CN106021906A - Cepstrum analysis-based chatter online monitoring method - Google Patents

Abstract

The invention provides a cepstrum analysis-based chatter online monitoring method. An acceleration signal in a vertical milling cutting process is acquired through an acceleration sensor mounted on a spindle of a vertical milling machine and is expressed as X=[x(1), x(2), ..., x(n)], wherein n represents the length of a signal, and the acceleration signal includes a stable-state signal, a transitional-state signal and a chatter-state signal. Based on wavelet packet decomposition and cepstrum analysis methods, the cepstrum analysis-based chatter online monitoring method comprises the steps of firstly, performing wavelet packet decomposition on the acceleration signal obtained in a cutting experiment, reconstructing decomposed frequency band signals, calculating energy of the frequency band signals, and determining a chatter occurrence frequency domain range; and secondly, performing cepstrum analysis on the chatter occurrence frequency band signals, and taking a cepstrum mean square root as a chatter characteristic. Compared with a conventional chatter monitoring method, the cepstrum analysis-based chatter online monitoring method has the advantages that a symptom of cutting chatter can be discovered more early and accurate identification can be realized on the eve of strong chatter to prevent irretrievable damage of strong vibration to workpieces and machine tool parts.

Description

Tremor on-line monitoring method based on cepstrum analysis

Technical field

The present invention relates to machine tooling technical field, particularly relate to a kind of tremor on-line monitoring side based on cepstrum analysis Method.

Background technology

The study mechanism of cutting-vibration can trace back to nineteen forty-six the earliest, in research initial stage, it is believed that tremor is led Negative damping is there is owing to cutting system.Along with deepening continuously of research, find that cutting-vibration is mainly by regeneration and mode coupling Group photo rings and causes, and wherein regeneration effect has become as the main cause that tremor occurs, and usually said tremor many fingers regeneration is quivered Shake.Tremor during End Milling Process can have a strong impact on workpiece surface quality and material removing rate, aggravation tool wear and deterioration Working environment.Occur although major part monitoring chatter system can monitor tremor, but to workpiece and cutter when tremor occurs Tool creates serious damage, accordingly, it would be desirable to monitor tremor feature in advance.Non-linear due to the course of processing causes vibration letter Number frequency content complexity, single Time-Frequency Analysis Method is difficult to obtain reliable tremor feature.

Summary of the invention

The technical problem to be solved in the present invention is: cannot obtain reliable tremor to solve existing monitoring chatter method The problem of feature, the invention provides a kind of tremor on-line monitoring method based on cepstrum analysis and solves the problems referred to above.

The technical solution adopted for the present invention to solve the technical problems is: a kind of tremor based on cepstrum analysis is supervised online Survey method, comprises the following steps:

S1, gather the acceleration in vertical milling working angles by the acceleration transducer that is arranged on the main shaft of vertical knee-type milling machine Signal be expressed as X=[x (1), x (2) ..., x (n)], n represents that signal length, described acceleration signal include that steady statue is believed Number, transitive state signal and chatter state signal；

S2, chatter state signal is carried out WAVELET PACKET DECOMPOSITION, obtain wavelet packet coefficient, then by wavelet packet inverse transformation weight The chatter state signal of each frequency range of structure:

Wherein, c_j0,kFor at yardstick j₀On approximation wavelet coefficients；d_j,kFor at j₀And concrete small echo on following yardstick Coefficient；

S3, the chatter state signal after above-mentioned reconstruct is carried out cepstrum analysis, extract the root-mean-square value of cepstrum amplitude Minima r_minWith maximum r_max；

S4, the described acceleration signal collected is carried out WAVELET PACKET DECOMPOSITION, obtain wavelet packet coefficient, then pass through small echo Bag inverse transformation reconstructs the acceleration signal of each frequency range, then carries out cepstrum analysis, the root-mean-square value of extraction cepstrum amplitude:

$r=\sqrt{\underset{i=1}{\overset{n}{\Σ}}{p}_i^2/n}$

Wherein, p_iFor the i-th discrete cepstrum amplitude of tremor generation frequency band signals, n is that cepstrum is discrete to count；

S5, generalThe on-line monitoring of tremor is carried out as tremor feature, ifIllustrate to enter tremor State.

The invention has the beneficial effects as follows, this tremor on-line monitoring method based on cepstrum analysis is based on WAVELET PACKET DECOMPOSITION With cepstrum analysis method, first, the acceleration signal obtaining cutting experiment carries out discrete wavelet packet decomposition, after reconstruct is decomposed Each frequency band signals, calculate each frequency band signals energy, determine tremor generation frequency domain；Then, to tremor generation frequency band signals Carry out cepstrum analysis, obtain the cepstrum of tremor generation frequency band signals, using cepstrum root-mean-square as tremor feature, with routine Monitoring chatter method compare it and can find the sign of cutting-vibration earlier, realize accurately at the eve that violent tremor occurs Identification, prevent violent vibration from workpiece and machine tool component are caused irremediable damage.

