CN108534735A - 3 cylindricity measuring devices based on V blocks and cylindricity error separation method - Google Patents
3 cylindricity measuring devices based on V blocks and cylindricity error separation method Download PDFInfo
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- 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
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Abstract
The invention discloses 3 cylindricity measuring devices and cylindricity error separation method based on V blocks, cylindricity measurement is carried out for cylindrical measured body, device is using measured body external cylindrical surface in an axial direction as guide rail, it is the test aircraft that slides axially with V blocks, sensor is set on V blocks, sliding test aircraft is supported on using the V-arrangement face of V blocks on the external cylindrical surface of measured body, using V blocks by the axial movement at setting interval, obtains the corresponding location for measured body；On location, measured body rotates a circle under the driving of its revolving support shafting, and V blocks keep circumferential position constant, and its V-arrangement face is kept to be in contact with the external cylindrical surface of measured body.The present invention especially applying in cylinder profile measures reconstruct；Portable large cylindrical profile in situ measurement can be achieved, it measures unrelated with revolving support shafting in situ and guide rail in situ, the full harmonic wave separation that the various error motions of measurement process are realized with minimum number of sensors has ensured that cylinder profile measures the high-precision of reconstruct.
Description
Technical field
The present invention relates to the design and manufacture of Precision Inspection and large-scale manufacturing equipment and field is used, more specifically
A kind of 3 cylindricity measuring devices based on V blocks, cylindricity error separation method and its in cylinder profile measures reconstruct
Using.
Background technology
Beaming roller is a kind of important large-scale component in Large-Scale Equipment manufacturing industry.In large scale solar panel, liquid crystal display, vapour
In the production equipment of vehicle steel plate, high-quality paper and industrial composite board etc., large-scale beaming roller is the core component of equipment, cylinder
Degree error is the mark of beaming roller profile precision.In process of producing product, beaming roller profile error will including cylindricity error etc.
It is copied to product surface, causes all kinds of flaws of product surface.Therefore the profile precision of large-scale beaming roller is to determine manufactured production
An important factor for product surface quality, and indicate a national technical merit for equipment manufacture and the international competitiveness of product.
Beaming roller cylindricity measurement is related to two aspects, first, by accurate measurement come reconstruction cylinder profile, second is that based on reconstruct
Cylinder profile realize form error include cylindricity error evaluation.Due to enormous size (0.3~1.0m of Φ, length 3~
8m), conventional cylindrical shape error measurement method is difficult to play a role, it is necessary to using the measurement of (in production and use) in situ
Mode realizes that the profile of large-scale beaming roller measures, and measuring system is related to that the revolving support shafting of tested beaming roller rotation and support is supported to survey
The linear guide that frame is axially moved.Scholar Li Jishun, Wang Zhongyu etc. are written by《Microtechnic in manufacturing engineering, mechanical industry
Publishing house, page 2001,86~87》In point out：How to evade or reduce shafting and guiding error movement is wide to measuring reconstruction cylinder
The influence of shape, with improve cylinder profile measure, separation and reconstruction accuracy be important in macrotype axes series parts shape measuring technology
Research topic.3 Roundness Error Separation Techniques (Error Separation Techniques, EST) have been widely used circularity
In error measure, such as：Scholar Li Shengyi, a sail is worn etc. written by《Precision and Ultra-precision Machining detects in place and error separate
Technology, publishing house of the National University of Defense technology, page 2007,202~213,254~261》Described in 3 leading errors of frequency domain circularity
Separation method uses special measuring technique and mathematical method, section circularity and shafting Radial Error Motion is separated,
Greatly improve roundness error measurement precision.It, cannot but since there are 1 order harmonics to inhibit problem by 3 circularity EST
1 order harmonics of section profile and 1 order harmonics of support shafting Radial Error Motion are separated, and then it is each to be unable to accurate extraction
A least square center vector for measuring section profile, it is difficult to realize the high-acruracy survey reconstruct of cylinder profile.
Invention content
The present invention is to provide a kind of 3 cylindricities survey based on V blocks to avoid the problems of above-mentioned prior art
Device and cylindricity error separation method are measured, to solve the original position accurate measurement of large cylindrical profile and reconstruct problem；Break away from former system
Influence that system center shafting and guiding error movement measure cylinder profile overcomes 1 order harmonics of 3 circularity EST to inhibit, realization
The each full harmonic wave for measuring section profile of cylinder is tested in measurement process to extract, the high-precision of guarantee cylinder profile measurement reconstruct,
Reduce large cylindrical profile in situ measurement cost.
