CN104390697B - A Milling Chatter Detection Method Based on C0 Complexity and Correlation Coefficient - Google Patents

Abstract

C is based on the invention discloses one kind₀Complexity and the milling parameter detection method of coefficient correlation, the status information of milling process is obtained by vibration acceleration sensor；The signal for being obtained is pre-processed using comb filter, filters cyclic component；Recycle C₀Complexity index calculates the complexity of residual signal, reflects the nonlinear degree of flutter；Then the coefficient correlation of primary signal and filtered signal is calculated, the proportion of flutter composition, portrays the flutter degree in process in reflection signal.The method is compared to traditional flutter detection method, the characteristic information and the characteristic information unrelated with flutter of reflection flutter are separated, fusion many indexes inherently characterize the physical characteristic of milling parameter, sensitiveness, accuracy and the reliability of flutter detection are effectively improved, misdiagnosis rate and rate of missed diagnosis is reduced.

Description

A Milling Chatter Detection Method Based on C0 Complexity and Correlation Coefficient

technical field

The invention relates to a mechanical processing state monitoring technology, in particular to a detection method for milling chatter of a high-speed milling machine.

Background technique

Milling technology has the advantages of high production efficiency, high processing accuracy and low processing cost, and is widely used in aviation, aerospace, mold, automobile and other manufacturing fields. Making full use of the advantages of advanced manufacturing technology largely depends on the ability to predict and control abnormal vibration phenomena (such as cutting chatter) in the milling process. During the milling process, due to the unreasonable selection of processing parameters, severe vibrations often occur between the tool and the workpiece, resulting in chatter. Chatter is a strong self-excited vibration between the tool and the workpiece in the metal cutting process. The occurrence of chatter not only reduces the surface quality and dimensional accuracy of the workpiece, but also causes premature fatigue damage to the machine tool parts, which improves the safety and reliability of the parts. And the strength is reduced, shortening the life of the tool, and the noise generated by chatter can stimulate the operator and reduce work efficiency. How to reasonably and accurately monitor the milling status of the high-speed milling machine to avoid the occurrence of chatter, so as to ensure the machining accuracy and machining efficiency is one of the core problems to be solved by the present invention.

At home and abroad, the research on milling chatter detection is very important. E.Kuljanic et al. (Kuljanic, E., M. Sortino and G.Totis, Multisensor approaches for chatter detection inmilling. Journal of Sound and Vibration, 2008. : 672--693.) Based on the strength of the periodic component in the autocorrelation coefficient detection signal of the vibration acceleration signal, thereby judging the flutter state; Finland's Katja M.Hynynen et al. (Hynynen, K.M., et al., Chatter Detection in Turning Processes Using Coherence of Acceleration and Audio Signals. Journal of Manufacturing Science and Engineering, 2014) detects flutter based on the coherence function of acceleration signals and audio signals during processing. Wu Shi et al. from Harbin University of Science and Technology (Wu Shi, Liu Xianli and Xiao Fei, Vibration nonlinear characteristic test during milling chatter. Vibration test and diagnosis, 2012, (06), 935-940) based on fractal dimension, maximum Lyapunov Non-linear indicators such as exponential and approximate entropy are used to detect the nonlinear characteristics of flutter. The Chinese invention patent with application number 201310113873.9 discloses a grinding chatter prediction method based on maximum information entropy and direction divergence, which is characterized in that the probability density distribution of vibration signals is accurately estimated by the principle of maximum information entropy, and then the initial The probability density distribution of the normal state is used as the benchmark, and the current processing state is judged by the change of the direction divergence. The Chinese invention patent with the application number 201410035719.9 discloses an online chatter monitoring method for mechanical processing equipment, which is characterized in that the vibration signal is analyzed by HHT time-frequency, and the vibration state of the system is determined by the characteristic parameters through the statistical pattern analysis of the time-frequency spectrum .

