A high speed milling chatter monitoring and fundamental chatter frequency estimation method

Abstract

The application discloses a high-speed milling chatter monitoring and basic chatter frequency estimation method, which comprises the following steps: firstly, a matrix filter is constructed through the spectrum of an idle signal to realize extraction and separation of a chatter signal; secondly, an accurate frequency domain parameter of a main component of the filtered signal is obtained through a rotation invariance parameter estimation technology based on a single-order signal energy ratio; and finally, a interval frequency distribution histogram is constructed according to the distribution characteristics of a regenerative chatter, and early weak milling chatter signal on-line monitoring is realized by taking the histogram information entropy as an index. The principle of the application is based on the distribution characteristics of the regenerative chatter frequency, a normalized dimensionless information entropy index is proposed, the influence of the signal energy change is small, and the weak chatter is sensitive. The parameter estimation method has strong anti-noise interference performance and extremely high resolution. Based on the constructed interval frequency distribution histogram, the basic frequency of the chatter can be obtained, which provides guidance for other chatter monitoring or suppression methods.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of detection of machining state, and particularly relates to the field of chatter monitoring and identification of high-speed milling, and specifically relates to a high-speed milling chatter monitoring and basic chatter frequency estimation method. BACKGROUND

[0002] Milling chatter is a strong self-excited vibration generated in the milling process, which seriously affects the processing efficiency and quality. The early research to avoid the phenomenon of chatter mainly focuses on the prediction of the stability region of chatter. The main idea is to establish a mechanical model of the cutting system, solve the dynamic equation to obtain the stability lobe diagram among the cutting depth, spindle speed and stability. This prediction method selects the conservative processing parameters in the stability region of the lobe diagram in actual processing, which restricts the improvement of processing efficiency. And the generation of milling chatter is related to processing parameters, tools, machine tool structure and processing materials and other factors, and the causes are complex, so it is an effective means to realize high-speed and high cutting rate to guide the machine tool system to react in the early stage of chatter through online monitoring of the milling state to avoid the occurrence of chatter.

[0003] A large number of scholars have proposed various chatter monitoring methods and achieved remarkable results, but it is still difficult to propose a method that is both fast in calculation, accurate in identification and has good robustness to various working conditions. In the chatter monitoring method based on frequency domain, the data segment in a short time can be regarded as a short-time stationary signal. The most commonly used method to obtain signal frequency is fast Fourier transform, but due to its frequency spectrum leakage and fence effect, the frequency information resolution obtained is low. The chatter identification algorithm based on signal component decomposition, for the weak chatter development stage, the distribution of chatter signal is not concentrated, and the selected intrinsic mode function (IMF) component sensitive to chatter has difficulty in ensuring the effect under different working conditions.

[0004] Therefore, how to effectively separate the chatter component mixed with other periodic components in the sensor signal and accurately estimate the frequency domain parameters of the signal is an important factor affecting the effect of online chatter monitoring. In addition, in various chatter monitoring methods, few scholars consider the influence of the basic frequency of chatter, and accurate estimation of the basic frequency of chatter can also provide new ideas for further chatter suppression or other chatter monitoring methods. SUMMARY

[0005] The purpose of the present application is to provide a high-speed milling chatter monitoring and main chatter frequency estimation method based on interval frequency information entropy, which has small calculation complexity, good robustness and can be used for online chatter monitoring. And it can obtain accurate regenerative chatter frequency, which can guide further chatter suppression.

