CN104390697A - C0 complexity and correlation coefficient-based milling chatter detection method - Google Patents

Abstract

The invention discloses a C0 complexity and correlation coefficient-based milling chatter detection method. The C0 complexity and correlation coefficient-based milling chatter detection method includes the following steps that: state information of a milling process is obtained through a vibration acceleration sensor; obtained signals are preprocessed through using a comb filter, so that periodic components can be filtered out; the complexity of residual signals is calculated through utilizing C0 complexity indexes, so that the degree of nonlinearity of chatter can be reflected; and the correlation coefficient of original signals and filtered signals is calculated, and therefore, the proportion of chatter components in the signals can be reflected, and chatter degree in the machining process can be described. Compared with a traditional chatter detection method, and according to the C0 complexity and correlation coefficient-based milling chatter detection method of the invention, characteristic information reflecting chatter and characteristic information irrelevant to chatter are separated out from each other, and various kinds of indexes are fused, and physical characteristics of milling chatter can be essentially characterized. With the C0 complexity and correlation coefficient-based milling chatter detection method adopted, the sensitivity, accuracy and reliability of chatter detection can be effectively improved, and misdiagnosis rate and missed diagnosis rate can be decreased.

Description

A kind of based on C 0the milling parameter detection method of complexity and related coefficient

Technical field

The present invention relates to a kind of machining Condition Monitoring Technology, particularly a kind of detection method of high-speed milling machine milling parameter.

Background technology

Milling technology has the advantages such as high efficiency, high manufacturing accuracy and low processing cost, is widely used in the manufacture field such as Aeronautics and Astronautics, mould, automobile.Play the advantage of advanced manufacturing technology, depend on the ability of Types of Abnormal Vibration Appearances in Milling Processes (as cutting-vibration) being carried out to prediction and control to a great extent.In milling process, because machined parameters is selected unreasonable, often make to produce violent vibration between cutter and workpiece, cause the generation of flutter.Flutter is autovibration strong between cutter and workpiece in metal cutting process, the generation of flutter not only makes workpiece surface quality and dimensional accuracy reduce, machine part premature fatigue also can be caused to destroy, the security of part, reliability and intensity are declined, shorten cutter life, the noise energy stimulation applications workman that flutter simultaneously produces, reduces work efficiency.How rationally, monitor high-speed milling machine milling state, avoid the generation of flutter, thus ensure that machining precision and working (machining) efficiency are one of key problems to be solved by this invention.

Both at home and abroad the research of milling parameter state-detection is paid much attention to, (the Kuljanic such as gondola E.Kuljanic, E., M.Sortino and G.Totis, Multisensor approaches for chatterdetection in milling.Journal of Sound and Vibration, 2008.312 (4): 672--693.) based on the intensity of periodic component in the coefficient of autocorrelation detection signal of vibration acceleration signal, thus chatter state is judged; (the Hynynen such as the Katja M.Hynynen of Finland, K.M., et al., ChatterDetection in Turning Processes Using Coherence of Acceleration and AudioSignals.Journal of Manufacturing Science and Engineering, 2014) coherence function based on acceleration signal in process and voice signal detects flutter.(the Wu Shi such as the Wu Shi of Harbin University of Science and Technology, Liu Xianli and Xiao Fei, vibration nonlinearity token test in milling parameter process. vibration-testing and diagnosis, 2012, (06), 935-940) nonlinear characteristic of flutter is detected based on the nonlinear indicator such as fractal dimension, maximum Lyapunov exponent, approximate entropy.Application number be 201310113873.9 Chinese invention patent disclose a kind of grinding trembling Forecasting Methodology based on maximum informational entropy and divergence, its feature is accurately to be estimated by the probability density distribution of Maximum Entropy Principle Method to vibration signal, then with the probability density distribution of initial normal condition for benchmark, by the change of divergence, current machining state is judged.Application number be 201410035719.9 Chinese invention patent disclose a kind of flutter on-line monitoring method of machining equipment, its feature is to carry out HHT time frequency analysis to vibration signal, by carrying out to time-frequency spectrum the vibrational state that statistical model analysis obtains characteristic parameter decision-making system.

