CN109540279A - The inverse compressed sensing restoration methods of machine tool high speed milling process lack sampling Dynamic Signal - Google Patents
The inverse compressed sensing restoration methods of machine tool high speed milling process lack sampling Dynamic Signal Download PDFInfo
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- 238000005070 sampling Methods 0.000 title claims abstract description 23
- 238000003801 milling Methods 0.000 title claims abstract description 22
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- 239000004615 ingredient Substances 0.000 claims abstract description 47
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- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
- G01H1/12—Measuring characteristics of vibrations in solids by using direct conduction to the detector of longitudinal or not specified vibrations
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Abstract
The inverse compressed sensing restoration methods of machine tool high speed milling process lack sampling Dynamic Signal, are related to the dynamic acquisition of machine tool high speed milling process vibration signal.In the non-processing region of high-speed milling process system, installation vibration acceleration sensor obtains Dynamic Signal first, can avoid handling using anti-aliasing filter in signal acquisition process.Signal is transformed into frequency domain by time domain by Fast Fourier Transform (FFT), and makes a thorough investigation of energy principle of centrality and piecemeal is carried out to frequency spectrum.It may determine that the type affiliation of feature according to the frequency multiplication relationship of the center of energy of frequency spectrum piecemeal and main shaft working frequency.For by compressed sensing ingredient, is handled by frequency, amplitude, the phase information of fast interior spectral line, the real frequency spectrum of original signal can be restored.Realize that high-precision time domain plethysmographic signal restores eventually by inverse fast Fourier transform.Numerical value computational efficiency is higher, has good engineer application promotional value.
Description
Technical field
The present invention relates to the dynamic acquisitions of machine tool high speed milling process vibration signal, and in particular to one kind is on frequency domain to hair
The signal of raw lack sampling carries out the inverse compression sensing method of high-precision recovery.
Background technique
High-speed cutting is one of the important development direction of modern mechanical processing.Chip power significantly reduces when due to high-speed milling
And process heat by chip fast speed belt separating process system, Milling Machining Center finishing passes main shaft rotary speed not
It is disconnected to improve.To assess process process system characteristic, vibration acceleration signal is often recorded using dynamic testing method.Due to
The responding range of the diversity of machine tool structure, rapidoprint, process tool, cutting process is very wide, is not conventional to have
Bandwidth signal is limited, therefore, it is difficult to select reasonable sampling frequency parameters.
In order to effectively be extracted to the dynamic element in signal, nyquist sampling theorem requires the sampling of dynamic test
Frequency is not less than 2 times of actual constituent highest frequency.Therefore in order to meet the requirement, often turn in analog/digital in engineering test
Filtered out frequency higher than all the components of sample frequency half by anti-aliasing filter measure before changing (Zhang Pengfei, Lin Jianhui,
Bearing failure diagnosis of what Liu based on complete anti-aliasing DTCWPT and envelope spectrum entropy, 2017, (4): 144-149).Though the measure
It can so make the signal of measurement that lack sampling and frequency folding not occur, but be likely to strangle the high frequency dynamic of physical significance special
Sign.Another method is to improve sample frequency as far as possible under the premise of not using anti-aliasing filter, it is expected all dynamics
Feature can be extracted really.This proposes higher requirement to the performance of data acquisition equipment.And due to high-speed machining process
Response range it is wide, radio-frequency component is abundant, is still easy lack sampling to occur to the radio-frequency component of part and occurrence frequency folds.
Summary of the invention
It is an object of the invention to the dynamic tests around machine tool high speed milling process, for not using anti-aliasing filter
Signal acquisition problem provides a kind of inverse compressed sensing restoration methods of machine tool high speed milling process lack sampling Dynamic Signal.