[0006] In order to achieve the above object, the technical scheme adopted by the present application is as follows: a high-speed milling chatter monitoring and basic chatter frequency estimation method, comprising the following steps:

[0007] S1, collecting vibration signals in the spindle milling process in real time, and performing chatter detection every time interval t;

[0008] S2, intercepting the spindle idle signal at the beginning of milling, and constructing a matrix filter capable of filtering out rotating base frequency harmonics and colored background noise based on the same, filtering the subsequent vibration signals through the filter to obtain a residual signal containing no rotating frequency harmonics and colored noise;

[0009] S3, estimating the frequency domain parameters of the time domain signal using a parameter estimation method based on rotational invariance, using a single-order signal energy ratio index to divide the signal subspace size, and obtaining the frequency vector and amplitude vector of the main component of the residual signal obtained in S2;

[0010] S4, according to the distribution characteristics that there is a constant frequency difference between the milling chatter frequency and the rotating frequency harmonics, constructing an interval frequency, and converting the frequency vector and amplitude vector obtained in S3 into an interval frequency distribution histogram;

[0011] S5, taking the information entropy of the interval frequency distribution histogram as a chatter monitoring index to monitor early weak milling chatter signals;

[0012] S6, when chatter occurs, the height of the square column corresponding to the basic chatter frequency in the interval frequency distribution histogram is obviously higher than that of other square columns, and the basic chatter frequency is obtained accordingly.

[0013] In S1, an acceleration sensor is used to measure the vibration signal, and a contact type installation is fixed on the spindle shell near the tool shank.

[0014] In S1, the long-time continuous vibration signal is divided into short-time signal frames, wherein the signal frame length is selected according to the sampling frequency f s , N = t*f s sampling points are collected, and f s is the sampling frequency.

[0015] In S3, the signal subspace order estimation method based on the rotational invariance parameter estimation of the single-order signal energy ratio is as follows: an L-row M-column Hankel matrix is constructed from the time domain signal, wherein L > M and M is an even number; singular value decomposition is performed on the Hankel matrix to obtain M singular values σ1, σ2, …, σ M ; the original time domain signal is divided into M / 2-order sinusoidal signals, and the amplitude A i of each order signal is The single-order signal energy ratio is:

[0016]

[0017] When R E is less than the threshold value, the current order signal is considered to belong to noise, i.e. the signal enters the noise subspace from the signal subspace i=1,2,3…M / 2.

[0018] The specific steps for constructing the matrix filter according to the main shaft speed and the colored noise in S2 are as follows:

[0019] First, the main shaft rotation frequency f sr is obtained according to the main shaft speed of milling. r = [f sr ,2f sr ,…,mf sr ], the matrix filter is established according to f r to filter out the rotation frequency and its multiple frequencies in the idling signal; mf sr is not greater than the Nyquist frequency, i.e. one-half of the sampling frequency.

[0020] The frequency vector f n of the main component of the signal after the filtering in the previous step is searched by using the rotation invariance parameter estimation method based on the single order signal energy ratio for the remaining signal, i.e. the colored background noise frequency, and all the frequency vectors to be filtered out are f filter = [f r ,f n ], and a complete matrix filter is constructed accordingly.

[0021] The distribution characteristics of the regenerative chatter in S4 refer to that a dynamic model is established for the formation process of the regenerative chatter, and according to the Floquet theory of time-delay differential equation, it is obtained that the chatter frequencies of Hopf bifurcation and period-doubling bifurcation both have a constant frequency interval relationship with the multiple frequencies of the main shaft speed, i.e. the chatter frequency is expressed as f chatter = |kf sr ±f c |, k=1,2,3…, f c is the basic chatter frequency, and the interval frequency is constructed to reflect the distribution characteristics of the chatter frequency.

[0022] The steps for obtaining the interval frequency of the chatter signal in step S4 are as follows:

[0023] The multiple frequency component vectors of the main component of the filtered signal obtained according to step S3 are f filtered = [f1,f2,f3,…].

[0024] The above frequencies are taken as remainders with respect to the main shaft rotation frequency to obtain the remainder vector Δf = mod(f filtered ,f sr ) = [Δf1,Δf2,Δf3…].

[0025] The interval frequency which is away from the multiple of the main shaft rotation frequency is: l is 1, 2, 3...

[0026] The specific steps for converting the chatter signal parameters in S4 into the interval frequency distribution histogram are as follows:

[0027] The interval frequency distribution range is (0, f sr / 2] and is uniformly divided into n sub-frequency bands, that is, the interval frequency and the corresponding amplitude are divided into n groups according to the frequency, and the frequency band width of each group is Δf=f sr / 2n.