The present invention is to solve technical problem to adopt the following technical scheme that：
The present invention is based on being structurally characterized in that for 3 cylindricity measuring devices of V blocks：The cylindricity measurement refers to being directed to
Cylindrical measured body carries out cylindricity measurement；The measuring device be using measured body external cylindrical surface in an axial direction as guide rail,
It is the test aircraft that slides axially with V blocks, sensor is provided on the V blocks, the sliding test aircraft is supported on using the V-arrangement face of V blocks
On the external cylindrical surface of measured body, using V blocks by the axial movement at setting interval, the corresponding location for measured body is obtained；
On the location, measured body rotates a circle in the driving of its revolving support shafting, and V blocks keep circumferential position constant, and keep its V
Shape face is in contact with the external cylindrical surface of measured body.
The present invention is based on the design features of 3 cylindricity measuring devices of V blocks to lie also in：
The V blocks are set as double V-arrangement faces structure, and section where the central point in V block axial directions is the measurement for installing sensor
The left and right sides for being in the measuring surface is symmetrically divided in face, the first V-arrangement face and the second V-arrangement face, forms double V-arrangement faces structures；And have：
Axial distance between first V-arrangement face and measuring surface is d；Axial distance between second V-arrangement face and measuring surface is
d；
The axial movement step pitch of the V blocks is d；Axial distance on the measured body between adjacent location is d；
The sensor includes first sensor, second sensor and 3rd sensor, and each sensor is in the measuring surface
On be arranged according to the requirement of 3 roundness fault separating methods.
Using in the present invention measuring device realize 3 cylindricity error separates method the characteristics of be as follows into
Row：
Step 1, data acquisition：
Step 1.1, using the axial V-arrangement face center line for being Z axis, V blocks of measured body as Y-axis, established and surveyed using left hand principle
Measure coordinate system OXYZ；
Step 1.2, divided in an axial direction on the measured body M+2 measure section J, J=0,1 ..., M+1；Adjacent measurement
Axial distance between section is d；Define location K, K=1,2 ..., M；
Step 1.3, initialization K=1；
The J that step 1.4, mobile V blocks make its measuring surface be located at measured body measures section, J=K；
Step 1.5, measured body utilize three sensings one week clockwise or counterclockwise under the driving of its revolving support shafting
Device synchronizes the measurement data that acquisition obtains one week on the J measurements section of the measured body, to complete the survey of K locations
Amount obtains the measurement data on the J measurements section of the measured body；
K values are increased by 1 by step 1.6, judge whether K ＞ M are true, if not, return to step 1.4；If so,
It then indicates the measurement that whole locations are completed, obtains the measurement data of M location；
Step 2, data prediction：The measurement data on section is measured using the J, it is leading according to 3 frequency domain circularity
Error separating method extraction obtains the harmonic vector R (J, p) that J on measured body measures section profile, and p is harmonic order, humorous
Do not include 1 rank and N-1 ranks in wave vector R (J, p), includes that J is measured on the profile of section in the harmonic vector R (J, p)
Radial misalignment r0(J) and deviation from circular from r1(J,i)；Measured body is obtained using the leading error separating method extraction of 3 frequency domain circularity
J measure section at X-direction error motion separating resulting in 1 order harmonics vectorI is the sampling of sensor
Point, i=0,1 ... N-1；N is the points of sensor sampling in one week, and the angular spacing δ between neighbouring sample point is：δ=2 π/N；
Step 3 is calculated as follows the 1 order harmonics vectors for obtaining all measurement section profiles on the measured body：
Step 3.1, initialization
For the 1st location, i.e. K=1, the measuring surface of the V blocks is in the 1st of measured body and measures axial position where section
It sets, the first V-arrangement face of V blocks is in the 0th of measured body and measures axial position where section, and the second V-arrangement face of V blocks is in measured body
The 2nd measure section where axial position；
Setting：The 0th of the measured body measures section and the 2nd and measures 1 order harmonics vector R (0,1) and R of section profile
(2,1) are zero, i.e. R (0,1)=0, R (2,1)=0；And it sets：The 1st of the measured body measures the X-direction error at section
1 order harmonics vector E of movementx(1,1) is zero, i.e. Ex(1,1)=0；Then, the 1st of the measured body measures 1 rank of section profile
Harmonic vector R (1,1) is：The X-direction error motion at section is measured for the 1st of measured body
1 order harmonics vector in separating resulting；
It is used to characterize the 2nd of the measured body as a result, and measures section and the least square center of the 1st measurement section profile
Differential vector Δ R1(1,1) it is：
Step 3.2 is directed to the 2nd location, i.e. K=2；
Step 3.3 calculates 1 rank for obtaining the X-direction error motion at the J=K measurements section of measured body using formula (1)
Harmonic vector Ex(J,1)
1 order harmonics vector R (J+1,1) of the J+1 measurement section profiles for obtaining measured body is calculated using formula (2)
R (J+1,1)=- [2Ex(J,1)+R(J-1,1)] (2)
It is calculated using formula (3) and obtains the minimum that the measurement sections J+1 for characterizing the measured body measure section profile with J
Two multiply centered difference vector Δ RK(J,1)
ΔRK(J, 1)=R (J+1,1)-R (J, 1) (3)
K values are increased by 1, and judge whether K ＞ M are true by step 3.4, if not, return to step 3.3；If at
It is vertical, then it represents that the calculating of all 1 order harmonics vectors for measuring section profile is completed, realizes that 3 cylindricities based on V blocks are missed
Difference from.
