accuracy and timeliness of flutter detection are improved; technical support is provided for the stability of machining, the influence of flutter on the machining quality and efficiency is reduced, and the competitiveness of the manufacturing industry is improved; in addition, the method conforms to the development trend of the manufacturing industry towards intelligentization and high precision, and has wide application prospects.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical system fault detection, and relates to a milling chatter detection method based on difference entropy (DiffEn). Background Art

[0002] In the field of modern machining, with the continuous improvement of the requirements for machining accuracy and efficiency, the stability and reliability of the machining process have become research hotspots. Chatter is a common and serious non-linear vibration phenomenon in the machining process, which has a significant impact on machining quality and efficiency. Research shows that in machining processes such as milling, turning, and drilling, when the cutting parameters (such as cutting speed, feed rate, cutting depth, etc.) are not properly selected, chatter will occur. Chatter not only reduces the machining surface quality, increases surface roughness, and increases waviness, but also exacerbates tool wear and damages the workpiece, thus directly affecting the milling machining accuracy and production efficiency and increasing production costs. Therefore, timely detection and control of chatter can improve the milling machining quality and efficiency.

[0003] Currently, chatter detection methods are mainly divided into two categories: data-driven methods and model-based methods. Although model-based methods can detect chatter, it is difficult to obtain highly reliable detection results in the detection of complex milling chatter. In addition, model-based methods require the establishment of a relatively accurate physical model. Due to the complexity of the actual machining process and the influence of various factors, it is generally difficult to establish a physical model that comprehensively reflects the actual situation. Therefore, model-based chatter detection methods are difficult to be applied to complex milling machining processes.

[0004] In data-driven chatter detection methods, entropy-based chatter detection methods have attracted more and more attention from researchers. Currently, researchers have proposed a variety of entropy-based chatter detection methods, and the entropies used include sample entropy, fuzzy entropy, permutation entropy, etc. Although the above-mentioned entropies can be used as chatter indicators to detect chatter, they cannot reliably identify periodic bifurcation chatter. To solve this problem, a Chinese patent (Patent No.: 202410194548.8) discloses a method based on multi-resolution asynchronous entropy, which has the advantage of being able to identify chatter and its types, but its disadvantages are: (1) the calculation cost is relatively high, and it may not be applicable to the chatter detection of high-speed or ultra-high-speed milling machining; (2) it cannot sensitively identify early period-2 bifurcation chatter or period-2 bifurcation chatter under strong noise background. Summary of the Invention

[0005] Aiming at the above problems, the object of the present invention is to propose a milling chatter detection method based on difference entropy, which can detect in real time and reliably whether chatter occurs through difference entropy.

[0006] The technical solution of the present invention is as follows: The milling chatter detection method based on differential entropy of the present invention has the following operating steps:

[0007] Step (1): Select the sensor type and installation position, and determine the relevant parameters for chatter detection;

[0008] Step (2): Obtain the synchronous vibration data X;

[0009] Step (3): Reconstruct the phase space P of the synchronous vibration data X;

[0010] Step (4): Subtract the adjacent two columns of data in the phase space P according to the difference rule to obtain the phase space P1;

[0011] Step (5): Calculate the cosine similarity between the adjacent two rows of data in the phase space P1;

[0012] Step (6): Divide the interval [-1, 1] into ε equal intervals, and count the probability distribution of the cosine similarity obtained in step (5) in each interval;

[0013] Step (7): Calculate the differential entropy and use it as the chatter index;

[0014] Step (8): Judge whether chatter occurs.

[0015] Further, in step (1), the sensors are vibration sensors and rotational speed sensors; the vibration sensor is installed on the workpiece or the spindle for measuring the vibration of the workpiece or the spindle; and the rotational speed sensor is installed near the spindle for measuring the rotational speed of the spindle;

[0016] The relevant parameters for chatter detection include: the number of synchronous sampling points M per revolution of the spindle, the sampling length, the embedding dimension m, the number of intervals ε, and the threshold r;

[0017] Among them, the sampling length is kM, where k is the number of revolutions of the spindle and M is the number of synchronous sampling points M per revolution of the spindle;

[0018] The embedding dimension m is determined according to the milling chatter characteristics;

[0019] The threshold r is determined according to the 3σ criterion.