[0028] The midpoint frequency of each group represents the original interval frequency; the sum of the normalized amplitudes of all interval frequencies in the group is the distribution weight, that is, the distribution probability where ε is a very small number added to the sum of the normalized amplitudes of each group to avoid a probability of 0; the midpoint frequency after grouping is taken as the horizontal coordinate, and the distribution probability is taken as the vertical coordinate to draw the interval frequency distribution histogram.

[0029] In S5, the normalized interval frequency information entropy is constructed as the chatter monitoring index according to the interval frequency distribution histogram, and the calculation formula is:

[0030]

[0031] where n is the number of horizontal axis groups of the histogram, is the distribution probability corresponding to each group, that is, the vertical coordinate of the histogram; when chatter occurs, the residual signal obtained in S2 is mainly the chatter signal, the interval frequency distribution is concentrated, and the information entropy value is relatively small; when no chatter occurs, the residual signal obtained in S2 is mainly the white noise signal, the interval frequency distribution is chaotic, and the information entropy value is relatively large.

[0032] The chatter monitoring index Htotal changes between 0 and 1, and when no chatter occurs, the index is close to 1; a constant H0 between 0 and 1 is selected as the chatter monitoring threshold, that is: when H>H0, the monitoring is in a steady cutting state; when H<H0, the monitoring is in a chatter cutting state.

[0033] Compared with the prior art, the present application has at least the following beneficial effects:

[0034] The principle of the present application is based on the regenerative chatter frequency distribution characteristics, a dimensionless information entropy index is proposed, the normalized dimensionless interval frequency information entropy index has clear physical meaning, and the index is very stable when cutting is stable, and it is easy to set a threshold value; false judgments will not occur for cutting in, cutting out and idling; it has the advantages of being less affected by signal energy changes and sensitive to weak chatter, and has strong anti-noise interference performance; the estimation of signal parameters via rotational invariance technique (ESPRIT) based on single order energy ratio (SOER) is used to estimate signal parameters, and the accurate chatter fundamental frequency can be obtained through the interval frequency distribution, which provides guidance for further chatter suppression; compared with the existing method of extracting chatter sensitive components, the method of the present application further realizes sufficient separation of chatter signals and other signals through the construction of a frequency conversion harmonic and colored noise filter with excellent performance, and can provide ideas for more chatter monitoring methods.

[0035] Further, the present application performs chatter recognition once every N data points, the interval time of chatter recognition is short, and the algorithm has small computational complexity, which is sufficient to complete recognition during sampling and meets the requirements of online real-time monitoring. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 Fig. 1 is a flowchart of a high-speed milling chatter monitoring method based on interval frequency information entropy according to the present application;

[0037] Figure 2 Fig. 2 is a schematic diagram of a milling chatter monitoring system;

[0038] Figure 3 Fig. 3 is a time-domain signal diagram of simulated milling;

[0039] Figure 4 Fig. 4 is a frequency spectrum diagram of simulated signals, wherein (a) is a frequency spectrum diagram of simulated signals in a stable state, and (b) is a frequency spectrum diagram of simulated signals in a chatter state;

[0040] Figure 5 Fig. 5 is a frequency spectrum diagram of filtered simulated signals, wherein (a) is a frequency spectrum diagram of filtered simulated signals in a stable state, and (b) is a frequency spectrum diagram of filtered simulated signals in a chatter state;

[0041] Figure 6 Fig. 6 is an interval frequency distribution histogram of simulated signals, wherein (a) is an interval frequency distribution histogram of simulated signals in a stable state, and (b) is an interval frequency distribution histogram of simulated signals in a chatter state;

[0042] Figure 7 The interval frequency information entropy index result of the analog signal.

[0043] Figure 2 In the figure, 1 is a main shaft, 2 is a tool holder, 3 is a milling cutter, 4 is a workpiece, 5 is a three-way acceleration sensor, 6 is a signal acquisition card, and 7 is a computer. DETAILED DESCRIPTION

[0044] The application will be further described in detail below in combination with the drawings and specific embodiments.