The characteristics of reconstructing method of cylinder profile curvature of space center line of the present invention is：
3 cylindricity error separates based on V blocks are realized according to the method for the present invention, obtain on the measured body (5) and own
Measure 1 order harmonics vector R (J, 1) of section profile；
If measured body is to rotate clockwise in measurement process, then on measured body in the least square of J measurements section profile
Heart vector is 2R (J, N-1)/N, conversely, being 2R (J, 1)/N；
According to Fourier transform principle, J measures the N-1 order harmonics vectors R (J, N-1) of section profile and is sweared for 1 order harmonics
Measure the conjugate vector of R (J, 1)；By total M+2 least square center vector 2R (J, N-1)/N, or most by total M+2
Curvature of space of the curve that small two vertex for multiplying center vector 2R (J, 1)/N are connected in sequence as the cylinder profile of measured body
Center line.
The characteristics of reconstructing method of cylinder profile of the present invention is：
The p order harmonics vectors R (J, p) of section profile is measured using the J that the method for the present invention is obtained, wherein not including 1
Rank and N-1 ranks；And using on the obtained measured body of the method for the present invention J measure section profile 1 order harmonics vector R (J, 1) and
It is conjugated R (J, N-1), and using IDFT inverse discrete Fourier transforms, reconstruct measured body (5) measures section from the 1st and cut to M measurements
One section of cylinder profile r (J, i) in face
R (J, i)=IDFT [R (J, p)] p=0,1,2 ..., N-1 (4).
The present invention by V blocks with 3 circularity EST are ingenious merges, realize the portable of cylinder profile measuring device, break away from
The influence that the error motion of support shafting in situ and guide rail in situ measures cylinder profile so that 1 rank of 3 circularity EST is humorous
Wave inhibits problem voluntarily to clear up, and realizes correct extraction and is tested the least square equation of the ecentre that cylinder each adjacent two measures section profile
Resolute, and by recursion obtain it is each measure section profile least square center vector, and then realize by it is each measure cut
The line of face profile least square center vector is reconstructed as the cylinder profile of curvature of space center line, substantially increases large-scale circle
The in situ measurement precision of column profile, compared with the prior art, the present invention has the beneficial effect that：
1, the Technology Ways of 3 cylindricity EST proposed by the present invention based on V blocks are：Double V-arrangement face impressions are tested in V blocks
The variation for the measurement section profile being in contact with it on cylinder makes the displacement sensor being located in V block measuring surface sense tested
The Radial Error Motion of cylinder comes from the variation that two contacted with double V-arrangement faces on V blocks on tested cylinder measure section profile,
And the revolving support shafting of non-supported measured circle column, this just eliminates tested cylinder original position revolving support shafting from measuring principle
With the influence of three sensor signals of error motion pair of guide rail, 1 order harmonics of 3 circularity EST is made to inhibit problem by nature
Resolution, this is the innovation in measurement theory.
2, the present invention is based on 4 continuous contacts in double V-arrangement faces and tested cylinder on V blocks；According to tested cylinder adjacent two
The constant fact of the least square centered difference vector of section profile is measured, modeling extracts in the least square of adjacent sections profile
Heart differential vector, separation simultaneously reject the unduplicated radial error fortune weekly of the tested cylinder caused by tested each section profile of cylinder
It is dynamic；It is proposed that a kind of recursive operation realizes that correct extraction is tested each least square center vector for measuring section profile on cylinder,
This is that 3 cylindricity EST methods based on V blocks are different from existing methods innovation on error separate model, this is also to ensure
The key of cylinder profile high-acruracy survey and High precision reconstruction.
3,3 cylindricity measuring devices based on V blocks are mancarried device, measurement process and support quilt in the present invention
The revolving support shafting for surveying cylinder is unrelated, and the cylinder profile that theoretically can be used for arbitrary back-up environment measures；Meanwhile it measuring
Principle of device is simple in structure, easy to use, greatly reduces that large cylindrical profile measurement cost is low, this is that the present invention applies valence
Where value and economic implications.