Find from existing searching document, current conventional flutter detection method generally lacks rationally effective pre-service in early stage, fails to open flutter composition with the component separating that flutter has nothing to do, and the extraction of flutter index is also is mostly based on simple statistical model parameter.Use traditional flutter detection method to detect flutter and there are following two aspect problems: the foundation of 1) traditional flutter Testing index is not completely based on the signal content of reflection flutter, thus can by the composition influence irrelevant with flutter, the index simultaneously set up mostly has been dimension index, responsive to working conditions change; 2) existing nonlinear indicator needs to carry out phase space reconfiguration to signal as arrangement entropy, approximate entropy, Li Yapunuo index etc., calculates consuming time and robustness is poor, and during phase space reconfiguration, the selection of Embedded dimensions is very large to Influence on test result in addition.

C ₀complexity is as a kind of outstanding nonlinear indicator, calculated amount is little and robustness is excellent, be applied to EEG signals (Shen Enhua. the analysis of complexity [D] of brain electricity. Fudan University, 2005) and Traffic flow systems complexity analyzing (Zhang Yong, Guan Wei. based on combination entropy and C ₀the Complexity Measure of Traffic Flow [J] of complexity. computer engineering and application, 2010,15:22-24:33) in.Can there is significant change in the constituent of signal in flutter evolutionary process, and the nonlinear characteristic of flutter simultaneously also will change.It is incorporated in the non-linear detection of flutter by the present invention first, by analyzing formation and the nonlinear degree of signal content in milling process, and then structure flutter index, the detection for milling parameter provides new approach.

Summary of the invention

The object of this invention is to provide a kind of based on C ₀the milling parameter detection method of complexity and related coefficient.

For reaching above object, the present invention takes following technical scheme to be achieved:

A kind of based on C ₀the milling parameter detection method of complexity and related coefficient, is characterized in that, comprises following step:

(1) collection signal

Gathered the status information in milling process by the vibration acceleration sensor being arranged on high-speed main spindle end, the flutter acceleration signal of acquisition be expressed as X=[x (1), x (2) ..., x (n)], n represents signal length;

(2) comb filtering is carried out to signal

By turn frequency, milling frequency and harmonic components thereof in comb filter filtered signal, retain vibrating signal place composition, thus separate the characteristic information of reflection flutter with the characteristic information that flutter has nothing to do, wherein, the transport function of comb filter is:

wherein N is filter order, is integer, f _sfor sample frequency, f _ofor wanting the frequency of filtering, Ω is the speed of mainshaft, and a is the constant of 0 ~ 1;

(3) C ₀complexity index calculates

C is carried out to the acceleration signal after comb filtering ₀complicated dynamic behaviour, C ₀complexity index is:

$C_0\left(r\right)=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{|y\left(k\right)-\tilde{y}\left(k\right)|}^2}{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{\left|y\left(k\right)\right|}^2}$

Using this index as flutter level index, the nonlinear degree of reflection flutter, C ₀the variation range of complexity index is [0,1];

(4) related coefficient index calculate

Calculating comb filtering post-acceleration signal Y=[y (1), y (2) ..., y (n)] and original acceleration signal X=[x (1), x (2) ..., x (n)] related coefficient:

$\mathrm{\ρ}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\sqrt{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2}}$

Wherein $\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}x\left(i\right),$ $\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}y\left(i\right),$ N is signal length;

Using this index as flutter level index, with the proportion of flutter composition in quantitative response original signal, the variation range of related coefficient index is [-1,1], the degree of correlation of reflection Two Variables;

(5) judgement of chatter state

When a, steadily milling, in acceleration signal, principal ingredient is for turning frequency, milling frequency and harmonic wave thereof, and the signal principal ingredient through these compositions of comb filtering filtering is noise, the C calculated ₀the value of complexity is close to 1, and related coefficient is close to 0;

When b, flutter, the principal ingredient of acceleration signal is flutter composition, and the signal principal ingredient after comb filtering is also flutter composition, the C calculated ₀the value of complexity is close to 0, and related coefficient is close to 1.

The present invention utilizes based on C ₀the milling parameter detection method of complexity and related coefficient, has the following significant advantage being different from classic method:

1, by carrying out comb filtering to original signal, the characteristic information irrelevant with flutter being separated, extracts effective flutter composition and set up index, improve susceptibility and the reliability of flutter detection.