[0045] The high-speed milling chatter monitoring and basic chatter frequency estimation method based on the interval frequency information entropy of the application is shown in the figure. Figure 1 The figure shows the main flow of the high-speed milling chatter monitoring and basic chatter frequency estimation method based on the interval frequency information entropy of the application.

[0046] The specific steps are described by using an analog simulation signal; the time domain graph of the analog signal is shown in the figure. Figure 3 The figure is an analog of an experimental signal with a rotating speed of 6000 rpm and a sampling frequency of 8192 Hz. The first 0.5 s is a stable milling signal s1, and the last 0.5 s adds a chatter component s2. It can be expressed as:

[0047]

[0048] s1 and s2 can be expressed as:

[0049] s1 = ∑a i sin(2πif sp t)

[0050] s2 = ∑b i sin(2πf chatter，i t)

[0051] The specific frequency and amplitude parameters are shown in Table 1.

[0052] Table 1 Analog signal parameters

[0053]

[0054] In order to determine the signal subspace order required by the ESPRIT method, the order determination method based on the single-order signal energy ratio proposed in this paper is first described.

[0055] The time domain sampling signal with a length of N is constructed into an L-row M-column Hankel matrix X, and singular value decomposition is performed on it: X = LΣU T Then L and U are L-dimensional left singular matrices and M-dimensional right singular matrices, respectively, and Σ is an L×M-dimensional diagonal matrix arranged in descending order of singular values, and each signal frequency corresponds to two adjacent singular values σ 2i-1 ,σ 2iThe size of the singular value reflects the signal energy.

[0056] The present application proposes a single-stage signal energy ratio index method to determine the signal order. The amplitude A i The specific relationship between the adjacent two singular values σ 2i-1 And σ 2i Can be approximated as:

[0057]

[0058] The energy ratio of each order signal is:

[0059]

[0060] Where i = 1, 2, 3…M / 2. When R E Is less than the threshold value, it is considered that the signal of this order, i.e. the Pth signal, belongs to noise, i.e. the signal enters the noise subspace from the signal subspace. In the present application, the threshold value can be 0.01, which can be adjusted according to the specific situation in actual application.

[0061] The signal order P obtained based on the single-stage signal energy ratio can be estimated by the ESPRIT method to obtain the frequency domain parameters of the main components in the time domain signal, i.e. the frequency and amplitude of multiple sinusoidal signals.

[0062] The frequency spectrum obtained by the SOER-ESPRIT method and the FFT method respectively in two states of the analog signal is shown in Figure 4 From the figure, it can be seen that the frequency domain parameters obtained by the SOER-ESPRIT method, whether the frequency or the amplitude, are closer to the actual value than the results obtained by the FFT method, which can prove that the parameter estimation method used in the present application is feasible, reliable and has advantages.

[0063] The specific steps of the high-speed milling chatter monitoring method based on interval frequency information entropy are as follows:

[0064] Step 1, signal acquisition:

[0065] The milling monitoring system is shown in Figure 2 The milling cutter 3 is clamped and installed on the spindle 1 by the tool holder 2, and the three-axis acceleration signal sensor 5 is installed at one end of the spindle 1 close to the milling cutter 3. The three-axis acceleration signal sensor 5, the data acquisition card 6 and the computer 7 together realize signal monitoring.

[0066] The three-axis acceleration signals collected in real time are selected as the chatter monitoring signals, and every time N new data points are collected, they are taken as a signal segment for chatter recognition. Here, N = 512 is selected.