4, the present invention realizes the measurement reconstruct for meeting cylinder profile mathematical model, can carry out cylindrical shape on this basis
Error：The error evaluation of circularity, cylindricity, bus straight line degree and taper, therefore be widely used.
Description of the drawings
Fig. 1 is that the present invention is based on the front views of the three of V blocks cylindricity EST measuring principles；
Fig. 2 is that the present invention is based on the vertical views of the three of V blocks cylindricity EST measuring principles；
Figure label：1 first sensor；2 second sensors；3 3rd sensors；4V blocks；The first V-arrangements of 4-1 face；The 2nd V of 4-2
Shape face；4-3 measuring surface；5 measured bodies.
Specific implementation mode
Referring to Fig. 1 and Fig. 2, the structure type of 3 cylindricity measuring devices based on V blocks in the present embodiment is：
Cylindricity measurement refers to carrying out cylindricity measurement for cylindrical measured body 5；Measuring device is with measured body 5
External cylindrical surface in an axial direction is guide rail, is the test aircraft that slides axially with V blocks 4, and sensor is provided on V blocks, and sliding test aircraft utilizes V
The V-arrangement face of block is supported on the external cylindrical surface of measured body 5, using V blocks by the axial movement at setting interval, is obtained and is directed to measured body
5 corresponding location；On location, measured body 5 rotates a circle in the driving of its revolving support shafting, and V blocks keep circumferential position
It is constant, and its V-arrangement face is kept to be in contact with the external cylindrical surface of measured body 5.
As shown in Fig. 2, V blocks are set as double V-arrangement faces structure in the present embodiment, section where the central point in V block axial directions is
The measuring surface 4-3, the first V-arrangement face 4-1 and the second V-arrangement face 4-2 for installing sensor are symmetrically divided to the left and right two for being in measuring surface 4-3
Side forms double V-arrangement faces structure；And have：Axial distance between first V-arrangement face and measuring surface is d, the second V-arrangement face and measuring surface
Between axial distance be d, the axial movement step pitches of V blocks is d, and the axial distance on measured body 5 between adjacent location is d, is passed
Sensor includes first sensor 1, second sensor 2 and 3rd sensor 3, and each sensor misses in measuring surface according to 3 circularity
The requirement of poor separation method is arranged.
It is to carry out as follows using the method that measuring device in the present embodiment realizes 3 cylindricity error separates：
Step 1, data acquisition：
Step 1.1, using the axial V-arrangement face center line for being Z axis, V blocks 4 of measured body 5 as Y-axis, established using left hand principle
Measuring coordinate system OXYZ；
Step 1.2, divided in an axial direction on measured body 5 M+2 measure section J, J=0,1 ..., M+1；Adjacent measure is cut
Axial distance between face is d；Define location K, K=1,2 ..., M；
Step 1.3, initialization K=1；
The J that step 1.4, mobile V blocks 4 make its measuring surface be located at measured body 5 measures section, J=K；
Step 1.5, measured body 5 pass one week clockwise or counterclockwise under the driving of its revolving support shafting using three
Sensor synchronizes the measurement data that acquisition obtains one week on the J measurements section of measured body, to complete the survey of K locations
Amount obtains the measurement data on the J measurements section of measured body；
K values are increased by 1 by step 1.6, judge whether K ＞ M are true, if not, return to step 1.4；If so,
It then indicates the measurement that whole locations are completed, obtains the measurement data of M location.
Step 2, data prediction：The measurement data on section is measured using J, according to 3 leading errors of frequency domain circularity
Separation method measures the J of measured body 5 the measurement data t of three sensor of section acquisition1(J,i)、t2(J, i) and t3(J,i)
It is weighted combination, due to the angle k of first sensor 1 and X-coordinate axle in 4 measuring surface of V blocks1× δ ≠ 0, as shown in Figure 1, because
And weighting coefficient c1=sin [(k3-k2) δ], c2=sin [(k1-k3) δ], c3=sin [(k2-k1) δ] so that in measurement in a closed series number
According toThe middle Radial Error Motion for rejecting measured body；And then it extracts and obtains J measurements section on measured body
The harmonic vector R (J, p) of face profile, p is harmonic order, 1 rank and N-1 ranks is not included in harmonic vector R (J, p), in harmonic wave
Vector R (J, p) includes the radial misalignment r on J measurement section profiles0(J) and deviation from circular from r1(J, i), and have：
r0(J)=R (J, 0)/N；
r1(J, i)=IDFT { [0,0, R (J, p), 0] }；
IDFT is inverse discrete Fourier transform operator, and i is the sampled point of sensor, i=0,1 ... N-1；N is sensor
The points of sampling in one week, the angular spacing δ between neighbouring sample point are：δ=2 π/N；
The J for obtaining measured body using the leading error separating method extraction of 3 frequency domain circularity measures the X-direction at section
1 order harmonics vector in error motion separating resultingSuch as formula (1.1)：
Wherein, T1(J, 1) and T2(J, 1) is 2 gathered data t of first sensor 1 and second sensor respectively1(J, i) and t2
The 1 order harmonics vector of (J, i), i.e.,：
T1(J, 1)=T1(J,p)|P=1；T1(J, p)=DFT { t1(J, i) } i, p=1,2 ..., N-1
T2(J, 1)=T2(J,p)|P=1；T2(J, p)=DFT { t2(J, i) } i, p=1,2 ..., N-1
DFT is discrete Fourier transform operator.