From the existing search literature, it is found that the currently commonly used chatter detection methods generally lack reasonable and effective pre-processing, fail to separate chatter components from unrelated components, and the extraction of chatter indicators is mostly based on simple Statistics mode parameters. There are two problems in using traditional chatter detection methods to detect chatter: 1) The establishment of traditional chatter detection indicators is not completely based on signal components reflecting chatter, so it will be affected by components that are not related to chatter. Most of the indicators are dimensioned indicators, which are sensitive to changes in working conditions; 2) Existing nonlinear indicators such as permutation entropy, approximate entropy, Lyapunt index, etc. need to reconstruct the phase space of the signal, and the calculation is time-consuming and less robust. In addition, the choice of embedding dimension during phase space reconstruction has a great influence on the result.

As an excellent nonlinear index, C ₀ complexity has a small amount of calculation and excellent robustness, and has been applied to EEG signals (Shen Enhua. Complexity Analysis of EEG [D]. Fudan University, 2005) and traffic flow systems Complexity analysis of (Zhang Yong, Guan Wei. Traffic flow complexity measure based on joint entropy and C ₀ complexity [J]. Computer Engineering and Application, 2010, 15:22-24:33). During the evolution of flutter, the components of the signal will change obviously, and at the same time, the nonlinear characteristics of flutter will also change. The present invention introduces it into the non-linear detection of chatter for the first time, and then constructs the chatter index by analyzing the composition of signal components and the degree of nonlinearity in the milling process, and provides a new way for the detection of milling chatter.

Contents of the invention

The purpose of the present invention is to provide a milling chatter detection method based on C ₀ complexity and correlation coefficient.

To achieve the above object, the present invention is achieved by taking the following technical solutions:

A milling chatter detection method based on C ₀ complexity and correlation coefficient, is characterized in that, comprises the following steps:

(1) Acquisition signal

The status information during milling is collected by the vibration acceleration sensor installed at the end of the high-speed spindle, and the obtained chatter acceleration signal is expressed as X=[x(1),x(2),…,x(n)], n represents the signal length ;

(2) Comb filtering the signal

The comb filter is used to filter the switching frequency, milling frequency and its harmonic components in the signal, and retain the components of the chatter signal, so as to separate the characteristic information reflecting chatter from the feature information that has nothing to do with chatter. Among them, The transfer function of the comb filter is:

Where N is the filter order, which is an integer, f _s is the sampling frequency, f _o is the frequency to be filtered out, Ω is the spindle speed, a is a constant from 0 to 1;

(3) C ₀ complexity index calculation

The C ₀ complexity calculation is performed on the comb-filtered acceleration signal, and the C ₀ complexity index is:

This index is used as the flutter degree index to reflect the non-linear degree of flutter, and the variation range of the C ₀ complexity index is [0,1];

(4) Calculation of correlation coefficient index

Calculate comb-filtered acceleration signal Y=[y(1),y(2),…,y(n)] and original acceleration signal X=[x(1),x(2),…,x(n) ] Correlation coefficient:

in n is the signal length;

This index is used as the flutter degree index to quantitatively reflect the proportion of the flutter component in the original signal, and the variation range of the correlation coefficient index is [-1,1], which reflects the degree of correlation between the two variables;

(5) Determination of flutter state

a. During smooth milling, the main components of the acceleration signal are the rotation frequency, the milling frequency and its harmonics. The main component of the signal after comb filtering these components is noise, and the calculated C ₀ complexity value is close to 1. The correlation coefficient is close to 0;

b. During flutter, the main component of the acceleration signal is the flutter component, and the main component of the signal after comb filtering is also the flutter component. The calculated C ₀ complexity value is close to 0, and the correlation coefficient is close to 1.

The present invention utilizes the milling chatter detection method based on C ₀ complexity and correlation coefficient, has the following remarkable advantage that is different from traditional method:

1. By comb filtering the original signal, the feature information irrelevant to flutter is separated, and effective flutter components are extracted to establish indicators, which improves the sensitivity and reliability of flutter detection.