The present invention the following steps are included:
1) vibration acceleration sensor is installed on the non-processing surface of part, acquisition vibration adds during milling carries out
Speed signal and the rotation speed f for recording main shaftw, unit Hz；Anti-aliasing filter is not used in dynamic testing process, or
It is required that the cutoff frequency of anti-aliasing filter is higher than sample frequency fs10 times or more；
2) after the completion of Milling Process, one section of dynamic data { x of process is taken outorg(n) | n=1,2 ..., N }, sampling
Length N is even number, to { xorgCarry out average value processing and obtain { x (n) }, it is shown below:
To going mean data { x (n) } to carry out Fast Fourier Transform (FFT), complex value frequency spectrum function is obtained
To amplitude spectrumMiddle f ∈ [0, fs/ 2] it is partially observed, former frequency spectrum is divided into m head and the tail by the principle concentrated according to energy
The frequency range ingredient to connect indicates are as follows:
Wherein, fi,minAnd fi,maxThe lower limiting frequency and upper cut off frequency of i-th of spectrum component are respectively indicated, and full
Foot:
f1, min=0
fi,min< fi,max
fi,max=fi+1,min
fm,max=fs/2
3) judge ppiIt whether is wherein i=1,2 ..., m by compressed sensing ingredient and additional frequency bands label；
(1) it calculatesIn ppiPass through frequency range [fl,i,fl,h] on average value ei:
(2) judge ppiWhether it is conventional perception ingredient, calculates:
In formula, int { } indicates to carry out the real number of input floor operation, that is, finds whole no more than the maximum of in-real
Number；If erri≤ 3 Δ f, then show ppiIt is normal perception ingredient, which is labeled asThis step terminates；It otherwise is pressure
Contracting perception ingredient, continues following step；
(3) judge the actual frequency of compressed sensing ingredient
A. integer variable j=2 is enabled；
B. calculating composition ppiWhether frequency range ((j-1) f is belonged tos/2,j·fs] on ingredient:
If erri≤ 3 Δ f, then mark the ingredient to beOtherwise j=j+1, and return step b are enabled；
Finally, the spectrum component of m tape label is obtained:
4) real frequency spectrum of original signal is restored by inverse compressed sensing and reconstructs original signal；
(1) remember sequence label { tiIn maximum value be l, i.e. l=max1≤i≤m{ti}；It is determined according to the label of each ingredient true
The frequency range of real frequency spectrum is [0, lfs/ 2], construct a length be lN complex value type array s (n)=0 | n=1,
2 ..., lN }, wherein the effect of operators m ax { } is to be maximized；
(2) by the frequency spectrum function in step 1)It is indicated according to its natural order are as follows:
(3) forDetermine it in frequency spectrumUpper corresponding ingredient:
Wherein, ki,min=int { fi,min/Δf},ki,max=int { fi,max/Δf}
(4) frequency spectrum of inverse compressed sensing signal is constructed in frequency spectrum { s (n) }；
To eachGradually handled, as follows:
For n >=lN/2, s (n)=conj { s (lN-n) }, wherein operator conj { } indicates to take being total to for plural number
Yoke；
(5) inverse Fourier transform is carried out to sequence { s (n) }, obtains the inverse compressed sensing time signal that length is lNThat is:
5) it drawsTime domain waveform and its envelope, and compared with the relevant information of mean value signal is gone.
In the non-processing region of high-speed milling process system, installation vibration acceleration sensor obtains dynamic to the present invention first
Signal can avoid in signal acquisition process handling using anti-aliasing filter.There are two kinds of behavioral characteristics in signal: (1)
The non-distorted ingredient of normal sample；(2) lack sampling distortion components.These ingredients are rendered as the frequency of several energy concentration on frequency spectrum
Compose piecemeal.
The present invention proposes one kind and carries out lack sampling distortion on frequency domain according to this feature of high-speed milling dynamic process
Signal is against compressed sensing restoration methods.Signal is transformed into frequency domain by time domain by Fast Fourier Transform (FFT), and makes a thorough investigation of energy
Principle of centrality carries out piecemeal to frequency spectrum.It may determine that according to the frequency multiplication relationship of the center of energy of frequency spectrum piecemeal and main shaft working frequency
The type affiliation of feature.For by compressed sensing ingredient, handled by frequency, amplitude, the phase information of fast interior spectral line, it can
To restore the real frequency spectrum of original signal.Realize that high-precision time domain plethysmographic signal is extensive eventually by inverse fast Fourier transform
It is multiple.
The present invention can pass through lower sampling under the premise of not knowing about high-speed milling dynamic process practical respective range
Frequency acquisition dynamic measuring signal restores according to the feature on signal spectrum by the true spectrum ingredient of compressed sensing ingredient, and most
Accurately restore time domain waveform eventually.The numerical value computational efficiency of this method is higher, has good engineer application promotional value.
Detailed description of the invention
Fig. 1 is the fast Fourier frequency spectrum for acquiring vibration signal.
Fig. 2 is that vibration signals spectrograph is divided into 5 ingredients that are end to end and not overlapping.
Fig. 3 is will be to the result of 5 vibration component affix frequency band tags.
Fig. 4 is 5 ingredient frequency spectrums for carrying out obtaining after inverse compressed sensing is restored to each tape label ingredient.
Fig. 5 is original signal and the comparison diagram for restoring signal.In Fig. 5, (a) original signal；(b) restore signal.
Specific embodiment
Following embodiment will be described in further detail the contents of the present invention in conjunction with attached drawing.
The embodiment of the present invention includes following steps:
1. installing vibration acceleration sensor on the non-processing surface of part, acquisition vibration during high-speed milling carries out
Dynamic acceleration signal (sample frequency fs, sampling length N is necessary for even number) and record the rotation speed f of main shaftw(unit: Hz).