Since 1 order harmonics inhibit, 3 leading error separating methods of frequency domain circularity can not extract measured body 5 J measurements and cut
R (J, 1), is usually assigned a value of " zero ", and the true value of R (J, 1) is pushed at the section by 1 order harmonics vector R (J, 1) of face profile
X-direction error motion separating resulting 1 order harmonics vectorIn, i.e.,：
Formula (1.2) shows that J measures 1 order harmonics vector of the X-direction error motion separating resulting at sectionIt is
The J of measured body measures 1 order harmonics vector E of the X-direction error motion at sectionxThe true value of (J, 1) and the J of measured body are surveyed
The synthesis of 1 order harmonics vector R (J, 1) true value of section profile is measured, they are inseparable；And measured body J measures section exterior feature
The J of 1 order harmonics vector R (J, 1) the characterization measured bodies of shape measures least square center vector 2R (J, 1)/N of section profile,
This illustrates that 3 roundness fault separating methods in the prior art can not correctly extract each measurement section profile of measured body
Least square center vector 2R (J, 1)/N, it is more difficult to correct reconstruct by each section profile least square center vector 2R (J,
1) the curvature of space center line of measured body cylinder profile made of/N fittings.
In three cylindricity error separating methods of the present embodiment based on V blocks, as shown in Figure 1, utilizing three sensing on V blocks
Device acquisition obtains one week on the J measurements section of measured body measurement data t1(J,i)、t2(J, i) and t3(J, i), including
The profile r (J, i) in the section and J of measured body measures X and Y-direction error motion [e at sectionx(J,i),ey(J,i)]；
Since V blocks are placed on measured body when measuring, the J-1 and J+1 in double V-arrangement faces and measured body thereon measure section and are connect by 4 points
It touches；When being rotated under driving of the measured body in its revolving support shafting while keeping V blocks there is no the fine motion of Z axis and about the z axis micro-
Turn, then the J for the measured body that three sensors sense in V blocks measuring surface measures X and Y-direction error motion [e at sectionx(J,
i),ey(J, i)] J-1 and J+1 that come from measured body corresponding to four contact points measure section profile r (J-1, i) and r
The variation of (J+1, i), it is unrelated with the Radial Error Motion of revolving support shafting of driving measured body rotation.
As shown in Figure 1, setting in V blocks V-arrangement face angle degree as u δ；Since movement is opposite, if it is considered to V blocks in measurement process
It is fixed, then, four contact points that the J-1 and J+1 of measured body 5 measure double V-arrangement faces of section profile and V blocks should
Motionless, measured body J-1 and J+1 measures section profile r (J-1, i) and the variation of r (J+1, i) will cause measured body respectively
J-1 and J+1 measures the Radial Error Motion at section；Therefore：
From the first V-arrangement face of V blocks 4, there is equation (1.3)：
From the second V-arrangement face of V blocks 4, there is equation (1.4)：
R (J-1, i) and r (J+1, i) is that the J-1 and J+1 of measured body measure section profile respectively；[ex(J-1,i),ey
(J-1, i)] and [ex(J+1,i),ey(J+1, i)] it is that measured body J-1 and J+1 measure X and Y-direction error at section respectively
Movement；After being arranged to formula (1.3) and formula (1.4), the error that measured body measures the X-direction at section in J-1 and J+1 is obtained
Move ex(J-1, i) and ex(J+1, i) such as formula (1.5)：
Discrete Fourier transform is carried out to formula (1.5), takes its 1 rank (p=1) harmonic wave E respectivelyx(J-1,1) and Ex(J+1,1)
Such as formula (1.6)：
Formula (1.6) shows that the J-1 and J+1 of measured body measure the 1 order harmonics vector point of the X-direction error motion at section
It is not the negative value that the J-1 and J+1 of the measured body measure 1 order harmonics vector of section profile；In view of measured body is rigid body,
Upper J measures the error motion e of the X-direction at sectionx(J, i) such as formula (1.7) characterizes：
Discrete Fourier transform is carried out to formula (1.7), takes its 1 rank (p=1) harmonic wave, then the J of measured body is measured at section
X-direction error motion 1 order harmonics vector Ex(J, 1) such as formula (1.8) characterizes：
Formula (1.8) presents measured body J and measures J-1 and J+1 that the error motion at section comes from the measured body
Measure the variation of section profile.
