CN108955616A - A kind of 4 cylindricity measuring methods based on the analysis of unusual rate - Google Patents
A kind of 4 cylindricity measuring methods based on the analysis of unusual rate Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
Abstract
The invention discloses a kind of 4 cylindricity measuring methods based on the analysis of unusual rate, measurement obtains the mixed signal of tested cylindrical section shape and shafting bounce and measurement bay straight line error motion by the collected multi-turn measuring signal of axial three sections, four sensor；According to the priori cross sectional shape signal period, singular value decomposition method is taken to extract fundamental signal first, then carries out the bounce period in unusual rate spectrum analysis measurement section to residue signal；Diameter sensor measurement signal is finally taken mutually to sum it up 3 straightness error separation methods of ordered vector, actual cross sectional shape is obtained after various error motions in removal measurement process, and then relative radius, out-of-roundness and the least square center vector of each section circle are obtained, the curvature of space middle line that tested cylinder is measured by fitting realizes the measurement reconstruct based on cylindrical body profile defined in international standard.The advantages of present invention has number of sensors few, strong antijamming capability, simple in measurement system structure.
Description
Technical field
The present invention relates to Precision Inspection and large-scale in situ measurement equipment Design manufacturing fields, specifically towards
A kind of 4 cylindricity measuring methods based on the analysis of unusual rate of large cylindrical cylindricity measurement.
Background technique
Large-scale precision beaming roller is the fields such as new energy, naval vessels, ship, papermaking, mining for making large scale solar-electricity
Pond plate, steamer autobody sheet, liquid crystal display, the core component of high-quality paper etc., size is greatly to the diameter sum number rice of meter level
Length, the precision of profile, i.e. cylindricity error equal error can copy on product produced, be to determine product surface quality
An important factor for.Therefore macrotype axes series parts SHAPE DETECTION accuracy flag the technical level of the high-end equipment manufacture of a state and its
The international competitiveness of product, therefore studying has important economy, scientific meaning towards large cylindrical degree error separating method and answers
With value.
It is verified in existing research: using multiple spot error separating technology realize shafting Error-motion in Rotation with lead
Rail linear motion full harmonic wave separation be obtain the in situ measurement of high-precision cylindricity only way [Endo K, Gao W,
Yiyono S.2003A new multi-
probearrangementforsurfaceprofilemeasurementofcylinders.JSMEIntJSerC461531-
1537].Based on this, many scholars propose 5~6 cylinder profile measurement methods [Gao W, YokoyamaJ, KojimaH,
Kiyono S.2002Precision measurement of cylinder
Straightnessusingascanningmulti-probesystem.PrecisEng.26 279-288], however multisensor
The systems sexual factor such as consistency of characteristic constrains the anti-interference ability of measuring system, increases error source.Therefore it reduces and passes
Sensor number has ensured cylinder profile measurement accuracy, while reducing the complexity of system structure, also reduces cost.
Summary of the invention
The invention proposes a kind of 4 cylindricity measuring methods based on the analysis of unusual rate, are reducing by a sensor
On the basis of can also realize measurement center shafting Radial mixing movement and guide rail straight line error motion full harmonic wave separation, in turn
Realize the High precision reconstruction of cylinder profile.
The present invention adopts the following technical scheme that in order to solve the technical problem
A kind of 4 cylindricity measuring methods based on the analysis of unusual rate are to be applied to be supported jointly by Z guide rail and Y guide rail
Measurement bay the direction Y-Z it is mobile, supported by support shafting and drive measured body rotate composed by measuring system, the Z
Guide rail is axial parallel with the measured body；And supporting the step pitch of measurement bay along the Z direction is d；It is characterized in that the measurement
Method is to carry out as follows:
Step 1, data acquisition:
The section of left, center, right three is arranged in step 1.1 on the measurement bay (8), and three sections are led perpendicular to the Z
Rail (7) moving direction, and the distance between three sections are d；Diameter configures two sensors, packet in X direction on left section
It includes first sensor (1), second sensor (2)；
Step 1.2 is distinguished in X direction and on the same bus of second sensor (2) on middle section and right section
Configured with 3rd sensor (3) and the 4th sensor (4)；
Step 1.3 along axial divides M measurement section on the measured body (6)；The distance between each measurement section is
d；Define side position J；J=1,2 ..., M；
Step 1.4, initialization J=1；
Step 1.5, traverse measurement frame (8) make left section on the measurement bay (8) be located at (6) J of measured body measurement section
On；
Step 1.6, drive the measured body (6) to rotate m week by support shafting (5), m value is 5-10, so that described the
One sensor (1), second sensor (2) can acquire m weeks on (6) section J of measured body measurement data, weekly data volume
For sampling number N weekly；The 3rd sensor (3) acquires m weeks on (6) J+1 of measured body measurement section measurement number
According to；4th sensor (4) acquires m weeks on (6) section J+2 of measured body measurement data；To complete J location
Measurement, obtain J location measurement data；The measurement data of the J location includes: the left cross-section data of J location,