Anti-aliasing filter is not used in dynamic testing process, or the cutoff frequency of anti-aliasing filter is required to be higher than the 10 of sample frequency
Times or more.
2. after the completion of machining, taking out one section of dynamic data { x of processorg(n) | n=1,2 ..., N }, sampling
Length N must be even number.To { xorgCarry out average value processing and obtain { x (n) }, it is shown below:
To going mean data { x (n) } to carry out Fast Fourier Transform (FFT) (FFT), complex value frequency spectrum function is obtained
As shown in Figure 1.In amplitude spectrumMiddle f ∈ [0, fs/ 2] it is partially observed, the principle concentrated according to energy is by former frequency spectrum
It is divided into m end to end frequency range ingredients, indicates are as follows:
Wherein, fi,minAnd fi,maxThe lower limiting frequency and upper cut off frequency of i-th of spectrum component are respectively indicated, and full
Foot:
f1, min=0
fi,min< fi,max
fi,max=fi+1,min
fm,max=fs/2
It is as shown in Figure 2 that vibration signals spectrograph is divided into 5 ingredients that are end to end and not overlapping.
3. judging ppi(i=1,2 ..., m) it whether is by compressed sensing ingredient and additional frequency bands label
1) is calculatedIn ppiPass through frequency range [fl,i,fl,h] on average value ei
2) judges ppiWhether it is conventional perception ingredient, calculates
Int { } indicates to carry out the real number of input floor operation in formula, that is, finds whole no more than the maximum of in-real
Number.If erri≤ 3 Δ f then show ppiIt is normal perception ingredient, which is labeled asThis step terminates；Otherwise it is
Compressed sensing ingredient continues following step.
3) judges the actual frequency of compressed sensing ingredient
3.1) integer variable j=2 is enabled
3.2) calculating composition ppiWhether frequency range ((j-1) f is belonged tos/2,j·fs] on ingredient
If erri≤ 3 Δ f, then mark the ingredient to beOtherwise j=j+1, and return step (c.2) are enabled.
Finally, the spectrum component of m tape label is obtained by these sub-steps
Result to 5 vibration component affix frequency band tags is as shown in Figure 3.
4. restoring the real frequency spectrum of original signal by inverse compressed sensing and reconstructing original signal.
1) remembers sequence label { tiIn maximum value be l, i.e. l=max1≤i≤m{ti}.It is determined according to the label of each ingredient true
The frequency range for being frequency spectrum is [0, lfs/ 2], construct a length be lN complex value type array s (n)=0 | n=1,
2,...,l·N}.Wherein the effect of operators m ax { } is to be maximized.
2) is by the frequency spectrum function in step 1It is indicated according to its natural order are as follows:
3) forDetermine it in frequency spectrumUpper corresponding ingredient:
Wherein, ki,min=int { fi,min/Δf},ki,max=int { fi,max/Δf}。
4) constructs the frequency spectrum of inverse compressed sensing signal in frequency spectrum { s (n) }
To eachGradually handled, as follows:
For n >=lN/2, s (n)=conj { s (lN-n) }.Wherein, operator conj { } indicates to take being total to for plural number
Yoke.
Frequency spectrum after composition adjustment is as shown in Figure 4.
5) carries out inverse Fourier transform to sequence { s (n) }, obtains the inverse compressed sensing time signal that length is lNI.e.
5. drawingTime domain waveform and its envelope, and compared with the relevant information of mean value signal is gone.Original letter
Number with restore signal comparison diagram it is as shown in Figure 5.
Below with reference to the content of a case history explanatory diagram 1~5.
The present embodiment mainly verifies the validity and accuracy of the method for the present invention.To aviation on vertical numerical control machining center
(trade mark: 7075) blank workpiece carries out high-speed planar milling processing to aluminium alloy, and rotation frequency of spindle is 265Hz (15900r/
min).Vibration acceleration sensor is mounted on to the non-processing surface of blank workpiece, vibration is recorded in milling process and is accelerated
Spend signal (sample frequency: 2000Hz, sampling length: 2000).Fast Fourier is carried out after carrying out average value processing to original signal
Transformation, frequency spectrum are as shown in Figure 1.According to energy principle of centrality, by the part of [0,1000] Hz in frequency spectrum be divided into 5 it is independent at
Point, it is expressed as { ppi| i=1,2 ..., 5 }, as shown in Figure 2.The energy barycenter of each ingredient is calculated, it can be found that pp2、pp3's
Energy barycenter is in error range multiple proportion with rotation frequency of spindle, is normal sample ingredient；And pp1、pp4、pp5Then with
Rotation frequency of spindle is not in multiple proportion, belong to that frequency folds by compressed sensing ingredient.Through the invention to each ingredient
Frequency range correction is carried out, 5 tape label ingredients are obtainedAs shown in Figure 3.Inverse compression sense is carried out to each ingredient
After knowing, the actual spectrum of signal reverts to [0,6000] Hz, as shown in Figure 4.Inverse Fourier transform is carried out to the frequency spectrum after recovery,
After being restored shown in time domain waveform such as Fig. 5 (b) of inverse compressed sensing signal, with the original signal waveform (Fig. 5 (a)) for going mean value
It compares, it can be found that the false amplitude modulated phenomenon occurred in Fig. 5 (a) has obtained effective inhibition.