Step 3 is calculated as follows the 1 order harmonics vectors for obtaining all measurement section profiles on measured body：
Step 3.1, initialization
For the 1st location, i.e. K=1, the measuring surface of V blocks is in the 1st of measured body and measures axial position where section, V blocks
The first V-arrangement face be in measured body the 0th measure section where axial position, the second V-arrangement face of V blocks is in the 2nd of measured body the
Axial position where measuring section；
Setting：The 0th of measured body measures section and the 2nd and measures the 1 order harmonics vector R (0,1) and R (2,1) of section profile
Be zero, i.e. R (0,1)=0, R (2,1)=0；And it sets：The 1st of measured body measures 1 rank of the X-direction error motion at section
Harmonic vector Ex(1,1) is zero, i.e. Ex(1,1)=0；Then, the 1st of measured body measures 1 order harmonics vector R (1,1) of section profile
For：1 rank in the X-direction error motion separating resulting at section is measured for the 1st of measured body
Harmonic vector, the measurement data specifically acquired from three sensor of the 1st location are calculated using formula (1.1) and are obtained；
It is used to characterize the 2nd of the measured body difference for measuring the least square center that section measures section profile with the 1st as a result,
Vector Δ R1(1,1) it is：
Step 3.2 is directed to the 2nd location, i.e. K=2；
Step 3.3, from the measurement data of three sensor synchronous acquisition of K locations, acquisition quilt can be calculated using formula (1.1)
The J=K for surveying body measures 1 order harmonics vector of the X-direction error motion separating resulting at sectionThen by formula (1.2)
The J that measured body can be obtained measures 1 order harmonics vector E of the X-direction error motion at sectionx(J, 1) such as formula (1.9) institute table
Sign：
In this Δ RK(J-1,1)=R (J, 1)-R (J-1,1) are characterized in the J and J-1 of the measured body of K locations acquisition
Measure the least square centered difference vector of section profile；Because preventing the rotation of V blocks 4 about the z axis in measurement process, then Δ RJ
(J-1,1) J and J-1 that should be equal to the measured body that previous location is obtained measure the least square equation of the ecentre of section profile
Resolute Δ RK-1(J-1,1), because the least square centered difference vector of the adjacent two measurements section profile of measured body immobilizes
It is the essential attribute of rigid body；Therefore the X-direction error motion obtained at the J=K measurements section of measured body is calculated using formula (1)
1 order harmonics vector Ex(J,1)
From formula (1.8), 1 order harmonics vector R (J+ of the J+1 measurement section profiles for obtaining measured body are calculated using formula (2)
1,1)
R (J+1,1)=- [2Ex(J,1)+R(J-1,1)] (2)
The measurement sections J+1 for obtaining characterization measured body are calculated using formula (3) and J measures the least square of section profile
Centered difference vector Δ RK(J,1)
ΔRK(J, 1)=R (J+1,1)-R (J, 1) (3)
K values are increased by 1, and judge whether K ＞ M are true by step 3.4, if not, return to step 3.3；If at
It is vertical, then it represents that the calculating of all 1 order harmonics vectors for measuring section profile is completed, realizes that 3 cylindricities based on V blocks are missed
Difference from.
Reconstructing method about cylinder profile curvature of space center line：
Using in the present embodiment 3 cylindricities based on V blocks are realized about the method for realizing 3 cylindricity error separates
Error separate obtains all 1 order harmonics vector R (J, 1) for measuring section profile on measured body 5；
If in measurement process measured body 5 be rotate clockwise, then on measured body 5 J measure section profile least square
Center vector is 2R (J, N-1)/N, conversely, being 2R (J, 1)/N；
According to Fourier transform principle, J measures the N-1 order harmonics vectors R (J, N-1) of section profile and is sweared for 1 order harmonics
Measure the conjugate vector of R (J, 1)；By total M+2 least square center vector 2R (J, N-1)/N, or most by total M+2
The curve that small two vertex for multiplying center vector 2R (J, 1)/N are connected in sequence is curved as the space of the cylinder profile of measured body 5
Bent center line.