[0020] Further, the implementation process of step (2) is as follows: Taking the spindle speed as the reference signal, synchronously obtain the vibration data during the milling process; the obtained vibration data is vibration displacement data, vibration velocity data or vibration acceleration data; the obtained synchronous vibration data can be expressed as:

[0021] X = {x(1), x(2), …, x(i), …, x(kM)}.

[0022] Further, the implementation process of step (3) is as follows: Set the time delay as the rotation period of the main shaft, and then perform phase space reconstruction on the synchronous vibration data X according to the embedding dimension m preset in step (1). The reconstructed phase space P is where the m-dimensional embedding vector is expressed as:

[0023]

[0024] Further, the implementation process of step (4) is as follows:

[0025] For each m-dimensional vector in the phase space, perform differential processing on the phase space P using the differential rule to obtain the phase space P1 with an embedding dimension of m - 1 as where

[0026]

[0027] Further, the implementation process of step (5) is as follows:

[0028] For the i-th row data in the phase space P1, calculate its cosine similarity D_D(i) with the (i + 1)-th row data, as shown in the following formula:

[0029]

[0030] where

[0031] Further, the implementation process of step (6) is as follows:

[0032] Divide the interval [-1, 1] into ε intervals (I1, I2, I3, …, Iε) at equal intervals, with an interval of 2 / ε; calculate the probability (pr1, pr2, pr3, …, pr ε ) of all the cosine similarities obtained in step (5) falling into each interval, where

[0033] Further, the implementation process of step (7) is as follows:

[0034] According to the probability (pr1, pr2, pr3, …, pr ε ) of each interval obtained in step (6), calculate the differential entropy, and its calculation formula is as follows:

[0035]

[0036] And take this differential entropy as the flutter index.

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

[0038] Judge whether chatter occurs according to the chatter index obtained in step (7) and the threshold r set in step (1); if the chatter index is less than or equal to the threshold r, it is considered that chatter has occurred, otherwise chatter has not occurred, and the detection program returns to step (2) to continue chatter detection until chatter is detected or the detection process ends.

[0039] The beneficial effects of the present invention are as follows: (1) The milling chatter detection method based on differential entropy of the present invention can reliably detect milling chatter; (2) The milling chatter detection method based on differential entropy of the present invention requires less computational cost and can quickly detect chatter; (3) The milling chatter detection method based on differential entropy of the present invention can sensitively identify early period-2 bifurcation chatter or period-2 bifurcation chatter under strong noise background, overcoming the deficiencies of the multi-resolution asynchronous entropy chatter detection method; (4) The milling chatter detection method based on differential entropy of the present invention is not affected by the spindle speed. Description of the Drawings

[0040] Figure 1 is the operation flowchart of the present invention;

[0041] Figure 2 is the workpiece vibration displacement diagram without chatter in the embodiment of the present invention;

[0042] Figure 3 is the workpiece vibration displacement diagram during period-2 bifurcation chatter in the embodiment of the present invention;

[0043] Figure 4 is the workpiece vibration displacement diagram during period-3 bifurcation chatter in the embodiment of the present invention;

[0044] Figure 5 is the workpiece vibration displacement diagram during Hopf bifurcation chatter in the embodiment of the present invention;

[0045] Figure 6 is the chatter detection result diagram of the embodiment of the present invention. Detailed Embodiments

[0046] The following further elaborates on the technical solutions of the present invention in conjunction with specific embodiments.

[0047] As Figure 1 shown, the specific operation steps of the milling chatter detection method based on differential entropy of the present invention are as follows:

[0048] Step (1): Select the sensor type and installation position, and determine the relevant parameters for chatter detection;

[0049] The number of sampling points in each rotation period of the milling cutter is determined by the sampling frequency; set the sampling frequency to Thus, it is ensured that enough data volume M can be obtained in each rotation period of the milling cutter, where n represents the rotational speed of the milling cutter (r / min).