The invention discloses a kind of inverse compressed sensing restoration methods of machine tool high speed milling process lack sampling Dynamic Signal.It should
Method carries out the recovery of lack sampling distortion data by the switching between frequency domain and time domain.It is characterized in that, first workpiece it is non-plus
The Ministry of worker point installation vibration acceleration sensor acquires its vibration signal.According to energy principle of centrality by its stroke on the frequency spectrum of signal
It is divided into several end to end frequency partitions.It calculates the center frequency of frequency partitions and calculates its times with main shaft working frequency
Frequency relationship calculates its true frequency range, judges it to be normally sampled into point or by compressed sensing ingredient.Its lack sampling is folded
Ingredient carries out inverse compressed sensing recovery and handles, i.e., carries out shift frequency, phase only pupil filter etc. for lack sampling folded signal spectral line therein
Data processing constructs the real frequency spectrum under high sample frequency.The dynamic repaired is obtained finally by inverse Fourier transform tests letter
Number.
Claims (1)
1. the inverse compressed sensing restoration methods of machine tool high speed milling process lack sampling Dynamic Signal, it is characterised in that including following step
It is rapid:
1) vibration acceleration sensor is installed on the non-processing surface of part, acquires vibration acceleration during milling carries out
Signal and the rotation speed f for recording main shaftw, unit Hz；Anti-aliasing filter is not used in dynamic testing process, or is required
The cutoff frequency of anti-aliasing filter is higher than sample frequency fs10 times or more；
2) after the completion of Milling Process, one section of dynamic data { x of process is taken outorg(n) | n=1,2 ..., N }, sampling length
N is even number, to { xorgCarry out average value processing and obtain { x (n) }, it is shown below:
To going mean data { x (n) } to carry out Fast Fourier Transform (FFT), complex value frequency spectrum function is obtainedTo width
Value spectrumMiddle f ∈ [0, fs/ 2] it is partially observed, it is end to end that former frequency spectrum is divided into m by the principle concentrated according to energy
Frequency range ingredient, indicate are as follows:
Wherein, fi,minAnd fi,maxThe lower limiting frequency and upper cut off frequency of i-th of spectrum component are respectively indicated, and is met:
f1, min=0
fi,min< fi,max
fi,max=fi+1,min
fm,max=fs/2
3) judge ppiIt whether is wherein i=1,2 ..., m by compressed sensing ingredient and additional frequency bands label；
(1) it calculatesIn ppiPass through frequency range [fl,i,fl,h] on average value ei:
(2) judge ppiWhether it is conventional perception ingredient, calculates:
In formula, int { } indicates to carry out floor operation to the real number of input, that is, finds the maximum integer for being not more than in-real；
If erri≤ 3 Δ f, then show ppiIt is normal perception ingredient, which is labeled asThis step terminates；Otherwise compression sense
Principal component continues following steps；
(3) judge the actual frequency of compressed sensing ingredient
A. integer variable j=2 is enabled；
B. calculating composition ppiWhether frequency range ((j-1) f is belonged tos/2,j·fs] on ingredient:
If erri≤ 3 Δ f, then mark the ingredient to beOtherwise j=j+1, and return step b are enabled；
Finally, the spectrum component of m tape label is obtained:
4) real frequency spectrum of original signal is restored by inverse compressed sensing and reconstructs original signal；
(1) remember sequence label { tiIn maximum value beI.e.True frequency is determined according to the label of each ingredient
The frequency range of spectrum isConstructing a length isComplex value type array
Wherein, the effect of operators m ax { } is to be maximized；
(2) by the frequency spectrum function in step 1)It is indicated according to its natural order are as follows:
(3) forDetermine it in frequency spectrumUpper corresponding ingredient are as follows:
Wherein, ki,min=int { fi,min/Δf},ki,max=int { fi,max/Δf}；
(4) frequency spectrum of inverse compressed sensing signal is constructed in frequency spectrum { s (n) }；
To eachGradually handled, as follows:
ForWherein, operator conj { } indicates to take the conjugation of plural number；
(5) inverse Fourier transform is carried out to sequence { s (n) }, obtaining length isInverse compressed sensing time signalThat is:
5) it drawsTime domain waveform and its envelope, and compared with the relevant information of mean value signal is gone.
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