Reconstructing method about cylinder profile：
The p order harmonics vectors R of section profile is measured using the J that 3 leading error separating methods of frequency domain circularity are obtained
(J, p), wherein not including 1 rank and N-1 ranks；1 rank that section profile is measured using J on iterative (2) obtained measured body is humorous
Wave vector R (J, 1) and its conjugation R (J, N-1), using IDFT inverse discrete Fourier transforms, reconstruct measured body 5 is measured from the 1st and is cut
Face measures one section of cylinder profile r (J, i) in section to M
R (J, i)=IDFT [R (J, p)] p=0,1,2 ..., N-1 (4).
Cause is in the 1st location, if 1 order harmonics vector of the 0th and the 2nd measurement section profile of measured body 5 is set to R
(0,1)=0 and R (2,1)=0, this makes the establishment of coordinate system for reconstructing measured body curvature of space center line exist：Origin is located at measured body
The 0th of 5 measure 1 order harmonics vector R (0,1) of section profile the specified position of true value, if measured body 5 the 0th and the 2nd measures
The true value of 1 order harmonics differential vector R (2,1)-R (0,1) of section profile is Δ R2,0, then trivector [Δ R2,0, d] and it determines
Reconstruct the Z-direction of coordinate system；Thus the measured body curvature of space center line profile reconstructed occur as a whole micro-shifting and
Low dip will not cause the measured body cylinder profile that measurement reconstructs to deform；In measurement process, current location V blocks
The axial position of first V-arrangement face and measuring surface distinguishes the axis with the measuring surface of previous location V blocks and the second V-arrangement face correspondingly
It is overlapped to position；When measurement, measured body rotation, V blocks Z axis to circumferencial direction should all remains stationary state, may be used sharp
Optical measurement techniques position the axial position of V blocks, and monitor the V blocks micro-shifting that may be present along Z axis in measurement process
About the z axis micro- turn.
Claims (5)
1. a kind of 3 cylindricity measuring devices based on V blocks, it is characterized in that：
The cylindricity measurement refers to carrying out cylindricity measurement for cylindrical measured body (5)；
The measuring device is using measured body (5) external cylindrical surface in an axial direction as guide rail, is the test aircraft that slides axially with V blocks (4),
Sensor is provided on the V blocks, the sliding test aircraft is supported on using the V-arrangement face of V blocks on the external cylindrical surface of measured body (5),
Using V blocks by the axial movement at setting interval, the corresponding location for measured body (5) is obtained；On the location, measured body
(5) it rotates a circle in the driving of its revolving support shafting, V blocks keep circumferential position constant, and keep its V-arrangement face and measured body
(5) external cylindrical surface is in contact.
2. 3 cylindricity measuring devices according to claim 1 based on V blocks, it is characterized in that：
The V blocks are set as double V-arrangement faces structure, and section where the central point in V block axial directions is the measuring surface (4- for installing sensor
3), the left and right sides for being in the measuring surface is symmetrically divided in the first V-arrangement face (4-1) and the second V-arrangement face (4-2), forms double V-arrangement faces knots
Structure；And have：
Axial distance between first V-arrangement face and measuring surface is d；Axial distance between second V-arrangement face and measuring surface is d；
The axial movement step pitch of the V blocks is d；Axial distance on the measured body between adjacent location is d；
The sensor includes first sensor (1), second sensor (2) and 3rd sensor (3), and each sensor is in the survey
It is arranged according to the requirement of 3 roundness fault separating methods on amount face.