[0050] In this embodiment, the data acquisition amount per revolution of the milling cutter is M. Therefore, the time delay τ for phase space reconstruction is set to the time used to acquire M data points, that is, the detected rotation period of the milling cutter.

[0051] The embedding dimension is set to 4, the time delay τ is set to the time used to acquire M data points, and the threshold r is set to 0.92.

[0052] Step (2): Obtain the synchronous vibration data X.

[0053] The vibration data obtained during the milling process can be expressed as:

[0054] X = {x(1), x(2), …, x(i), …, x(kM)};

[0055] Step (3): Reconstruct the phase space P of the synchronous vibration data X.

[0056] According to the embedding dimension m and time delay τ set in step (1) and step (2), perform phase space reconstruction on the synchronous vibration data X:

[0057]

[0058] In the formula, the embedding vector is an m-dimensional vector expressed as:

[0059]

[0060] Step (4): Subtract two adjacent columns of data in the phase space P according to the difference rule to obtain the phase space P1.

[0061] For each m-dimensional vector in the phase space, perform difference processing on the phase space P using the difference subtraction rule, ensuring subtraction according to the rule of subtracting the previous column from the next column, and obtaining P1 as: Among them,

[0062]

[0063] Step (5): Calculate the cosine similarity between adjacent two rows of data in the phase space P1.

[0064] For the i-th row of data in the phase space P1, calculate its cosine similarity D_D(i) with the (i + 1)-th row of data, and its formula is as follows:

[0065]

[0066] Among them,

[0067] Step (6): Divide the interval [-1, 1] into ε equal intervals, and count the probability distribution of the cosine similarities obtained in step (5) in each interval.

[0068] Divide the interval [-1, 1] into ε equal intervals (I1, I2, I3, …, Iε), with an interval of 2 / ε; calculate the probability (pr1, pr2, pr3, …, pr ε ) that all the cosine similarities obtained in step (5) are in each interval, where

[0069] Step (7): Calculate the differential entropy and use it as the chatter index.

[0070] According to the probabilities (pr1, pr2, pr3, …, pr ε ) of each interval obtained in step (6), calculate the differential entropy, and its calculation formula is as follows:

[0071]

[0072] And use this differential entropy as the chatter index.

[0073] Step (8): Determine whether chatter occurs; according to the chatter index obtained in step (7) and the threshold r set in step (1), determine whether chatter occurs; if the chatter index is less than or equal to the threshold r, it is considered that chatter has occurred, otherwise chatter has not occurred, and the detection program returns to step (2) to continue chatter detection until chatter is detected or the detection process ends.

[0074] In this embodiment, the differential method is used to process the synchronous sampling vibration data. It should be noted that the differential method here does not directly perform differential processing on the synchronous sampling vibration data, but performs differential processing on each dimension of data after phase space reconstruction; after the processing is completed, the differential entropy value is calculated. When the milling process is chatter-free, the synchronous sampling vibration signal of the workpiece is as Figure 2 shown. When the milling process is periodic-2 bifurcation chatter, the synchronous sampling vibration signal of the workpiece is as Figure 3 shown. Figure 4 And 5 respectively show the synchronous sampling vibration signals when the milling process is periodic-3 bifurcation chatter and Hopf-type chatter. Figure 6 is the chatter detection result of the embodiment of the present invention. It can be seen from the figure that the differential entropy when there is no chatter is close to 1, while the differential entropy in the three cases of chatter is less than 0.5. In this embodiment, the threshold is set to 0.92 according to the 3σ rule. From Figure 6It can be seen that the differential entropy values of the three types of chatter are all less than the threshold value of 0.92, so it can be determined that chatter has occurred. The differential entropy value without chatter is greater than the threshold value of 0.92. Therefore, it can be determined that the milling process is in a state of chatter-free machining. The method of the present invention can reliably detect milling chatter.

[0075] The method of the present invention can detect chatter in real time. Compared with the existing asynchronous entropy method, it has less computational cost. After testing, it takes about 2.6 seconds to run the asynchronous entropy 1000 times, while it takes about 1.9 seconds to run our differential entropy 1000 times. The computational cost of the method of the present invention is only 73.1% of the existing asynchronous entropy method. The method of the present invention can detect the chatter generated in the milling process in real time.

