CN105758285A - Online measurement reconstruction method for large-scale cylinder profile based on parallel error separation method - Google Patents

Abstract

The invention discloses an online measurement reconstruction method for a large-scale cylinder profile based on a parallel error separation method, and the reconstruction method comprises the steps: extracting the relative change amount of the geometric meter of two adjacent measurement section circles through the parallel error separation of three axial sections; obtaining the geometric center of each measurement section circle through stacking, thereby achieving the reconstruction of a cylinder profile through taking the connection line of the geometric centers of all measurement section circles of a measured shaft as the reference axis. The method can achieve the high-precision measurement and evaluation of the circular degree, cylindricity, bus linearity and taper of the cylinder profile based on the above. The method can the full-harmonic separation of radial rotation error movement and guide rail linear error movement of a shaft system in a measurement process, guarantees the high-precision measurement reconstruction of the cylinder profile, and reduces the manufacture cost of online measurement equipment of the large-scale cylinder profile.

Description

Large cylindrical profile on-line measurement reconstructing method based on parallel error separation method

Technical field

The present invention relates to Precision Inspection and large-scale on-line measurement equipment Design manufactures field, specifically a kind of large cylindrical profile on-line measurement reconstructing method based on parallel error separation method.

Background technology

Big axle is an important large-scale component of class in large-scale high-end equipment manufacture, such as, on the production equipment of large scale solar panel, liquid crystal display screen, autobody sheet, high-quality paper and industry composite board etc., large-scale precision beaming roller is the core component of equipment, its profile precision, is determine the key factor of product quality (sheet material precision), the technical merit indicating a high-end equipment manufacture of country and international competitiveness including circularity, cylindricity, bus linearity and tapering etc..

Due to enormous size (Φ 0.3～1.0m, length 3～8m), must adopt online (in place, side) metering system, measurement system must relate to supporting the rotary axis system that tested big axle rotates and the line slideway supporting test aircraft axially-movable, how eliminating the impact on measuring of the error motion of axle system and guide rail to improve profile certainty of measurement is the most noticeable key issue [Sun Jia in macrotype axes series parts profile measuring technology in recent years, Zhang Lei. the measuring method [J] of large-diameter workpiece. machinery and electronics, 2006 (3): pp12～15] [Li Huipeng, Zhang Jun, Tang Wenyan etc. large scale revolving body profile point coordinates and centroidal axis measure the development [J] of system. Chinese journal of scientific instrument, Vol.25No.5, 2005 (5): pp534～536].Error separating technology (ErrorSeparationTechniques, EST) [Li Shengyi during flat shape (circularity and linearity) is measured it is widely used to, Dai Yifan waits. Precision and Ultra-precision Machining detection in place and error separating technology [M]. and publishing house of the National University of Defense technology, 2007], it uses certain measurement technology and mathematical method, circularity is separated with shafting ratdial rotating error motion, linearity and guide rail straight line error motion, improves shape measure precision greatly.But, due to EST inherent shortcoming: single order harmonics restraint, make its order harmonic component being difficult to when being applied to cylinder profile on-line measurement properly separate out measurement system center shafting Radial Error Motion, cause the geometric center that cannot correctly extract each measurement cross section circle, the datum axis (being frequently not straight line) of the line structure being finally difficult to the correct geometric center (order harmonic component of cross sectional shape) realized with each measurement cross section circle carrys out reconstruction cylinder profile [Hong Maisheng, Li Zijun, Li Jishun etc. the purification [J] of cylindricity surface profile reconstruction datum. Shanghai Communications University's journal, 2002, 36 (8): 1068～1070].

Summary of the invention

In order to overcome existing EST inherent shortcoming, the present invention proposes a kind of based on parallel error separation method (ParallelErrorSeparationTechniques, PEST) large cylindrical profile on-line measurement reconstructing method, the full harmonic wave separation of Radial mixing motion and guide rail straight line error motion to realize measurement process center shafting, to ensure that cylinder profile is measured the high accuracy of reconstruct, reduced the manufacturing cost that large cylindrical profile on-line measurement is equipped.