3. the method for realizing 3 cylindricity error separates using the measuring device described in claim 2, it is characterized in that by as follows
Step carries out：
Step 1, data acquisition：
Step 1.1, using the axial direction of measured body (5) as Z axis, V blocks (4) V-arrangement face center line for Y-axis, using left hand principle establish
Measuring coordinate system OXYZ；
Step 1.2, divided in an axial direction on the measured body M+2 measure section J, J=0,1 ..., M+1；Adjacent measurement section
Between axial distance be d；Define location K, K=1,2 ..., M；
Step 1.3, initialization K=1；
The J that step 1.4, mobile V blocks make its measuring surface be located at measured body measures section, J=K；
Step 1.5, measured body its revolving support shafting driving under one week clockwise or counterclockwise, using three sensors into
The J that row synchronous acquisition obtains the measured body measures one week on section measurement data, so that the measurement of K locations is completed,
Obtain the measurement data on the J measurements section of the measured body；
K values are increased by 1 by step 1.6, judge whether K ＞ M are true, if not, return to step 1.4；If so, then table
Show the measurement that whole locations are completed, obtains the measurement data of M location；
Step 2, data prediction：The measurement data on section is measured using the J, according to 3 leading errors of frequency domain circularity
Separation method extraction obtains the harmonic vector R (J, p) that J on measured body measures section profile, and p is harmonic order, is sweared in harmonic wave
It measures and does not include 1 rank and N-1 ranks in R (J, p), include the radius on J measurement section profiles in the harmonic vector R (J, p)
Deviation r0(J) and deviation from circular from r1(J,i)；The J of measured body is obtained using the leading error separating method extraction of 3 frequency domain circularity
Measure 1 order harmonics vector in the X-direction error motion separating resulting at sectionI is the sampled point of sensor, i=
0,1,…N-1；N is the points of sensor sampling in one week, and the angular spacing δ between neighbouring sample point is：δ=2 π/N；
Step 3 is calculated as follows the 1 order harmonics vectors for obtaining all measurement section profiles on the measured body：
Step 3.1, initialization
For the 1st location, i.e. K=1, the measuring surface of the V blocks is in the 1st of measured body and measures axial position where section, V blocks
The first V-arrangement face be in measured body the 0th measure section where axial position, the second V-arrangement face of V blocks is in the 2nd of measured body the
Axial position where measuring section；
Setting：The 0th of the measured body measures section and the 2nd and measures the 1 order harmonics vector R (0,1) and R (2,1) of section profile
Be zero, i.e. R (0,1)=0, R (2,1)=0；And it sets：The 1st of the measured body measures the X-direction error motion at section
1 order harmonics vector Ex(1,1) is zero, i.e. Ex(1,1)=0；Then, the 1st of the measured body measures 1 order harmonics of section profile
Vector R (1,1) is： The X-direction error motion at section is measured for the 1st of measured body detaches knot
1 order harmonics vector in fruit；
It is used to characterize the 2nd of the measured body difference for measuring the least square center that section measures section profile with the 1st as a result,
Vector Δ R1(1,1) it is：
Step 3.2 is directed to the 2nd location, i.e. K=2；
Step 3.3 calculates 1 order harmonics for obtaining the X-direction error motion at the J=K measurements section of measured body using formula (1)
Vector Ex(J,1)
1 order harmonics vector R (J+1,1) of the J+1 measurement section profiles for obtaining measured body is calculated using formula (2)
R (J+1,1)=- [2Ex(J,1)+R(J-1,1)] (2)
It is calculated using formula (3) and obtains the least square that the measurement sections J+1 for characterizing the measured body measure section profile with J
Centered difference vector Δ RK(J,1)
ΔRK(J, 1)=R (J+1,1)-R (J, 1) (3)
K values are increased by 1, and judge whether K ＞ M are true by step 3.4, if not, return to step 3.3；If so, then
It indicates the calculating that all 1 order harmonics vectors for measuring section profile are completed, realizes 3 o'clock cylindricity error minute based on V blocks
From.
4. a kind of reconstructing method of cylinder profile curvature of space center line, it is characterized in that：
3 cylindricity error separates based on V blocks are realized according to claim 3 the method, are obtained on the measured body (5)
All 1 order harmonics vector R (J, 1) for measuring section profile；
If in measurement process measured body (5) be rotate clockwise, then on measured body (5) J measure section profile least square
Center vector is 2R (J, N-1)/N, conversely, being 2R (J, 1)/N；
According to Fourier transform principle, the N-1 order harmonics vectors R (J, N-1) that J measures section profile is 1 order harmonics vector R
The conjugate vector of (J, 1)；By least square center vector 2R (J, N-1)/N of total M+2, or by total M+2 minimums
The curve that two vertex for multiplying center vector 2R (J, 1)/N are connected in sequence is curved as the space of the cylinder profile of measured body (5)
Bent center line.
5. a kind of reconstructing method of cylinder profile, it is characterized in that：
The p order harmonics vectors R (J, p) that section profile is measured using the J that step 2 in claim 3 is obtained, wherein not including
1 rank and N-1 ranks；And using step 3 in claim 3 obtain J on measured body measure section profile 1 order harmonics vector R (J,
1) and its conjugation R (J, N-1) is reconstructed measured body (5) and is measured section to M surveys from the 1st using IDFT inverse discrete Fourier transforms
Measure one section of cylinder profile r (J, i) in section
R (J, i)=IDFT [R (J, p)] p=0,1,2 ..., N-1 (4).
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| CN111113018A (en) * | 2019-12-25 | 2020-05-08 | 厦门理工学院 | Precise shaft butt joint equipment and precise shaft butt joint method |
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