[0076] The method of the present invention can sensitively detect period-2 bifurcation chatter because the method of the present invention makes the chatter characteristics of period-2 bifurcation chatter more obvious through differential calculation.

[0077] The present invention discloses a new type of differential entropy and proposes a milling chatter detection method based on this differential entropy; the differential entropy described in the present invention can overcome the shortcomings of traditional entropy, improve the accuracy, timeliness and reliability of chatter detection, provide more effective technical support for the stability control of the machining process, reduce the influence of chatter on the machining quality and efficiency, reduce production costs, and improve the competitiveness of the manufacturing industry; in addition, the method of the present invention conforms to the development trend of the manufacturing industry towards intelligence and high precision, and has broad application prospects.

Claims

1. A milling chatter detection method based on differential entropy, characterized in that: The operation steps are as follows: Step (1): Select the sensor type and installation location, and determine the relevant parameters for chatter detection; Step (2): obtaining synchronous vibration data X; Step (3): reconstruct the phase space P of the synchronous vibration data X; Step (4): Subtract two adjacent columns of data in the phase space P according to the difference rule to obtain the phase space P1; Step (5): Calculate the cosine similarity between two adjacent rows of data in the phase space P1; Step (6): Divide the interval [-1, 1] into ε intervals at equal intervals, and calculate the probability distribution of the cosine similarity obtained in step (5) in each interval; Step (7): Calculate the differential entropy and use it as a chatter indicator; Step (8): Determine whether chattering occurs.

2. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: In step (1), the type of the sensor is a vibration sensor and a rotation speed sensor; The vibration sensor is placed on the workpiece or the spindle to measure the vibration of the workpiece or the spindle; The speed sensor is placed near the main shaft to measure the speed of the main shaft; The vibration detection related parameters include: the number of synchronous sampling points M per spindle revolution, the sampling length, the embedding dimension m, the number of intervals ε, and the threshold r.

3. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: The sampling length is kM, where k is the number of spindle revolutions and M is the number of synchronous sampling points per spindle revolution; The embedding dimension m is determined according to the milling chatter characteristics; The threshold r is determined according to the 3σ criterion.

4. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: In step (2), the implementation process of obtaining the synchronous vibration data X is specifically: 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)}.

5. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: In step (3), the implementation process of reconstructing the phase space P of the synchronous vibration data X is specifically as follows: the time delay is set as the rotation period of the main shaft, and then the phase space of the synchronous vibration data X is reconstructed according to the embedding dimension m pre-set in step (1). The reconstructed phase space P is Among them, the m-dimensional embedding vector It is expressed as:

6. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: The implementation process of step (4) is specifically as follows: For each m-dimensional vector in the phase space, the phase space P is differentiated using the difference rule to obtain the phase space P1 with an embedding dimension of m-1: in, 7. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: In step (5), the implementation process of calculating the cosine similarity between two adjacent rows of data in the phase space P1 is specifically: for the i-th row of data in the phase space P1, the cosine similarity D_D(i) between it and the i+1-th row of data is calculated, as shown in the following formula: in, 8. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: The implementation process of step (6) is as follows: Divide the interval [-1,1] into ε intervals (I1,I2,I3,…,I ε ), with an interval of 2 / ε; calculate the probability that all cosine similarities obtained in step (5) are in each interval (pr1, pr2, pr3, ..., pr ε ), where 9. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: In step (7), the implementation process of calculating the differential entropy and using it as a chatter indicator is as follows: According to step (6), the probability of each interval (pr1, pr2, pr3, ..., pr ε ) to calculate the differential entropy, the calculation formula is as follows: The differential entropy is used as a chatter indicator.

10. The milling chatter detection method based on differential entropy according to claim 1, characterized in that: In step (8), the implementation process of determining whether chattering occurs is specifically as follows: Determining whether chatter occurs based on the chatter index obtained in step (7) and the threshold value r set in step (1); If the chatter index is less than or equal to the threshold value r, it is considered that chatter has occurred. Otherwise, chatter has not occurred and the detection procedure returns to step (2) to continue the chatter detection until chatter is detected or the detection process is completed.

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