The middle section data of J location and the right section data of J location；
J+1 is assigned to J by step 1.7, and judges whether J > M is true, if so, it then indicates to complete the measurement of each location of M；
Obtain the measurement data of M location；Otherwise, 1.5 sequence of steps are returned to execute；
Step 2, the fundamental signal that J measurement section is extracted with singular value decomposition method；
Step 2.1 sets yJ(n) n=1,2,3...m × N indicates the data in second sensor (2) section collected J
Sequence is split it by primitive period N, constructs window matrix:
Step 2.2, with the singular value decomposition method (abbreviation SVD method) in linear algebra to above-mentioned matrix Am×NIt is decomposed,
Obtain three vectors, respectively UJ=[u1,u2,L,um]m×m, VJ=[v1,v2,…,vN]N×N, SJ=[diag { σ1,σ2,…,
σp}:0]。σkIt is matrixK-th of singular value, uk,vkIt is and σkCorresponding k-th of left singular vector and k-th of right side are unusual
Vector.Take vector σ1,u1,v1 TThree vectors are carried out to be multiplied the matrix after being reconstructedIt willEach column be added after take
Average value, then carry out m periodic extension just obtained the section J it is decomposed and reconstituted after fundamental signal data sequence
Step 2.3, take it is above-mentionedIn top n data carry out discrete Fourier transform obtain J measurement section fundamental wave
SignalIt beats on shape signal and X-direction containing J measurement section in the fundamental signal
In harmonic component identical with shape；
Step 3 measures the bounce period S on section in X-direction with unusual rate spectral analysis method identification J；
Step 3.1, to take out fundamental signal afterResidue signal sequence by l, (l can use in 1~m × N times
Meaning value) it is split, construct window matrix:
Step 3.2, with singular value decomposition method to above-mentioned matrix Am×lIt is decomposed, obtains vector SJ=[diag { σ1,
σ2,…,σp}:0]；If ρ=σ1/σ2For unusual rate, the curve that ρ changes with the length l of every row element is constructed, which is referred to as
Unusual rate composes (abbreviation SVR spectrum)；The SVR spectrum for observing residue signal finds the corresponding cycle length of the higher some wave crests of peak value,
And multiply period of relationship again wherein picking out cycle length and presenting, wherein the smallest cycle length is that J measurement section is jumped
Dynamic period S；
Step 4, the common divisor P for calculating J cross sectional shape period and period of beating, take the value of N/P namely the period is P's
Signal is the N/P order harmonic component of shape, and judges that N/P order is odd number also even number；If even number, then following steps 5 are executed；
If odd number, then following steps 6 are executed；
Step 5, the N/P order harmonic component for obtaining J measurement section true form when N/P is even number, while also obtaining
J measures the relative radius (deviation) of section circle namely 0 order harmonic component of shape；
Step 5.1, the first sensor (1) for taking two diameter of left section of J location to place and second sensor (2) acquisition
The first weekly data be added to obtainZJ=J × d indicates the axial position in (6) J of measured body measurement section；i
Indicate the point number of sampling in any sensor one week；I=0,1,2 ... N-1；N indicates the points of sampling in any sensor one week, and
The angular spacing of sampling is δ=2 π/N；
It is step 5.2, rightTop n data carry out discrete Fourier transform, obtained J measurement section shape
All even-order harmonic R (Z of shapeJ, 2k) and k=0,1,2 ... (N-1)/2 finds the corresponding harmonic component R (Z of N/P rankJ,N/
P), substituted in the fundamental signal extractedJust bounce and R (Z in fundamental wave are eliminatedJ, N/P) and identical humorous
Wave component ingredient；Since P represents any one common divisor in J measurement cross sectional shape period and period of beating, so for
All N/P do this processing when being even number, just eliminate all even-order harmonics components identical with shape of beating in fundamental wave
It influences；
Step 5.3 takes R (ZJ, k) and k=0,1,2 ... 0 order harmonic component R (Z in N-1J, 0), it can also acquire J survey
Measure relative radius (deviation) r in section0(ZJ)；
Step 6 obtains J measurement section reality when N/P is odd number with 3 straightness error separation methods of ordered vector
The N/P order harmonic component of shape, while also obtaining the least square center of J measurement section circle namely an order harmonics of shape
Component；
Step 6.1, the data sequence for taking J measurement section fundamental waveIn top n data, discrete Fu is carried out to it
In leaf transformation, and k=N/P is taken to obtainIt comprises measured body (6) the shape signal in the section J N/P rank
Harmonic component R (ZJ, N/P) and support shafting (5) in the N/P order harmonics of error motion bounce caused by the section J of X-direction
ComponentNamely:
The top n data of step 6.2, the 3rd sensor (3) for taking J measurement section and the 4th sensor (4), and to it
Carrying out discrete Fourier transform takes N/P rank to obtainWith
Step 6.3 calculates the Obliquity error movement of the support shafting in X direction using following formula (4) in the phase of J location
Adjacent two measurements section causes the estimated value δ of the N/P order harmonic component of the difference of bounceJ:
Step 6.4, the N/ that the measured body J measurement cross sectional shape and J+1 measurement cross sectional shape are extracted using formula (5)
The relative variation Θ of P order harmonic componentJ:
Step 6.5, the N/P order harmonic component R (Z that the measured body J measurement cross sectional shape can be calculated using formula (6)J,
N/P):
R(ZJ, N/P) and=R (ZJ-1,N/P)+ΘJ-1 (6)
Step 6.6, the N/P order harmonic component for assuming the 1st cross sectional shape of measured body are R (Z1, N/P) and=B, the 1st section