2, in flutter evolutionary process, based on C ₀the nonlinear degree of complexity index reflection flutter, robustness is good, and calculated amount is little; Based on the proportion of related coefficient reflection flutter composition in original signal, accuracy is good, highly sensitive.The index set up is dimensionless index, insensitive to operating mode, and can reflect the essential physical characteristics of flutter.

The inventive method is compared to traditional flutter detection method, separate the characteristic information of reflection flutter with the characteristic information that flutter has nothing to do, merge the physical characteristics that many indexes inherently characterizes milling parameter, the susceptibility that effective raising flutter detects, accuracy and reliability, reduce misdiagnosis rate and rate of missed diagnosis.

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram.

Fig. 2 is the amplitude-frequency response of comb filter in the inventive method.

Fig. 3 is the time-domain diagram (b) of signal after original acceleration signal time-domain diagram (a) under normal milling state and comb filtering.Find that the amplitude of acceleration signal is less, the signal after comb filtering is mainly noise contribution, there is larger difference with original signal time domain waveform.Abscissa representing time in figure, unit is s; Ordinate represents vibration signal amplitude, and unit is m/s ².

Fig. 4 is the spectrogram (b) of signal after original acceleration signal spectrogram (a) under normal milling state and comb filtering.Find that the amplitude spectrum energy of acceleration signal mainly concentrates on to turn on frequency, milling frequency and harmonic components thereof, the signal spectrum power dissipation after comb filtering is in each frequency range.In figure, horizontal ordinate represents frequency, and unit is Hz; Ordinate represents vibration signal amplitude, and unit is m/s ².

Fig. 5 is the time-domain diagram (b) of signal after original acceleration signal time-domain diagram (a) under slight flutter milling state and comb filtering.Find that the amplitude of acceleration signal is compared plateau and increased, the signal after comb filtering has certain similarity.Abscissa representing time in figure, unit is s; Ordinate represents vibration signal amplitude, and unit is m/s ².

Fig. 6 is the spectrogram (b) of signal after original acceleration signal spectrogram (a) under slight flutter milling state and comb filtering.Find that the amplitude spectrum energy of acceleration signal mainly concentrates on to turn on frequency, milling frequency and harmonic components thereof, the new flutter frequency produced, the signal spectrum energy after comb filtering mainly concentrates on flutter frequency.In figure, horizontal ordinate represents frequency, and unit is Hz; Ordinate represents vibration signal amplitude, and unit is m/s ².

Fig. 7 is the time-domain diagram (b) of signal after original acceleration signal time-domain diagram (a) under violent flutter milling state and comb filtering.Find that the amplitude of acceleration signal sharply increases, the signal waveform after comb filtering and original signal are substantially identical.Abscissa representing time in figure, unit is s; Ordinate represents vibration signal amplitude, and unit is m/s ².

Fig. 8 is the spectrogram (b) of signal after original acceleration signal spectrogram (a) under violent flutter milling state and comb filtering.Find that the amplitude spectrum energy of acceleration signal mainly concentrates on flutter frequency, the signal spectrum energy after comb filtering also concentrates on flutter frequency.In figure, horizontal ordinate represents frequency, and unit is Hz; Ordinate represents vibration signal amplitude, and unit is m/s ².

In Fig. 3 ~ Fig. 8: S8500: the speed of mainshaft [r/min]; F1500: feed rate [mm/min]; A (1,3,5): axial cutting-in [mm].

Embodiment

Below in conjunction with the drawings and the specific embodiments, the present invention is described in further detail.

With reference to figure 1, the present invention is based on C ₀the milling parameter detection method of complexity and related coefficient comprises the steps:

1) acquisition of signal:

The vibration information in milling process is gathered by the vibration acceleration sensor (sensitivity is 10.09mv/g) being arranged in high-speed main spindle end, obtain signal be expressed as X=[x (1), x (2) ... x (n)], n represents signal length.

2) comb filtering of signal:

The transport function of comb filter system is wherein N is filter order, (N is integer), f _sfor sample frequency (Hz), for wanting the frequency (Hz) of filtering, Ω is the speed of mainshaft (r/min), a is the constant of 0 ~ 1.When a increases, filter frequency plateau, little on the impact of other frequency signals, but filter effect is deteriorated; When a reduces, filter frequency curve is uneven, large on the impact of other frequency signals, but filter effect improves.