The present invention solves that technical problem adopts the following technical scheme that

A kind of large cylindrical profile on-line measurement reconstructing method based on parallel error separation method of the present invention, being be applied to be moved in X-Z direction by Z guide rail and X guide rail common support measurement bay, support axle system support and drive measured body to rotate in the measurement system formed, described Z guide rail is axially in parallel with described measured body；And support measurement bay moving step pitch along the Z direction is d；It is characterized in that described on-line measurement reconstructing method is to carry out as follows:

Step 1, data acquisition:

Step 1.1, arranging cross section, three, left, center, right on measurement bay, described three cross section orthogonal are in described Z guide rail moving direction, and the distance between three cross sections is d；Middle section configures three sensors according to 3 roundness error separation measuring methods, including: first sensor, the second sensor and the 3rd sensor；

Step 1.2, on left cross section and right section, it is each configured with the 4th sensor and the 5th sensor in X direction；

Step 1.3, described measured body divide M vertically and measures cross section；Each distance measured between cross section is d；Definition location J；J=1,2 ..., M；

Step 1.4, initialization J=1；

Step 1.5, traverse measurement frame, make middle section on described measurement bay be positioned at measured body J and measure on cross section；

Step 1.6, move described measured body and rotate a circle by supporting axle frenulum so that described first sensor, the second sensor and the 3rd sensor can gather the measurement data of a week on described measured body J measurement cross section；Measured body J-1 described in described 4th sensor acquisition measures the measurement data of a week on cross section；Measured body J+1 described in described 5th sensor acquisition measures the measurement data of a week on cross section；Thus completing the measurement of J location, it is thus achieved that the measurement data of J location；The measurement data of described J location includes: the right section data of the middle section data of J location, the left cross-section data of J location and J location；

Step 1.7, J+1 is assigned to J, and judges whether J > M sets up, if setting up, then it represents that complete the measurement of M location；Obtain the measurement data of M location；Otherwise, return step 1.5 order to perform；

Step 2, data prediction:

Step 2.1, middle section data according to J location, utilize 3 leading roundness fault separating methods of frequency domain to extract described measured body J and measure the circularity r on cross section₂(z_J, i) with radius relative value r₀(z_J)；Obtain described measured body J simultaneously and measure the order harmonic component that cross section X-direction is beated in separating resultingz_J=J × d represents that described measured body J measures the axial location in cross section；I represents the period of any sensor sampling in a week；I=0,1 ... N-1；N represents counting of any sensor sampling in a week, and the angular spacing of sampling is δ=2 π/N；

Step 2.2, respectively left cross-section data and right section data to J location carry out discrete Fourier transform, obtain an order harmonic component of transformation resultsWith

Step 3, calculate on described measured body M the order harmonic component measuring cross sectional shape:

Step 3.1, initialization J=1；

Step 3.2, move described measured body and rotate a circle by supporting axle frenulum, if the estimated value of adjacent two order harmonic component measuring the difference beated on cross sections of measured body that the Obliquity error movement that described support axle system is in X direction causes is δ¹=C；

Step 3.3, formula (1) is utilized to extract the described measured body J relative variation Θ measuring an order harmonic component of cross sectional shape and J-1 measurement cross sectional shape_J:

${\mathrm{\Θ}}_J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-C---\left(1\right)$

Step 3.4, set described measured body J-1 and measure an order harmonic component of cross sectional shape as R (z_J-1, 1) and=B, utilize formula (2) to calculate described measured body J and measure an order harmonic component R (z of cross sectional shape_J, 1):

R(z_J, 1) and=R (z_J-1,1)+Θ_J=B+ Θ_J(2)

Step 3.5, J+1 is assigned to J, and judges whether J > M sets up, if setting up, then it represents that completed the calculating of an order harmonic component of M measurement cross sectional shape；Otherwise, step 3.6 is performed；

Step 3.6, described support axle frenulum move described measured body and rotate a circle；Formula (3) is utilized to calculate the described support axle system Obliquity error movement in X direction estimated value δ in adjacent two order harmonic component measuring the difference that cross sections cause to beat of J location^J:

${\mathrm{\δ}}^J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-\[T_5^{J-1}(z_J,1)-{\hat{E}}_x(z_{J-1},1)\]+{\mathrm{\δ}}^{J-1}---\left(3\right)$

Step 3.7, utilize formula (4) to extract measured body J to measure the relative variation Θ that cross sectional shape and J-1 measure an order harmonic component of cross sectional shape_J:

${\mathrm{\Θ}}_J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-{\mathrm{\δ}}^J---\left(4\right)$

Step 3.8, utilize formula (5) calculate described measured body J measure cross sectional shape an order harmonic component R (z_J, 1):

$R(z_J,1)=R(z_{J-1},1)+{\mathrm{\Θ}}_J=B+\underset{j=1}{\overset{J}{\Σ}}{\mathrm{\Θ}}_j---\left(5\right)$