The N/P order harmonic component estimated value δ of the difference of caused bounce on the two neighboring measurement section in face1=C (zero or small plural number)；Benefit
The N/P order harmonic component R (Z of the measured body J measurement cross sectional shape is calculated with formula (7)J,N/P):
Step 6.7, by R (Z obtained aboveJ, N/P) and it substitutes in fundamental signalN/P is replaced with 1,
Just an order harmonic component of J measurement cross sectional shape namely the least square center vector in J measurement section have been obtained；
The cylinder profile r (Z of step 7, the reconstruct measured bodyJ,i).It is upper by by N/P being even number in step 5 and step 6
The N/P order harmonic component for measuring section true form with J when odd number is humorous instead of the N/P rank in the fundamental signal of extraction
Wave component can eliminate the influence that J measurement section bounce neutralizes the identical harmonic component of shape, thus obtain J measurement section
Actual shape R (ZJ, k) and k=1,2 ... N-1, and then obtain cylinder defined in international standard ISO12180-1,2:2011
The three elements of body profile reconstruct: relative radius (deviation) (the zeroth order harmonic component of shape), the least square center arrow of section circle
Measure (order harmonic component of shape) and out-of-roundness (second order of shape and above all of harmonic component)；It is measured by fitting
The curvature of space middle line of tested cylinder, and then realize and be based on international standard ISO12180-1, cylindrical body defined in 2:2011 is wide
The measurement of shape reconstructs.
Compared with the prior art, the invention has the advantages that:
1, the technology of the present invention path is: measurement is obtained by the collected multi-turn measuring signal of axial three sections, four sensor
To tested cylindrical section shape and shafting bounce and the mixed signal of measurement bay straight line error motion, according to priori cross sectional shape
Signal period extracts fundamental signal with singular value decomposition method first, carries out unusual rate spectrum analysis measurement section to residue signal
It beats the period；The common divisor in shape period and period of beating is sought again, namely is determined each measurement cross sectional shape and beated identical
Harmonic component；It finally takes diameter sensor measurement signal mutually to sum it up 3 straightness error separation methods of ordered vector, removes
Various error motions in measurement process, obtain actual cross sectional shape, and then have obtained the relative radius of each section circle (partially
Difference), out-of-roundness and least square center vector, the curvature of space middle line of tested cylinder is measured by fitting, and then realize base
The measurement of the cylindrical body profile defined in international standard ISO12180-1,2:2011 reconstructs.It is a kind of based on unusual rate point as a result,
4 cylindricity measuring methods of analysis are that the accurate measurement in situ of cylinder profile opens a new Technology Ways, enrich mistake
The intension of poor partition method；
2, verified in existing research: using multiple spot error separating technology realize shafting Error-motion in Rotation with
Guide rail linear motion full harmonic wave separation be obtain the in situ measurement of high-precision cylindricity only way [EndoK, GaoW,
YiyonoS.2003A new multi-probearrangement for surface profile measurement of
cylinders.JSME Int J Ser C461531-1537].Based on this, many scholars propose 5~6 cylinder profiles and survey
Amount method [GaoW, YokoyamaJ, Kojima H, KiyonoS.2002Precision measurement of cylinder
Straightness using a scanning multi-probesystem.PrecisEng.26279-288], however more biographies
The systems sexual factor such as consistency of sensor characteristic constrains the anti-interference ability of measuring system, increases error source, therefore set
It is to improve the mainstream path of measurement accuracy that method, which reduces number of sensors, and the cylindricity proposed by the present invention based on the analysis of unusual rate is missed
Poor separation method uses four sensors, one of has preferably agreed with mainstream path, has effectively ensured cylinder profile measurement accuracy.
3,4 cylindricity error separating methods proposed by the present invention based on the analysis of unusual rate are turned round in lower shafting
Under conditions of precision and lower guide rail kinematic accuracy, the High precision reconstruction of cylinder also can be correctly realized；Therefore, to measuring system
In corresponding shafting and guide rail there is no high-precision requirement, simultaneously because the reduction of number of sensors, apparatus structure more simplifies, this
The manufacturing cost of large cylindrical profile in situ measurement equipment is significantly reduced, this is economic value place of the invention.
In conclusion the present invention passes through 4 cylindricity error separating methods of singular spectrum analysis, correctly extract tested
Each cross sectional shape of cylinder realizes the Error-motion in Rotation of each cross sectional shape and shafting and the full harmonic wave point of guide rail linear motion
From, while reducing number of sensors, it reduces costs, simplifies measuring system structure, while substantially increasing large-scale circle again
The in situ measurement precision of column profile.
Detailed description of the invention
Fig. 1 is that the present invention is based on 4 cylindricity error separating method measuring principle figures of unusual rate analysis；
Fig. 2 is the main view for the side formula cylinder profile measuring device established based on the present invention；
Fig. 3 is the side view for the side formula cylinder profile measuring device established based on the present invention.