To the acceleration signal X=gathered in Milling Processes [x (1), x (2),, x (n)], by turn frequency, milling frequency and harmonic components thereof in comb filter filtered signal, thus separate vibrating signal composition with the cyclic component that flutter has nothing to do, filtered signal be Y=[y (1), y (2) ... y (n)], n represents signal length.

3) C ₀complexity index calculates:

C ₀the variation range of complexity is [0,1], and describe the random degree size of time series, signal random element is more, C ₀the value of complexity is larger.C is carried out to the acceleration signal after comb filtering ₀complicated dynamic behaviour, can the nonlinear degree of quantitative response flutter.

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

$F_n\left(j\right)=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}y\left(k\right)W_n^{-\mathrm{kj}},j=\mathrm{1,2},...,n$

F _nj () represents its Fourier transform sequence, wherein represent imaginary unit.

If { F _n(j), j=1,2 ..., the mean square value of n} is introduce parameter r, retain and exceed mean square value r frequency spectrum doubly, and remainder is set to zero, that is:

Wherein r (r>1) is a given normal number, in actual applications parameter r be taken as 5 ~ 10 comparatively suitable.Right do Fourier inverse transformation

$\tilde{y}\left(k\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{F}_n\left(j\right)W_n^{\mathrm{kj}},k=\mathrm{1,2},...,n$

Definition C ₀complexity index $C_0\left(r\right)=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{|y\left(k\right)-\tilde{y}\left(k\right)|}^2}{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{\left|y\left(k\right)\right|}^2}$

4) calculating of related coefficient index:

The variation range of related coefficient index is [-1,1], the degree of correlation of reflection Two Variables.Calculate the related coefficient of comb filtering post-acceleration signal and original signal, using this index as flutter level index, can the proportion of flutter composition in quantitative response original signal.

Note original acceleration signal be X=[x (1), x (2) ..., x (n)], comb filtering post-acceleration signal be Y=[y (1), y (2) ..., y (n)].The related coefficient of both calculating

$\mathrm{\ρ}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\sqrt{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2}},$

Wherein $\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}x\left(i\right),$ $\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}y\left(i\right),$ N is signal length.

5) judgement of chatter state:

Acceleration signal in Milling Processes is made up of three parts: turn frequency, milling frequency and harmonic components thereof, flutter composition, noise.During steady milling, in acceleration signal, principal ingredient is for turning frequency, milling frequency and harmonic wave thereof, and the signal principal ingredient through these compositions of comb filtering filtering is noise, the C calculated ₀the value of complexity is very large, and related coefficient is very little; During flutter, the principal ingredient of acceleration signal is flutter composition, and the signal principal ingredient after comb filtering is also flutter composition, the C calculated ₀the value of complexity is close to 0, and related coefficient is close to 1.

The validity of the present invention in engineer applied is verified below by way of an instantiation.

Status monitoring is carried out to certain 7050 aerolite Milling Processes, sample frequency 25600Hz, cutter is the carbide end mill of 2 swords, speed of mainshaft 8500r/min, feed rate 1500mm/min, be followed successively by 1mm by the axial milling depth adjusting milling cutter, 3mm, 5mm tri-kinds of operating modes, milling process be experienced by steadily, slight flutter, violent flutter three phases, Milling Process parameter is as shown in table 1.

After acceleration signal under 3 kinds of milling states and comb filtering, the time-domain diagram of signal and spectrogram are respectively see Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8.

Table 1 Milling Process parameter

Find along with milling process develops into violent chatter state by plateau from figure, the amplitude of time domain plethysmographic signal constantly increases, after original signal and comb filtering, the similarity of signal increases, reflect the enhancing along with flutter degree, flutter composition proportion in original signal constantly increases, and the related coefficient of the two moves closer in 1; From frequency spectrum, find the enhancing of the spectrum energy of comb filtering signal with flutter degree simultaneously, concentrate on flutter frequency place gradually, illustrate that filtered signal becomes periodic sequence from random series, complexity reduces, C ₀the value of complexity reduces close to 0.