Step 3.9, return step 3.5 perform；

Step 4, extract on described measured body M the order harmonics measuring cross sectional shape:

Step 4.1, with measured body J measure cross sectional shape an order harmonic component R (z_J, 1), and utilize formula (6) to build sequence Γ (z_J, k):

$\mathrm{\Γ}(z_J,k)=\left\{\begin{array}{cc}R(z_J,1)& k=1\\ 0& k=0,2,3,...N-2\\ \stackrel{\‾}{R}(z_J,1)& k=N-1\end{array}\right.,J=1,2,...,M---\left(6\right)$

In formula (6),Represent R (z_J, 1) conjugation；

Step 4.2, utilize formula (7) to described sequence Γ (z_J, k) carry out inverse discrete Fourier transform, thus extracting described measured body J to measure an order harmonics r of cross sectional shape₁(z_J, i):

r₁(z_J, i)=IDFT [Γ (z_J, 1)] J=1,2 ..., M (7)

Step 5, formula (8) is utilized to reconstruct the cylinder profile r (z of described measured body_J, i):

r(z_J, i)=r₀(z_J)+r₁(z_J,i)+r₂(z_J, i) J=1,2 ..., M (8).

Compared with the prior art, the present invention has the beneficial effect that:

1, the Technology Ways of the parallel error separation method that the present invention proposes is: by the parallel error separate to axial three section gauge results, extract the relative variation of adjacent two geometric centers measuring cross section circle, due to this change sign relatively is adjacent two characteristics measuring that cross sectional shapes are intrinsic, even if the Radial Error Motion supporting axle system each week does not repeat, the relative variation extracting adjacent two geometric centers measuring cross section circle is not constituted impact, each geometric center measuring cross section circle is obtained again through superposition, this Technology Ways is the innovation on error separate theory is higher level.

2, the present invention has abandoned the motion of existing method shaft Radial mixing and has had the constraint of good reproducibility, when axle system Radial Error Motion do not have repeat weekly, parallel error separating method by 3 roundness fault separating methods and axial three cross sections, realize Radial mixing motion and the guide rail full harmonic wave separation of straight line error motion of measurement process center shafting, this is one of parallel error separating method innovation of being different from existing error separating method, is also the parallel error separating method key point that ensures cylinder profile on-line measurement High precision reconstruction.

3, the parallel error separating method that the present invention proposes does not require that axle system Radial Error Motion has repeatability, when relatively low axle system rotating accuracy and relatively low guide rail movement precision, it is also possible to realize the correct relative variation extracting each adjacent two geometric centers measuring cross section circle.Therefore, axle system corresponding in measurement system and guide rail not being had high-precision requirement, and This effectively reduces the manufacturing cost of large cylindrical profile on-line measurement equipment, this is the economic worth place of the present invention.

4, the measuring method of the present invention belongs to the section gauge method of cylinder profile, achieve the reconstruct meeting cylinder profile mathematical model, cylindrical shape error can be carried out on this basis: the error evaluation of circularity, cylindricity, bus linearity and tapering, therefore be widely used.

In sum, the present invention parallel error separate by axial three cross sections, can correctly extract the relative variation that the geometric center of cross section circle measured by tested cylinder each adjacent two, and the value of each geometric center measuring cross section circle is obtained by superposition, thus solving the correct extraction problem of each geometric center measuring cross section circle in large cylindrical profile on-line measurement, and then achieve the cylinder profile using the line separating each geometric center measuring cross section circle obtained as datum axis (being frequently not straight line) and reconstruct, substantially increase the on-line measurement precision of large cylindrical profile.

Accompanying drawing explanation

Fig. 1 is the parallel error separation method measuring principle figure of the present invention；

Fig. 2 is based on the front view of the side formula cylinder profile measurement apparatus that the present invention sets up；

Fig. 3 is based on the side view of the side formula cylinder profile measurement apparatus that the present invention sets up；

Number in the figure: 1 first sensor；2 second sensors；3 the 3rd sensors；4 the 4th sensors；5 the 5th sensors；6 measured bodies；7 support axle system；8 measurement bays；9X guide rail；10Z guide rail.