Figure label: 1 first sensor；2 second sensors；3 3rd sensors；4 the 4th sensors；5 support shaftings；6
Measured body；7Z guide rail；8 measurement bays；9Y guide rail.
Specific embodiment
In the present embodiment, as shown in Fig. 2, a kind of 4 cylindricity measuring methods based on the analysis of unusual rate, measurement bay (8)
The movement in the direction Y-Z can be carried out under the common support of Z guide rail (7) and Y guide rail (9)；Support shafting (5) supports and drives quilt
Survey body (6) rotation；Z guide rail (7) is parallel to the axial direction of measured body (6)；When measurement starts, measurement bay (8) is supported in Y guide rail (9)
It is lower to move into location along Z-direction close to measured body 6, under Z guide rail (7) support along Y-direction, and measurement bay (8) is along the Z direction
Moving step pitch be d；In specific implementation, measurement is obtained by the collected multi-turn measuring signal of axial three sections, four sensor
The mixed signal of tested cylindrical section shape and shafting bounce and measurement bay straight line error motion, believes according to priori cross sectional shape
Number period extracts fundamental signal with singular value decomposition method first, carries out unusual rate spectrum analysis measurement section to residue signal
It beats the period；The common divisor in shape period and period of beating is sought again, namely is determined each measurement cross sectional shape and beated identical
Harmonic component；It finally takes diameter sensor measurement signal mutually to sum it up 3 straightness error separation methods of ordered vector, removes
Various error motions in measurement process obtain the true form in each section, and then have obtained the relative radius of each section circle (partially
Difference), out-of-roundness and least square center vector, the curvature of space middle line of tested cylinder is measured by fitting, and then realize base
The measurement of the cylindrical body profile defined in international standard ISO 12180-1,2:2011 reconstructs；Specifically as follows into
Row:
Step 1, data acquisition:
The section of left, center, right three is arranged in step 1.1 on the measurement bay (8), and three sections are led perpendicular to the Z
Rail (7) moving direction, and the distance between three sections are d；Diameter configures two sensors, packet in X direction on left section
It includes first sensor (1), second sensor (2)；
The left section diameter of measurement bay (8) of the present invention places two sensors (1), (2), and its purpose is to eliminate Z guide rail
(7) error caused by linear motion in (6) section J X-direction of measured body；
Step 1.2 is distinguished in X direction and on the same bus of second sensor (2) on middle section and right section
Configured with 3rd sensor (3) and the 4th sensor (4)；
See Fig. 1 and Fig. 3,2,1,1 sensor be respectively configured in the measurement section of the left, center, right of measurement bay (8) three,
It may be simply referred to as 211 modes of sensor configuration herein；Certainly in actual measurement, according to measurement task or environment can be measured,
112 or 121 modes of three cross-section sensors configuration are designed, method proposed by the present invention is applicable；
Step 1.3 along axial divides M measurement section on the measured body (6)；The distance between each measurement section is
d；Define location J；J=1,2 ..., M；
Step 1.4, initialization J=1；
1.5, traverse measurement frame (8) are located at left section on the measurement bay (8) on (6) J of measured body measurement section；
1.6, the measured body (6) is driven to rotate m week (the general value of m is 5-10) by support shafting (5), so that described the
One sensor (1), second sensor (2) can acquire m weeks on (6) section J of measured body measurement data, weekly data volume
For sampling number N weekly；The 3rd sensor (3) acquires m weeks on (6) J+1 of measured body measurement section measurement number
According to；4th sensor (4) acquires m weeks on (6) section J+2 of measured body measurement data；To complete J location
Measurement, obtain J location measurement data；The measurement data of the J location includes: the left cross-section data of J location,
The middle section data of J location and the right section data of J location；
Be using brass tacks based on more week measurements: axial system error movement shows asynchronous characteristic, i.e. shafting is missed
Difference moves each Zhou Buhui and repeats, and each week, widely different [bear had the mathematical method China metering publication of human relations accurate measurement sometimes
Society, Beijing, 1989]；Think in engineering, the tested part Error-motion in Rotation formed in revolution in closing bearing hole should have
Periodically, the only period unknown [purification of the cylindricity surface topography reconstruction datum such as Hong Maisheng, Li Zijun, Li Jishun
[J] Shanghai communications university's journal, 2002,36 (8): 1068~1070].And in the present invention unusual rate spectral analysis method premise
It is caused by being based in measured body (6) each cross sectional shape period and supporter (5) rotary course in measured body (6) X-direction
The difference in the period of bounce, to be recognized to the bounce period on above-mentioned each section.In order to allow the collected number of sensor
According to embodying as much as possible, above-mentioned each section bounce is periodical, therefore uses the scheme of more week measurements, and rule of thumb, generally take m
It is more appropriate for 5~10；
J+1 is assigned to J by step 1.7, and judges whether J > M is true, if so, it then indicates to complete the survey of each location of M
Amount；Obtain the measurement data of M location；Otherwise, 1.5 sequence of steps are returned to execute；
Step 2, the fundamental signal that J measurement section is extracted with singular value decomposition method；
Step 2.1 sets yJ(n) n=1,2,3...m × N indicates the data in second sensor (2) section collected J
Sequence is split it by primitive period N, constructs window matrix:
Step 2.2, with the singular value decomposition method (abbreviation SVD method) in linear algebra to above-mentioned matrix Am×NIt is decomposed,
Obtain three vectors, respectively UJ=[u1,u2,L,um]m×m, VJ=[v1,v2,…,vN]N×N, SJ=[diag { σ1,σ2,…,
σp}:0]。σkIt is matrixK-th of singular value, uk,vkIt is and σkCorresponding k-th of left singular vector and k-th of right side are unusual
Vector.Take vector σ1,u1,v1 T, carry out three vectors and be multiplied the matrix after being reconstructedIt willEach column be added after take
Average value, then carry out m periodic extension and just obtained the data sequence of the section J fundamental signal
Singular value decomposition method is with the periodic component of different cycles length in the sequence extraction information source of fade out, due to this
The shape period in invention is it is known that therefore can extract in advance fundamental signal without first doing unusual rate spectrum analysis；Simultaneously at this
In invention, the contribution that lesser singular value is usually beated with noise after SVD is decomposed, therefore singular value σ1Just mainly by fundamental wave
Signal generates, and utilizes σ1×u1×v1 TThe reconstruct that can carry out fundamental signal, greatly reduces the influence of noise.