In this example, to the acceleration signal X=gathered in Milling Processes [x (1), x (2), x (n)], by turn frequency 141.7Hz, milling frequency 283.3Hz and harmonic components thereof in comb filter filtered signal, from

Separate vibrating signal composition with the cyclic component that flutter has nothing to do, filtered signal is:

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

To filtered burst Y={y (k), k=1,2 ..., n} carries out Fourier conversion:

$F_n\left(j\right)=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}y\left(k\right)W_n^{-\mathrm{kj}},j=\mathrm{1,2},...,n$

Wherein represent imaginary unit.

If { F _n(j), j=1,2 ..., the mean square value of n} is introduce parameter r=5, retain and exceed mean square value r frequency spectrum doubly, and remainder is set to zero, that is:

Right do Fourier inverse transformation

$\tilde{y}\left(k\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{F}_n\left(j\right)W_n^{\mathrm{kj}},k=\mathrm{1,2},...,n$

Calculate C ₀complexity index $C_0\left(r\right)=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{|y\left(k\right)-\tilde{y}\left(k\right)|}^2}{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{\left|y\left(k\right)\right|}^2}$

C ₀more close to 0, illustrate that the nonlinear degree of flutter is less, in signal, periodic component is more.

Calculating original acceleration signal X=[x (1), x (2) ..., x (n)] and comb filtering post-acceleration signal Y=[y (1), y (2) ..., y (n)] related coefficient:

$\mathrm{\ρ}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\sqrt{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2}}$

Wherein $\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}x\left(i\right),$ $\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}y\left(i\right),$ N is signal length;

Correlation coefficient ρ, more close to 1, illustrates that the flutter composition proportion in signal is larger.

The judged result of chatter state is as shown in table 2, consistent with the virtual condition in Milling Processes, demonstrates the validity of the method for the invention.

The result of determination of certain aerolite milling state of table 2

Claims (1)

1. one kind based on C ₀the milling parameter detection method of complexity and related coefficient, is characterized in that, comprises following step:

(1) collection signal

Gathered the status information in milling process by the vibration acceleration sensor being arranged on high-speed main spindle end, the flutter acceleration signal of acquisition be expressed as X=[x (1), x (2) ..., x (n)], n represents signal length;

(2) comb filtering is carried out to signal

By turn frequency, milling frequency and harmonic components thereof in comb filter filtered signal, retain vibrating signal place composition, thus separate the characteristic information of reflection flutter with the characteristic information that flutter has nothing to do, wherein, the transport function of comb filter is:

wherein N is filter order, is integer, f _sfor sample frequency, f _ofor wanting the frequency of filtering, Ω is the speed of mainshaft, and a is the constant of 0 ~ 1;

(3) C ₀complexity index calculates

C is carried out to the acceleration signal after comb filtering ₀complicated dynamic behaviour, C ₀complexity index is:

$C_0\left(r\right)=\frac{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{|y\left(k\right)-\tilde{y}\left(k\right)|}^2}{\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{\left|y\left(k\right)\right|}^2}$

Using this index as flutter level index, the nonlinear degree of reflection flutter, C ₀the variation range of complexity index is [0,1];

(4) related coefficient index calculate

Calculating comb filtering post-acceleration signal Y=[y (1), y (2) ..., y (n)] and original acceleration signal X=[x (1), x (2) ..., x (n)] related coefficient:

$\mathrm{\ρ}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\sqrt{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2}}$

Wherein $\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}x\left(i\right),\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}y\left(i\right),$ N is signal length;

Using this index as flutter level index, with the proportion of flutter composition in quantitative response original signal, the variation range of related coefficient index is [-1,1], the degree of correlation of reflection Two Variables;

(5) judgement of chatter state

When a, steadily milling, in acceleration signal, principal ingredient is for turning frequency, milling frequency and harmonic wave thereof, and the signal principal ingredient through these compositions of comb filtering filtering is noise, the C calculated ₀the value of complexity is close to 1, and related coefficient is close to 0;

When b, flutter, the principal ingredient of acceleration signal is flutter composition, and the signal principal ingredient after comb filtering is also flutter composition, the C calculated ₀the value of complexity is close to 0, and related coefficient is close to 1.