[0067] Step 2, construct matrix filter

[0068] The first 0.5s of the analog signal is a stable cutting state, which can be regarded as an idle signal, and a filter is constructed. The steps of constructing a matrix filter are as follows:

[0069] 1) First, the spindle rotation frequency f is obtained according to the spindle speed of milling sr = 100 Hz, and the rotation frequency vector f is composed of the spindle rotation frequency and its multiples r = [f sr , 2f sr , …, mf sr ], and a preliminary matrix filter is established according to f r to filter out the rotation frequency and its multiples in the analog signal; mf sr is not greater than the Nyquist frequency (i.e. half of the sampling frequency);

[0070] 2) The frequency vector f n of the main components of the signal filtered in the previous step is searched by the SOER-ESPRIT method, and the final matrix filter capable of filtering out the signal rotation frequency harmonics and colored noise is constructed in combination with f r , which is represented as an N-row and N-column matrix F filter .

[0071] Step 3, filtering the signal and estimating the remaining signal parameters

[0072] The time-domain signal with a length of N is denoted as a column vector x = [x1, x2, …, x N ] T , and the filter F filter obtained in step 2 is multiplied by the time-domain signal x, so that the harmonic and colored noise components in the output signal are filtered out.

[0073] The filtered signal obtained in the previous step is estimated by the SOER-ESPRIT method, and the obtained multiple frequencies and corresponding amplitudes are saved as the remaining signal frequency vector f filtered = [f1, f2, f3, …] and A filtered = [a1, a2, a3, …], respectively.

[0074] The frequency domain parameters of the signals in the stable milling and chatter states are shown in Figure 5 , respectively. Figure 5 (a) is the frequency spectrum of the filtered signal in the stable milling state, and the SOER-ESPRIT method estimates several noise frequencies with very small amplitudes, Figure 5 (b) is the frequency spectrum of the filtered signal in the chatter milling state, and the SOER-ESPRIT method estimates three main chatter signals and several weak noise frequencies. The effectiveness of the filtering method and the SOER-ESPRIT method is verified.

[0075] Step 4, construct the interval frequency distribution histogram

[0076] Take the remainder of the remaining signal frequency vector f filtered = [f1, f2, f3, …] obtained in the previous step with respect to the fundamental rotational frequency of the main axis, and obtain the remainder vector Δf = mod(f filtered , f sr ) = [Δf1, Δf2, Δf3…]; then the interval frequency between the chatter frequency and the multiple frequency of the main axis rotation is:

[0077]

[0078] where l is 1, 2, 3…, the distribution range of the interval frequency is (0, f sr / 2], and it is evenly divided into n groups according to the frequency. Then the bandwidth of each group is Δf = f sr / 2n.[[ID=​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0087] Step 6, obtaining the base dither frequency

[0088] When the signal is determined to be in the dither state, the dither frequency expression f chatter = | kf sr ± f c |, k = 1, 2, 3…, it can be known that the interval frequency with the maximum distribution probability in the interval frequency histogram is the base dither frequency f c .

Claims

1. A high speed milling chatter monitoring and base chatter frequency estimation method, characterized by, The method comprises the following steps: S1, collecting vibration signals in the spindle milling process in real time, and performing chatter detection every time interval t; S2, intercepting the spindle idle signal at the beginning of milling, and constructing a matrix filter capable of filtering rotating base frequency harmonics and colored background noise according to the signal, filtering the subsequent vibration signals through the filter to obtain a residual signal without rotating frequency harmonics and colored noise; S3, estimating the frequency domain parameters of the time domain signal by using the parameter estimation method based on the rotation invariance, dividing the signal subspace size by using the single order signal energy ratio index, and obtaining the frequency vector and amplitude vector of the main component of the residual signal obtained in S2; the signal subspace order estimation method based on the rotation invariance parameter estimation of the single order signal energy ratio is as follows: constructing a Hankel matrix with L rows and M columns by using the time domain signal, wherein L > M and M is an even number; performing singular value decomposition on the Hankel matrix to obtain M singular values ; dividing the original time domain signal into M / 2 order sinusoidal signals, and the amplitude A i of each order signal is ; and the single order signal energy ratio is: When If the current step signal is less than the threshold value, it is considered to belong to noise, i.e. the signal enters the noise subspace from the signal subspace i =1,2,3…M / 2; S4, according to the distribution characteristics of the constant frequency difference between the milling chatter frequency and the rotating frequency harmonics, constructing an interval frequency, and converting the frequency vector and amplitude vector obtained in S3 into an interval frequency distribution histogram; S5, taking the information entropy of the interval frequency distribution histogram as a chatter monitoring index to monitor early weak milling chatter signals; S6, when chatter occurs, the height of the square column corresponding to the chatter base frequency in the interval frequency distribution histogram is obviously higher than that of other square columns, and the base chatter frequency is obtained accordingly.

2. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 1, characterized in that, In S1, an acceleration sensor is used to measure the vibration signal, and a contact type installation is fixed on the spindle shell near the tool shank.

3. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 1, characterized in that, In S1, the long continuous vibration signal is divided into short signal frames, wherein the signal frame length is determined according to the sampling frequency f s N = t f s sampling points are collected, f s the sampling frequency.

4. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 1, characterized in that, In S2, the specific steps for constructing the matrix filter according to the spindle speed and the colored noise are as follows: Firstly, the spindle rotation frequency is obtained according to the spindle speed Then, the rotation frequency vector is composed of the spindle rotation frequency and its multiple frequencies According to f r The matrix filter is established to filter the rotation frequency and its multiple frequencies in the idle signal; Not greater than the Nyquist frequency, that is, one-half of the sampling frequency The remaining signal is searched for the frequency vector of the main component of the signal after the previous filtering step using a parameter estimation method based on the energy ratio of the single order of rotation invariance f n If the background noise is colored, i.e. has a frequency, then all the frequency vectors to be filtered out are f filter = [ f r , f n ] from which the complete matrix filter is constructed.

5. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 1, characterized by, The distribution characteristic of constant frequency difference between the milling chatter frequency and the rotation frequency harmonic is that, a dynamic model is established for the formation process of the regenerative chatter, according to the Floquet theory of time-delay differential equation, the chatter frequencies of Hopf bifurcation and period-doubling bifurcation are obtained, and the frequencies have constant frequency interval relationship with the multiple frequency of the spindle speed, that is, the chatter frequency is expressed as , f c The interval frequency is constructed to reflect the distribution characteristic of the chatter frequency.

6. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 1, characterized in that, In step S4, the steps for obtaining the interval frequency of the chatter signal are as follows: The plurality of frequency component vectors of the main components of the filtered signal obtained according to step S3 are: ; The above frequency is divided by the spindle rotation frequency to obtain a remainder vector ; The interval frequency of the chatter frequency from the multiple frequency of the spindle rotation frequency is: , l is 1, 2, 3, … 7. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 6, characterized in that, In S4, the specific steps for converting the chatter signal parameters into an interval frequency distribution histogram are as follows: The interval frequency distribution range is (0, f sr / 2] is uniformly divided into n sub-frequency bands, that is, the interval frequency and the corresponding amplitude are divided into n groups according to the frequency, and the frequency bandwidth of each group is ; with the midpoint frequency of each group representing the original interval frequency; the sum of the normalized amplitudes corresponding to all interval frequencies in a group is the distribution weight, i.e. the distribution probability ; wherein, is a very small number added to the sum of the normalized amplitudes of each group to avoid a group having a probability of 0; a histogram of the interval frequency distribution is plotted with the midpoint frequency of each group as the abscissa and the distribution probability as the ordinate.

8. A high speed milling chatter monitoring and underlying chatter frequency estimation method according to claim 7, characterized in that, In S5, according to the interval frequency distribution histogram, a normalized interval frequency information entropy is constructed as a chatter monitoring index, and the calculation formula is as follows: wherein n is the number of horizontal grouping of the histogram, is the distribution probability corresponding to each group, i.e. the vertical coordinate of the histogram; when chatter occurs, the residual signal obtained by S2 is mainly the chatter signal, the interval frequency distribution is concentrated, and the information entropy value is relatively small; when no chatter occurs, the residual signal obtained by S2 is mainly white noise signal, the interval frequency distribution is chaotic, and the information entropy value is relatively large.

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