Step 2.3, take it is above-mentionedIn top n data carry out discrete Fourier transform obtain J measurement section base
Wave signalIn shape and X-direction containing J measurement section in the fundamental signal in bounce
Harmonic component identical with J measurement cross sectional shape；
Since singular value decomposition is that the different cycles based on signal component each in composite signal are separated, with week
Phase or period will be separated together in the signal for multiplying relationship again, and can not be separated again.Become by discrete fourier
It changes it is found that the two different cycles but period is there are the signal of common divisor harmonic component having the same, thus causes in separation the
When a cycle signal, harmonic component identical in residual signal can be separated together.Therefore it is decomposed above-mentioned with SVD method
To the fundamental signal in J measurement sectionIn, in shape and X-direction comprising J measurement section
Harmonic component identical with cross sectional shape in bounce, so fundamental signalIt is not the shape in actual J measurement section
Shape still needs to more accurately be extracted；
Step 3 measures the bounce period S on section in X-direction with unusual rate spectral analysis method identification J；
Step 3.1, to take out fundamental signal afterResidue signal sequence by l, (l can use in 1~m × N times
Meaning value) it is split, construct window matrix:
Step 3.2, with singular value decomposition method to above-mentioned matrix Am×lIt is decomposed, obtains vector SJ=[diag { σ1,
σ2,…,σp}:0].If ρ=σ1/σ2For unusual rate, the curve that ρ changes with the length l of every row element is constructed, which is referred to as
Unusual rate composes (abbreviation SVR spectrum)；The SVR spectrum for observing residue signal finds the corresponding cycle length of the higher some wave crests of peak value
L, and multiply period of relationship again wherein picking out cycle length and presenting, wherein the smallest cycle length is J measurement section
The period S of bounce；
Here, being illustrated to singular spectrum analysis method.From matrix theory: if measurement data sequence do not have noise and
It is stringent periodic signal, using cycle length as above-mentioned window matrix Am×lThe length l of every row element, matrix Am×lOrder be
1, after carrying out SVD decomposition to it, vector SJ=[diag { σ1,σ2,…,σp}: only one non-zero singular value σ in 0]1, remaining is complete
It is 0；If measurement data sequence is the signal sequence with period but amplitude variation, in this case, Am×lIt will be one full
Order battle array, but the result that SVD is decomposed still generates a main singular value σ1, but σ at this time1> > σp.SVD decomposes resulting surprise
Lesser singular value is the contribution of noise He remaining signal in different value.The matrix structure anyway of practical measurement signals sequence composition
It makes, is generally full rank battle array, this is because caused by noise signal superposition.As a result, to different row element l length can construct ρ=
σ1/σ2, then ratio ρ just may be defined as unusual rate spectrum, abbreviation SVR spectrum relative to the distribution of l.It is right in periodic data sequence
Most strong period l and its multiply can show strong peak value at the period again；And to white noise, chaos sequence, then it shows in spectrum
Lack any apparent cyclic component.According to this, SVR spectrum can be used to recognize periodic sequence and its corresponding period is long
Degree, and the effect for removing noise is also good.