2. During the flutter evolution process, based on the C ₀ complexity index to reflect the nonlinear degree of flutter, the robustness is good and the calculation amount is small; based on the correlation coefficient to reflect the proportion of flutter components in the original signal, the accuracy is good, high sensitivity. The established index is a dimensionless index, which is not sensitive to working conditions and can reflect the essential physical characteristics of flutter.

Compared with the traditional chatter detection method, the method of the present invention separates the feature information reflecting chatter from the feature information irrelevant to chatter, integrates multiple indexes to characterize the physical characteristics of milling chatter in essence, and effectively improves chatter The sensitivity, accuracy and reliability of vibration detection can be improved, and the misdiagnosis rate and missed diagnosis rate can be reduced.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Fig. 2 is the amplitude-frequency response curve of the comb filter in the method of the present invention.

Fig. 3 is the time-domain diagram (a) of the original acceleration signal and the time-domain diagram (b) of the comb-filtered signal in the normal milling state. It is found that the amplitude of the acceleration signal is small, and the signal after comb filtering is mainly noise components, which are quite different from the original signal time domain waveform. The abscissa in the figure represents the time, the unit is s; the ordinate represents the vibration signal amplitude, the unit is m/s ² .

Fig. 4 is the spectrogram (a) of the original acceleration signal and the spectrogram (b) of the comb-filtered signal in the normal milling state. It is found that the amplitude spectrum energy of the acceleration signal is mainly concentrated in the rotation frequency, milling frequency and its harmonic components, and the spectrum energy of the signal after comb filtering is scattered in each frequency band. In the figure, the abscissa represents the frequency, the unit is Hz; the ordinate represents the vibration signal amplitude, the unit is m/s ² .

Fig. 5 is the time-domain diagram (a) of the original acceleration signal and the time-domain diagram (b) of the comb-filtered signal under the slight chatter milling state. It is found that the amplitude of the acceleration signal increases compared with the steady state, and the signal after comb filtering has a certain similarity. The abscissa in the figure represents the time, the unit is s; the ordinate represents the vibration signal amplitude, the unit is m/s ² .

Fig. 6 is the spectrogram (a) of the original acceleration signal and the spectrogram (b) of the comb-filtered signal in the milling state of slight chatter. It is found that the amplitude spectrum energy of the acceleration signal is mainly concentrated on the rotation frequency, milling frequency and its harmonic components, and the newly generated flutter frequency, and the spectrum energy of the signal after comb filtering is mainly concentrated on the flutter frequency. In the figure, the abscissa represents the frequency, the unit is Hz; the ordinate represents the vibration signal amplitude, the unit is m/s ² .

Fig. 7 is the time-domain diagram (a) of the original acceleration signal and the time-domain diagram (b) of the comb-filtered signal under the severe chatter milling state. It is found that the amplitude of the acceleration signal increases sharply, and the waveform of the signal after comb filtering is basically the same as the original signal. The abscissa in the figure represents the time, the unit is s; the ordinate represents the vibration signal amplitude, the unit is m/s ² .

Fig. 8 is the spectrogram (a) of the original acceleration signal and the spectrogram (b) of the comb-filtered signal under severe chatter milling state. It is found that the amplitude spectrum energy of the acceleration signal is mainly concentrated on the flutter frequency, and the spectrum energy of the signal after comb filtering is also concentrated on the flutter frequency. In the figure, the abscissa represents the frequency, the unit is Hz; the ordinate represents the vibration signal amplitude, the unit is m/s ² .

In Fig. 3 to Fig. 8: S8500: spindle speed [r/min]; F1500: feed rate [mm/min]; a(1, 3, 5): axial depth of cut [mm].

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

With reference to Fig. 1, the milling chatter detection method of the present invention based on C ₀ complexity and correlation coefficient comprises the following steps:

1) Acquisition of signal:

Vibration information during milling is collected through a vibration acceleration sensor (sensitivity of 10.09mv/g) arranged at the end of the high-speed spindle, and the obtained signal is expressed as X=[x(1),x(2),…,x(n)] , n represents the signal length.