Accompanying drawing explanation

The present invention is further described with embodiment below in conjunction with the accompanying drawings.

Fig. 1 is the wavelet tree structure chart that present invention tremor based on cepstrum analysis on-line monitoring method uses.

Fig. 2 is the signal graph after the wavelet package reconstruction of chatter state signal.

Fig. 3 is the spectrogram of chatter state signal reconstruction signal.

Fig. 4 is the scramble spectrogram of each status signal in acceleration signal.

Fig. 5 is the changing trend diagram of cepstrum accounting coefficient.

Fig. 6 is the schematic diagram that wavelet packet successively decomposes according to wavelet tree.

Detailed description of the invention

Embodiments of the invention are described below in detail, and the example of described embodiment is shown in the drawings, the most from start to finish Same or similar label represents same or similar element or has the element of same or like function.Below with reference to attached The embodiment that figure describes is exemplary, is only used for explaining the present invention, and is not considered as limiting the invention.On the contrary, originally Inventive embodiment includes all changes in the range of the spirit falling into attached claims and intension, revises and be equal to Thing.

In describing the invention, it is to be understood that term " " center ", " longitudinally ", " laterally ", " length ", " width ", " thickness ", " on ", D score, "front", "rear", "left", "right", " vertically ", " level ", " top ", " end " " interior ", " outward ", " axially ", " radially ", the orientation of the instruction such as " circumferential " or position relationship be based on orientation shown in the drawings or position relationship, merely to just In describe the present invention and simplifying describe rather than instruction or the hint device of indication or element must have specific orientation, with Specific azimuth configuration and operation, be therefore not considered as limiting the invention.

Additionally, term " first ", " second " etc. are only used for describing purpose, and it is not intended that indicate or imply relatively important Property.In describing the invention, it should be noted that unless otherwise clearly defined and limited, term " is connected ", " connection " should It is interpreted broadly, connects for example, it may be fixing, it is also possible to be to removably connect, or be integrally connected；Can be that machinery connects Connect, it is also possible to be electrical connection；Can be to be joined directly together, it is also possible to be indirectly connected to by intermediary.Common for this area For technical staff, above-mentioned term concrete meaning in the present invention can be understood with concrete condition.Additionally, in description of the invention In, except as otherwise noted, " multiple " are meant that two or more.

The invention provides a kind of tremor on-line monitoring method based on cepstrum analysis, comprise the following steps:

S1, gather the acceleration in vertical milling working angles by the acceleration transducer that is arranged on the main shaft of vertical knee-type milling machine Signal be expressed as X=[x (1), x (2) ..., x (n)], n represents that signal length, acceleration signal include steady state signal, mistake Cross status signal and chatter state signal；

S2, chatter state signal is carried out WAVELET PACKET DECOMPOSITION, obtains wavelet packet coefficient,

The wave filter that definition is used:

G [n]: low pass filter, can filter the high frequency part of input signal and output low frequency part.

H [n]: high pass filter, contrary with low pass filter, filter frequency component and export high frequency part.

↓ Q: desampling fir filter；

WAVELET PACKET DECOMPOSITION is successively decomposed according to the wavelet tree shown in Fig. 1 and Fig. 6, and WAVELET PACKET DECOMPOSITION is not only to low frequency signal even Continuous decompose, high frequency band signal be also carried out same decomposition:

In framework the 1st layer:

$x_{1,L}\[n\]=\underset{k=0}{\overset{K-1}{\Σ}}x\[2n-k\]g\[k\]$

$x_{1,H}\[n\]=\underset{k=0}{\overset{K-1}{\Σ}}x\[2n-k\]h\[k\]$

In framework the 2nd layer:

$x_{2,L}\[n\]=\underset{k=0}{\overset{K-1}{\Σ}}{x}_{1,L}\[2n-k\]g\[k\]$

$x_{2,H}\[n\]=\underset{k=0}{\overset{K-1}{\Σ}}{x}_{1,L}\[2n-$

Then wavelet packet is passed throughInverse transformation reconstructs quivering of each frequency range Shake status signal:

Wherein, c_j0,kFor at yardstick j₀On approximation wavelet coefficients；d_j,kFor at j₀And concrete small echo on following yardstick Coefficient；

Fig. 2 is the wavelet package reconstruction result of chatter state signal；

Fig. 3 is the frequency spectrum of chatter state signal reconstruction signal；

S3, the chatter state signal after above-mentioned reconstruct is carried out cepstrum analysis, extract the root-mean-square value of cepstrum amplitude Minima r_minWith maximum r_max；