Step 4, the common divisor P for calculating J cross sectional shape period and period of beating, take the value of N/P namely the period is P's
Signal is the N/P order harmonic component of shape, and judges that N/P order is odd number also even number；If even number, then following steps 5 are executed；
If odd number, then following steps 6 are executed；
Step 5, the N/P order harmonic component for obtaining J measurement section true form when N/P is even number, while also obtaining
J measures the relative radius (deviation) of section circle namely 0 order harmonic component of shape；
Step 5.1, the first sensor (1) for taking two diameter of left section of J location to place and second sensor (2) acquisition
The first weekly data:
In formula (3), ZJ=J × d indicates the axial position in (6) J of measured body measurement section；I indicates any sensing
The point number of sampling in device one week；I=0,1,2,3...N-1；N indicates the points of sampling in any sensor one week, and between the angle sampled
It is divided into δ=2 π/N；r(ZJ, i), r'(ZJ, i) and i=0,2 ... N-1 is that (6) J of the measured body measurement under sensor 1,2 measures is cut
Face shape；D1,D2For the zero-bit of first sensor and second sensor；ex(ZJ, i) and it is the error for supporting the X-direction of shafting (5)
Move the caused bounce on (6) section J of measured body；εx(ZJ, i) and it is Z guide rail (7) straight line error motion in measured body (6) the
J measures the offset of X-direction caused by the axial position of section；It is first sensor and the second sensing respectively
First weekly data in the section J on the measured body (6) of device acquisition；
Offset ε caused by Z guide rail (7) straight line error motion in (6) section J X-direction of measured bodyX(ZJ, i) and anti-
Opposite number each other is reflected in first sensor (1) and second sensor (2), supports shafting (5) in X-direction error motion in J
Beat e caused by sectionX(ZJ, i) and opposite number each other is reflected in first sensor (1) and second sensor (2).By above-mentioned two
Formula is added to obtain
Therefore guide rail (7) and support shafting (5) mistake of X-direction on the section J are eliminated after being added in resulting result
Deviation caused by difference moves；
R (Z in above-mentioned formula (4)J,i)+r'(ZJ, i), there is following derivation:
(6) J of measured body measurement section is the irregular closed curve using 2 π as the period, therefore its cross sectional shape can also table
It is shown as:
R (θ)=r (+2 π k of θ) (5)
Wherein 0≤θ≤2 π, k integer.Therefore for the r under (6) J cross-section sensor (1) (2) of measured body1(θ),r2(θ+
Fourier expansion formula π) is as follows:
In formula (6), θ is first sensor (1) and measured body (6) X-direction angulation, and in the present invention, θ is 0 °；r
(ZJ, 0) and it is 0 order harmonic component of J cross sectional shape namely the radial misalignment in the section J；ak,bkFor the k rank of J cross sectional shape
The Fourier coefficient of harmonic component.
Two formulas in above-mentioned (6) are added, are obtained such as following formula (7):
Above-mentioned formula (7) indicates r1(θ)+r2The radial misalignment and even-order of J cross sectional shape are contained only in the result of (θ+π)
Harmonic component；This makes it possible to obtain conclusion: diameter place two sensors (1), (2) collect J cross-section data addition after
ResultContain 2 times of relative radius values in J measurement section and the sum of the even-order harmonic component of 2 times of shapes and
The zero-bit of first sensor (1) and second sensor (2)；
It is step 5.2, rightTop n data carry out discrete Fourier transform, obtained J measurement section shape
All even-order harmonic R (Z of shapeJ, 2k) and k=0,1,2 ... (N-1)/2 finds the corresponding harmonic component R (Z of N/P rankJ,N/
P), substituted in the fundamental signal extractedJust bounce and R (Z in fundamental wave are eliminatedJ, N/P) and identical humorous
Wave component ingredient；Since P represents any one common divisor in J measurement cross sectional shape period and period of beating, so for
All N/P do this processing when being even number, just eliminate all even-order harmonics components identical with shape of beating in fundamental wave
It influences；
Step 5.3 takes R (ZJ, 2k) and k=0,1,2 ... 0 order harmonic component R (Z in (N-1)/2J, 0), it can also acquire
Relative radius (deviation) r in J measurement section0(ZJ)；
Step 6 obtains J measurement section reality when N/P is odd number with 3 straightness error separation methods of ordered vector
The N/P order harmonic component of shape, while also obtaining the least square center of J measurement section circle namely an order harmonics of shape
Component；
Step 6.1, the data sequence for taking J measurement section fundamental waveIn top n data namely first week number
According to carrying out discrete Fourier transform to it, and k=N/P rank is taken to obtainContain measured body
(6) the section J shape signal N/P order harmonic component R (ZJ, N/P) and support shafting (5) in the error motion of X-direction
The N/P order harmonic component of the bounce caused by the section JNamely:
First weekly data of step 6.2, the 3rd sensor (3) for taking J measurement section and the 4th sensor (4)
In formula (9): r (ZJ+1,i),r2(ZJ+2, i) i=0,1,2...N-1 be measured body (6) J+1 and J+2 measure section
Shape；D3,D4For the zero-bit of 3rd sensor (3) and the 4th sensor (4)；ex(ZJ+1,i),ex(ZJ+2, i)) it is support shafting
(5) the caused bounce on measured body (6) J+1 and J+2 measurement section of X-direction error motion；εx(ZJ+1),εx(ZJ+2) it is Z
Guide rail (7) straight line error motion causes the X-direction of measurement bay (8) in measured body (6) J+1 and J+2 measurement section axial position
Offset；It is J on the measured body (6) of 3rd sensor (3) and the acquisition of the 4th sensor (4) respectively
+ 1 and J+2 measures the first weekly data of section.