Detailed description of the invention

In the present embodiment, as in figure 2 it is shown, measurement bay 8 can carry out the movement in X-Z direction under the common support of Z guide rail 10 and X guide rail 9；Support axle system 7 support and drive measured body 6 to rotate；Z guide rail 10 is parallel to the axial of measured body 6.Measuring when starting, measurement bay 8 in X direction near measured body 6, move into location along Z-direction under X guide rail 9 supports under Z guide rail 10 supports, and the moving step pitch that measurement bay 8 is along the Z direction is d.In being embodied as, a kind of large cylindrical profile on-line measurement reconstructing method based on parallel error separation method, extract measured body 6 each circularity measuring cross section and relative radius by 3 roundness error separations；Parallel error separate by axial three cross sections, extract the relative variation of adjacent two geometric centers measuring cross section circle, each geometric center (order harmonic component of cross sectional shape) measuring cross section circle is obtained again through superposition, and then realize the line respectively measuring the geometric center of cross section circle using measured axis and reconstruct as the cylinder profile of datum axis (being frequently not straight line), the high-acruracy survey evaluation of the circularity of cylinder profile, cylindricity, bus linearity and tapering can be carried out on this basis, specifically say and carry out as follows:

Step 1, data acquisition:

Step 1.1, seeing Fig. 1 and Fig. 3, be provided with cross section, three, left, center, right on measurement bay 8, in Z guide rail 10 axially, and the distance between three cross sections is d to three cross section orthogonal；Middle section configures three sensors according to 3 circularity error separation methods, including: first sensor the 1, second sensor 2 and the 3rd sensor 3；

3 circularity error separation methods that the present invention adopts and existing method [Li Jishun, Wang Zhongyu, Lin Minzhu. the microtechnic [M] in manufacturing engineering. Beijing: China Machine Press, 2001.4] difference be in that: the angle p of first sensor 1 and X-coordinate axle on measurement bay 8 middle section₁× δ ≠ 0, sees Fig. 1, and wherein, δ=2 π/N is the angular spacing of sampling；N is counting of any sensor sampling in a week.The purpose being configured so that is when measuring task requires that on measured body 6, the two distance d measuring between cross section are less, leaves Z-direction installing space to the 4th sensor 4 and the 5th sensor 5；It addition, in order to avoid the non-single order harmonics restraint of 3 circularity error separation methods, p₁,p₂,p₃Selection principle be: p₁,p₂For positive integer, p₃For negative integer, (p₂-p₁) and (p₁-p₃) for prime number.

Step 1.2, on left cross section and right section, it is each configured with the 4th sensor 4 and the 5th sensor 5 in X direction；

Seeing Fig. 1 and Fig. 3, the left, center, right three on measurement bay 8 is measured and is respectively configured 1,3 and 1 sensor on cross section, hereon referred to as the parallel 131 pattern measurement bays in three cross sections.It is of course possible to according to the requirement of concrete measuring task and the constraint measuring environment, designing parallel 113 patterns in three cross sections or 311 pattern measurement bays, the present invention proposes technical scheme and is capable of the Radial mixing motion of measurement process center shafting and the full harmonic wave separation of guide rail straight line error motion equally.

Step 1.3, measured body 6 divide M vertically and measures cross section；Each distance measured between cross section is d；Definition location J；J=1,2 ..., M；

Step 1.4, initialization J=1；

Step 1.5, traverse measurement frame 8, make middle section on measurement bay 8 be positioned at measured body 6 J and measure on cross section；

Step 1.6, rotate a circle by supporting axle system 7 drive measured body 6 so that first sensor the 1, second sensor 2 and the 3rd sensor 3 can gather measured body 6 J and measure the measurement data of a week on cross section；4th sensor 4 gathers measured body 6 J-1 and measures the measurement data of a week on cross section；5th sensor 5 can gather measured body 6 J+1 and measure the measurement data of a week on cross section；Thus completing the measurement of J location, it is thus achieved that the measurement data of J location；The measurement data of J location includes: the right section data of the middle section data of J location, the left cross-section data of J location and J location；

Step 1.7, J+1 is assigned to J, and judges whether J > M sets up, if setting up, then it represents that complete the measurement of M location；Obtain the measurement data of M location；Otherwise, return step 1.5 order to perform；

Step 2, data prediction:

Step 2.1, middle section data according to J location, utilize 3 leading roundness error separation methods of frequency domain to extract measured body 6 J and measure the circularity r on cross section₂(z_J, i) with radius relative value r₀(z_J)；z_J=J × d represents that measured body 6 J measures the axial location in cross section；I represents the period of any sensor sampling in a week；I=0,1 ... N-1；N represents counting of any sensor sampling in a week, and the angular spacing of sampling is δ=2 π/N；

It should be noted that 3 leading roundness fault separating methods of frequency domain are difficult to extract absolute radius, relative radius r₀(z_J) value is on cylinder profile reconstruct not impact.