Cepstrum is defined as follows: set the amplitude spectrum density function of time-domain signal x (t) as S_x(f), the scramble of signal x (t) Spectral function is C (τ):

C (τ)={ F^-1[lgS_x(f)]}²

In formula, τ is inverted frequency, and the big person of τ-value is high inverted frequency, represents rapid fluctuations and intensive harmonics on cepstrum；Otherwise, τ-value Little person is low inverted frequency, represents and slowly fluctuates and sparse harmonics, F on cepstrum^-1Represent inverse Fourier transform；

And amplitude cepstrum is:

Due to S_xF () is even function, amplitude cepstrum can be write as C_x(τ)=F [lgS_x(f)]；

The side frequency of vibration signal can be composed a single spectral line being reduced to be easy to observe by cepstrum analysis, can distinguish again vibration The analysis of vibration signal of the complicated processing process in signal source and path, beneficially multisignal source；

S4, the acceleration signal collected is carried out WAVELET PACKET DECOMPOSITION, obtain wavelet packet coefficient, then inverse by wavelet packet Conversion reconstructs the acceleration signal of each frequency range, then carries out cepstrum analysis, and analysis result is as shown in Figure 4, it can be seen that and Steady statue is compared, and the cepstrum amplitude of chatter state signal increases substantially, and the cepstrum amplitude of transitive state vibration signal is situated between In stablizing between chatter state, illustrate to be difficult in time domain and frequency domain the tremor feature of identification, cepstrum only passes through amplitude Just can well distinguish；

Then the root-mean-square value of extraction cepstrum amplitude:

$r=\sqrt{\underset{i=1}{\overset{n}{\Σ}}{p}_i^2/n}$

Wherein, p_iFor the i-th discrete cepstrum amplitude of tremor generation frequency band signals, n is that cepstrum is discrete to count；

S5, generalThe on-line monitoring of tremor is carried out as tremor feature, ifIllustrate to enter tremor State.

In order to verify the effectiveness of tremor feature in this monitoring method, calculate the variation tendency of T, as it is shown in figure 5, surely Surely cutting the stage, tremor feature T overall variation amplitude is little, is maintained at about 16%.Entering transition stage, tremor feature T is opened Begin to be increased rapidly to about 60%, increase to tremor always and occur completely.The cepstrum accounting coefficient in tremor stage about maintains About 95%.More than analyzing discovery, in the different phase of working angles, cepstrum accounting index variation is obvious, is suitable as Tremor feature is to realize the early prediction of tremor.

In the description of this specification, reference term " embodiment ", " some embodiments ", " example ", " specifically show Example " or the description of " some examples " etc. means to combine this embodiment or example describes specific features, structure, material or spy Point is contained at least one embodiment or the example of the present invention.In this manual, to the schematic representation of described term not Necessarily refer to identical embodiment or example.And, the specific features of description, structure, material or feature can be any One or more embodiments or example in combine in an appropriate manner.

With the above-mentioned desirable embodiment according to the present invention for enlightenment, by above-mentioned description, relevant staff is complete Entirely can carry out various change and amendment in the range of without departing from this invention technological thought.The technology of this invention The content that property scope is not limited in description, it is necessary to determine its technical scope according to right.

Claims (1)

1. a tremor on-line monitoring method based on cepstrum analysis, it is characterised in that comprise the following steps:

S1, gather the acceleration signal in vertical milling working angles by the acceleration transducer that is arranged on the main shaft of vertical knee-type milling machine Be expressed as X=[x (1), x (2) ..., x (n)], n represents that signal length, described acceleration signal include steady state signal, mistake Cross status signal and chatter state signal；

S2, chatter state signal is carried out WAVELET PACKET DECOMPOSITION, obtain wavelet packet coefficient, then each by wavelet packet inverse transformation reconstruct The chatter state signal of individual frequency range:

Wherein, c_j0,kFor at yardstick j₀On approximation wavelet coefficients；d_j,kFor at j₀And concrete wavelet coefficient on following yardstick；

S3, the chatter state signal after above-mentioned reconstruct is carried out cepstrum analysis, extract the root-mean-square value of cepstrum amplitude Little value r_minWith maximum r_max；

S4, the described acceleration signal collected is carried out WAVELET PACKET DECOMPOSITION, obtain wavelet packet coefficient, then inverse by wavelet packet Conversion reconstructs the acceleration signal of each frequency range, then carries out cepstrum analysis, the root-mean-square value of extraction cepstrum amplitude:

$r=\sqrt{\underset{i=1}{\overset{n}{\Σ}}{p}_i^2/n}$

Wherein, p_iFor the i-th discrete cepstrum amplitude of tremor generation frequency band signals, n is that cepstrum is discrete to count；

S5, generalThe on-line monitoring of tremor is carried out as tremor feature, ifIllustrate to enter chatter state.