IfDiscrete Fourier transform be respectivelyWithTo formula
(9) both sides carry out discrete Fourier transform and take kth=N/P order harmonic component:
Since the straight line error motion of Z guide rail (7) causes the offset of measurement bay (8) X-direction to be for signal to this week
One constant, by formula (9) it is found that and the discrete Fourier transform of constant is all 0 to the harmonic component in addition to zeroth order harmonic wave, because
This, formula (10) eliminates influence of the straight line error motion of guide rail (7) to measurement naturally.
Obviously, on J location, the N/P that (6) J+1 of measured body measures cross sectional shape is obtained by 3rd sensor (3)
Order harmonic component R (ZJ+1, N/P) draw with the error motion in support shafting (5) X-direction in (6) J+1 of measured body measurement section
The N/P order harmonic component of the X-direction bounce risenSynthesisSimilarly, pass through the 4th sensing
Device 4 obtains the N/P order harmonic component R (Z of J+2 measurement cross sectional shapeJ+2, N/P) with support shafting (5) X-direction on error
Move the order harmonic component that X-direction caused by measuring section in 6 J+2 of measured body is beatedSynthesisIn addition, obtaining J with the method for singular value decomposition by second sensor (2) collected data
Measure the fundamental signal in section(10) first formula of formula is subtracted formula (8), the second formula of formula (10) subtracts the first formula
Have:
In formula (11), with R (ZJ+1,N/P)-R(ZJ, N/P) and R (ZJ+2,N/P)-R(ZJ+1, N/P) and it is characterized in J survey respectively
The variation of the N/P order harmonic component of position (6) J+1 of measured body and J measurement section circle and J+2 and J+1 measurement section circle shape
Amount.WithBranch when for measured body rotation in (6) one weeks
The N/P rank for the difference that the X-direction error motion of support shafting (5) is beated on adjacent two measurement section on (6) J location of measured body is humorous
Wave component.According to the definition of international machinery production Research Society CIRP shaft error motion, " shafting has pure diameter in X and Y-direction
To error motion x (θ), y (θ) and axial error move z (θ) and the Obliquity error movement along X and Y-axis
", then:
In formula (12), θ=i × δ；xJ(zJ, θ) andIt is characterized in J location support shafting (5) X-direction turn error
Movement caused bounce (purely radial error motion) and along the Obliquity error movement of X-axis on (6) J of measured body measurement section.
Therefore δJIt is characterized in when J location measured body (6) rotates a circle and supports the Obliquity error movement of shafting (5) in X direction adjacent
The N/P order harmonic component estimated value of the difference of caused bounce on two measurement sections.
Step 6.3 can extract the measured body J measurement cross sectional shape and J+1 measurement cross sectional shape using formula (13)
N/P order harmonic component relative variation ΘJ:
Θ in formula (13)JCharacterize the N/P order harmonic component of (6) J+1 of J location measured body and J measurement cross sectional shape
Relative variation.
To J+1 location, the left right section of measurement bay 8 is axial with measured body (6) J+1, J+2 and J+3 measurement section respectively
Position overlapping, therefore sensor (1-2), sensor (3) and sensor 4 acquire J+1, J+2 and J+3 on measured body (6) respectively
The data in section are measured, identical as the measurement process of J location, similar formula (13) have:
Θ in formula (13) and formula (14)J+1J+2 and the J+1 measurement for being all characterized in J+1 location measured body (6) are cut
The relative variation of the N/P order harmonic component in face, it is clear that the two should be equal.So that
δ in formula (15)J+1It is to support the inclination angle of shafting (5) in X direction to miss when measured body (6) rotates a circle in J+1 location
The N/P order harmonic component estimated value of difference movement difference of caused bounce on two neighboring measurement section.Thus it just cooks up
A kind of recurrence relation, it can thus be concluded that:
Step 6.4, the N/P order harmonic component R (Z that the measured body J measurement cross sectional shape can be calculated using formula (17)J,
N/P):
R(ZJ, N/P) and=R (ZJ-1,N/P)+ΘJ-1 (17)
Step 6.5, the N/P order harmonic component for assuming that the measured body the 1st measures cross sectional shape are R (Z1, N/P) and=B (zero
Or small plural number), the 1st two neighboring N/P order harmonic component estimated value for measuring the difference of caused bounce on section in measurement section
δ1=C (zero or small plural number)；The N/P order harmonic component R of the measured body J measurement cross sectional shape is calculated using formula (18)
(ZJ, N/P):
Here, R (ZJ, N/P) and characterize the N/P order harmonic component that J on measured body (6) measures section circle shape.It is worth note
The value of meaning, B and C can will only make the measured body (6) reconstructed that small translation and deflection integrally occur, and not influence measured circle
The reconstruct of column entirety profile；
Step 6.6, by R (Z obtained aboveJ, N/P) and it substitutes in the fundamental signal extractedJust it removes
Bounce and R (Z in fundamental waveJ, N/P) and identical harmonic component ingredient；Since P represents J measurement cross sectional shape period and jump
Any one common divisor in dynamic period, so just eliminating all jumps in fundamental wave for doing this processing when all N/P are odd number
The influence of dynamic odd-order harmonics component identical with shape；
Step 6.7, by above-mentioned R (ZJ, N/P) in N/P replace with 1, just obtained J measurement cross sectional shape single order it is humorous
Wave component namely the least square center vector in J measurement section；