2) Comb filtering of the signal:

The transfer function of the comb filter system is where N is the filter order, (N is an integer), f _s is the sampling frequency (Hz), is the frequency to be filtered out (Hz), Ω is the spindle speed (r/min), and a is a constant between 0 and 1. When a increases, the filter frequency response curve is flat, which has little influence on other frequency signals, but the filtering effect becomes worse; when a decreases, the filter frequency response curve is not flat, which has a great influence on other frequency signals, but the filtering effect becomes better.

For the acceleration signal X=[x(1),x(2),…,x(n)] collected during the milling process, the conversion frequency, milling frequency and its harmonic components in the signal are filtered out by a comb filter , so as to separate the flutter signal component from the periodic component irrelevant to flutter, the filtered signal is Y=[y(1),y(2),...,y(n)], n represents the signal length.

3) C ₀ complexity index calculation:

The range of C ₀ complexity is [0,1], which describes the degree of randomness of the time series. The more random components of the signal, the greater the value of C ₀ complexity. Computing the C ₀ complexity of the comb-filtered acceleration signal can quantitatively reflect the nonlinearity of flutter.

Note that Y={y(k),k=1,2,...,n} is a time series of length n,

F _n (j) represents its Fourier transform sequence, where Indicates the imaginary unit.

Let the mean square value of {F _n (j),j=1,2,…,n} be Introduce the parameter r, keep the spectrum that exceeds r times the mean square value, and set the rest to zero, that is:

Among them, r (r>1) is a given normal number, and it is more appropriate to take the parameter r as 5-10 in practical applications. right Do the Fourier inverse transform

Define the C ₀ complexity metric

4) Calculation of correlation coefficient index:

The variation range of the correlation coefficient index is [-1,1], which reflects the degree of correlation between the two variables. Calculate the correlation coefficient between the comb-filtered acceleration signal and the original signal, and use this index as the flutter degree index, which can quantitatively reflect the proportion of the flutter component in the original signal.

Record the original acceleration signal as X=[x(1),x(2),…,x(n)], and the comb-filtered acceleration signal as Y=[y(1),y(2),…,y( n)]. Calculate the correlation coefficient between the two

in n is the signal length.

5) Judgment of flutter state:

The acceleration signal in the milling process consists of three parts: rotation frequency, milling frequency and its harmonic components, flutter components, and noise. During smooth milling, the main components of the acceleration signal are the rotation frequency, the milling frequency and its harmonics. The main component of the signal after comb filtering these components is noise. The calculated C ₀ complexity value is very large, and the correlation coefficient is very large. Small; when fluttering, the main component of the acceleration signal is the fluttering component, and the main component of the signal after comb filtering is also the fluttering component, the calculated _C0 complexity value is close to 0, and the correlation coefficient is close to 1.

The effectiveness of the present invention in engineering application is verified by a specific example below.

Carry out state monitoring on the milling process of a 7050 aviation aluminum alloy, the sampling frequency is 25600Hz, the tool is a 2-blade carbide end mill, the spindle speed is 8500r/min, the feed rate is 1500mm/min, by adjusting the axial milling of the milling cutter The depth is 1mm, 3mm, and 5mm in three working conditions, so that the milling process has experienced three stages of smooth, slight chatter, and severe chatter. The milling parameters are shown in Table 1.

The acceleration signals in the three milling states and the time-domain diagrams and frequency spectrum diagrams of the comb-filtered signals are shown in Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, and Fig. 8, respectively.

Table 1 Milling parameters

It is found from the figure that as the milling process develops from a steady state to a severe chattering state, the amplitude of the time domain waveform of the signal increases continuously, and the similarity between the original signal and the comb-filtered signal increases, which reflects that the degree of chattering The enhancement of the flutter component in the original signal is increasing, and the correlation coefficient between the two is gradually close to 1; at the same time, it is found from the spectrum that the spectrum energy of the comb filter signal gradually concentrates on the flutter frequency as the flutter degree increases. , indicating that the filtered signal changes from a random sequence to a periodic sequence, the complexity is reduced, and the value of C ₀ complexity is reduced close to 0.

In this example, for the acceleration signal X=[x(1),x(2),…,x(n)] collected during the milling process, the frequency of 141.7Hz in the signal is filtered out by a comb filter, and the milling Frequency 283.3Hz and its harmonic components, from

The flutter signal component is separated from the periodic component not related to flutter, and the filtered signal is:

Y=[y(1),y(2),...,y(n)], n represents the signal length;

Perform Fourier transform on the filtered signal sequence Y={y(k),k=1,2,…,n}:

in Indicates the imaginary unit.

Let the mean square value of {F _n (j),j=1,2,…,n} be Introduce the parameter r=5, retain the frequency spectrum exceeding r times the mean square value, and set the rest to zero, namely:

right Do the Fourier inverse transform

Compute the C ₀ complexity metric

The closer C ₀ is to 0, the smaller the non-linearity of flutter and the more periodic components in the signal.

Calculate the original acceleration signal X=[x(1),x(2),…,x(n)] and comb-filtered acceleration signal Y=[y(1),y(2),…,y(n) ] Correlation coefficient:

in n is the signal length;

The closer the correlation coefficient ρ is to 1, the greater the proportion of flutter components in the signal.

The judging result of the flutter state is shown in Table 2, which is consistent with the actual state in the milling process, which verifies the effectiveness of the method of the present invention.

Table 2 Judgment results of the milling state of an aviation aluminum alloy

Claims (1)

1. a milling chatter detection method based on C ₀ complexity and correlation coefficient, is characterized in that, comprises the following steps: (1) Acquisition signal The status information during milling is collected by the vibration acceleration sensor installed at the end of the high-speed spindle, and the obtained chatter acceleration signal is expressed as X=[x(1),x(2),…,x(n)], n represents the signal length ; (2) Comb filtering the signal The comb filter is used to filter the switching frequency, milling frequency and its harmonic components in the signal, and retain the components of the chatter signal, so as to separate the characteristic information reflecting chatter from the feature information that has nothing to do with chatter. Among them, The transfer function of the comb filter is: Where N is the filter order, which is an integer, f _s is the sampling frequency, f _o is the frequency to be filtered out, Ω is the spindle speed, a is a constant from 0 to 1; (3) C ₀ complexity index calculation The C ₀ complexity calculation is performed on the comb-filtered acceleration signal, and the C ₀ complexity index is: ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ This index is used as the flutter degree index to reflect the non-linear degree of flutter, and the variation range of the C ₀ complexity index is [0,1]; (4) Calculation of correlation coefficient index Calculate comb-filtered acceleration signal Y=[y(1),y(2),…,y(n)] and original acceleration signal X=[x(1),x(2),…,x(n) ] Correlation coefficient: $\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}$ in $\stackrel{\&OverBar;}{x}=\frac{1}{\mathrm{no}}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}x\left(i\right),\stackrel{\&OverBar;}{\mathrm{the\; y}}=\frac{1}{\mathrm{no}}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}\mathrm{the\; y}\left(i\right),$ n is the signal length; This index is used as the flutter degree index to quantitatively reflect the proportion of flutter components in the original signal, and the variation range of the correlation coefficient index is [-1,1], which reflects the degree of correlation between the two variables; (5) Determination of flutter state a. During smooth milling, the main components of the acceleration signal are the rotation frequency, the milling frequency and its harmonics. The main component of the signal after comb filtering these components is noise, and the calculated C ₀ complexity value is close to 1. The correlation coefficient is close to 0; b. During flutter, the main component of the acceleration signal is the flutter component, and the main component of the signal after comb filtering is also the flutter component. The calculated C ₀ complexity value is close to 0, and the correlation coefficient is close to 1.