So far, the fundamental signal in the J measurement section gone out with singular value decompositionBy upper
After the processing for stating step 4 and step 5, harmonic component identical with shape in bounce is eliminated, it is practical to have obtained J measurement section
Shape R (ZJ, k) and k=0,1,2 ... N-1；
Step 7, by R (ZJ, k) and k=0,1,2 ... N-1 carries out inverse discrete Fourier transform, and the cylinder for obtaining measured body is wide
Shape r (ZJ,i)。
Claims (1)
1. a kind of 4 cylindricity measuring methods based on the analysis of unusual rate are applied to be supported jointly by Z guide rail and Y guide rail
Measurement bay the direction Y-Z it is mobile, supported by support shafting and drive measured body rotate composed by measuring system, the Z is led
Rail is axial parallel with the measured body, and supporting the step pitch of measurement bay along the Z direction is d；It is characterized in that the measurement side
Method is to carry out as follows:
Step 1, data acquisition:
The section of left, center, right three is arranged in step 1.1 on the measurement bay (8), and three sections are perpendicular to the Z guide rail
(7) moving direction, and the distance between three sections are d；Diameter configures two sensors in X direction on left section, respectively
For first sensor (1), second sensor (2)；
Step 1.2, on middle section and right section in X direction and be respectively configured on the same bus of second sensor (2)
There are 3rd sensor (3) and the 4th sensor (4)；
Step 1.3 along axial divides M measurement section on the measured body (6), and the distance between each measurement section is d；It is fixed
Adopted location J, J=1,2 ..., M；
Step 1.4, initialization J=1；
Step 1.5, traverse measurement frame (8) are located at left section on the measurement bay (8) on (6) J of measured body measurement section；
Step 1.6 drives the measured body (6) to rotate m weeks by support shafting (5), and m value is 5-10, so that described first passes
Sensor (1), second sensor (2) can acquire m weeks on (6) section J of measured body measurement data, and data volume is every weekly
All sampling number N；The 3rd sensor (3) acquires m weeks on (6) J+1 of measured body measurement section measurement data；Institute
State the measurement data that the 4th sensor (4) acquires m weeks on (6) section J+2 of measured body；To complete the survey of J location
Amount obtains the measurement data of J location；The measurement data of the J location includes: the left cross-section data of J location, J survey
The middle section data of position and the right section data of J location；
J+1 is assigned to J by step 1.7, and judges whether J > M is true, if so, it then indicates to complete the measurement of M location, obtain
The measurement data of M location；Otherwise, return step 1.5 sequentially executes；
Step 2 extracts the fundamental signal that J measures section with singular value decomposition method, cuts in the fundamental signal containing J measurement
Harmonic component identical with shape in bounce on the shape signal and X-direction in face；How all steps below removes if surrounding
Harmonic component identical with shape in beating in X-direction in fundamental wave obtains J measurement actual cross-section shape signal expansion；
Step 3 measures the bounce period S on section in X-direction with unusual rate spectral analysis method identification J；
Step 3.1 will extract the residue signal data sequence after fundamental signal and be split by l, construct window matrix, l can
Take arbitrary value in 1~m × N:
Step 3.2, with singular value decomposition method to above-mentioned matrix Am×lIt is decomposed, obtains vector SJ=[diag { σ1,σ2,…,
σp}:0]；If ρ=σ1/σ2For unusual rate, the curve that ρ changes with the length l of every row element is constructed, which is referred to as unusual rate
Spectrum, abbreviation SVR spectrum；The SVR spectrum for observing residue signal finds the corresponding cycle length of the higher some wave crests of peak value, and at it
In pick out cycle length and present and multiply period of relationship again, wherein the smallest cycle length is the week of J measurement section bounce
Phase S；
Step 4, the common divisor P for calculating J cross sectional shape period and period of beating take value namely the period of N/P for the signal of P
It is the N/P order harmonic component of shape, judges that N/P order is odd number also even number；If even number, then following steps 5 are executed；If odd
Number, then execute following steps 6；
Step 5, the first sensor (1) placed with two diameter of left section of J location and second sensor (2) measurement data phase
The method added obtains the N/P order harmonic component that J when N/P is even number measures section true form, is substituted fundamental signal
In N/P order harmonic component；The relative radius of J measurement section circle namely 0 order harmonic component of shape are also obtained simultaneously；
Step 6 obtains J measurement section true form when N/P is odd number with 3 straightness error separation methods of ordered vector
N/P order harmonic component, substituted the N/P order harmonic component in fundamental signal；J measurement section circle is also obtained simultaneously
Least square center namely shape an order harmonic component；
Step 7, by step 5 and step 6 by N/P be even number and odd number when J measure section true form N/P rank it is humorous
Wave component is instead of the N/P order harmonic component in the fundamental signal of extraction, to extract the J measurement actual shape in section
Shape, and then relative radius, out-of-roundness and the least square center vector of each section circle have been obtained, measured circle is measured by fitting
The curvature of space middle line of column, and then realize the survey based on cylindrical body profile defined in international standard ISO 12180-1,2:2011
Amount reconstruct.
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