Apply 3 leading roundness fault separating method [Li Shengyi of frequency domain, Dai Yifan waits. Precision and Ultra-precision Machining detection in place and error separating technology [M]. and publishing house of the National University of Defense technology, 2007] measurement data of measurement bay 8 middle section three sensor acquisition is weighted combination, at this, due to the angle p of first sensor 1 and X-coordinate axle on measurement bay 8 middle section₁× δ ≠ 0, sees Fig. 1 and Fig. 3, therefore weighting coefficient c₁=sin [(p₃-p₂) δ], c₂=sin [(p₁-p₃) δ], c₃=sin [(p₂-p₁) δ] can make composite signal is rejected the Radial mixing motion supporting axle system 7 and guide rail 10 straight line error motion, it is achieved effective error separate.

Obtain measured body 6 J to measure cross section X-direction and beat the order harmonic component in separating resulting simultaneously

At this, two problems are had to need to explain, one is that the error motion supported on axle system 7X direction makes measured body 6 entirety produce translation and yaw motion in X-direction, cause on measured body 6 a certain measurement cross section to produce X-direction to beat, beat and measure the difference of axial location in cross section with J on measured body 6 and different；Two is that 3 leading roundness error separation methods of frequency domain cannot extract measured body 6 J and measure an order harmonic component R (z of cross sectional shape due to single order harmonics restraint_J, 1), it is generally recognized that it is " zero " that measured body 6 J measures an order harmonic component of cross sectional shape separating resulting, and by R (z_J, 1) true value push an order harmonic component of separating resulting of beatingIn, namely

${\hat{E}}_x(z_J,1)=R(z_J,1)+E_x^J(z_J,1)---\left(1\right)$

Formula (1) explanationIt is that the error motion supporting axle system 7X direction measures, at measured body 6 J, the order harmonic component that the X-direction that causes of cross section is beatedWith the order harmonic component R (z that measured body 6 J measures cross sectional shape_J, 1) synthesis, this, claimMeasure cross section X-direction for measured body 6 J to beat an order harmonic component of separating resulting.

Step 2.2, respectively left cross-section data and right section data to J location carry out discrete Fourier transform, take an order harmonic component of transformation resultsWith

At J location, measured body 6 rotates a circle, and the 4th sensor 4 and the 5th sensor 5 gather measured body 6 J-1 and J+1 respectively and measure cross section one weekly data:

$\begin{array}{c}{t}_4^J(z_{J-1},i)=r(z_{J-1},i)-D_4+e_x(z_{J-1},i)+{\mathrm{\ϵ}}_x\left(z_{J-1}\right)\\ t_5^J(z_{J+1},i)=r(z_{J+1},i)-D_5+e_x(z_{J+1},i)+{\mathrm{\ϵ}}_x\left(z_{J+1}\right)\end{array}---\left(2\right)$

In formula (2): r (z_J-1,i),r(z_J+1, i) i=0,2 ..., N-1 is that measured body 6 J-1 and J+1 measures cross sectional shape；D₄,D₅It it is the zero-bit of the 4th sensor 4 and the 5th sensor 5；e_x(z_J-1,i),e_x(z_J+1, what i) the X-direction error motion for supporting axle system 7 caused on measured body 6 J-1 and J+1 measurement cross section beats；ε_x(z_J-1),ε_x(z_J+1) cause the X-direction of measurement bay 8 to offset for Z guide rail 10 straight line error motion at measured body 6 J-1 and J+1 measurement cross section axial location；It is that on the measured body 6 of the 4th sensor 4 and the collection of the 5th sensor 5, J-1 and J+1 measures cross section one weekly data respectively.

IfWithDiscrete Fourier transform respectivelyWithFormula (2) both sides are carried out discrete Fourier transform, and take k=1, have:

$\begin{array}{c}{T}_4^J(z_{J-1},1)=R(z_{J-1},1)+E_x^J(z_{J-1},1)\\ T_5^J(z_{J+1},1)=R(z_{J+1},1)+E_x^J(z_{J+1},1)\end{array}---\left(3\right)$

Owing to the straight line error motion of Z guide rail 10 causes the X-direction skew ε of measurement bay 8_x(z_J-1),ε_x(z_J+1) it is a constant for one week signal, see formula (2), and an order harmonic component of the discrete Fourier transform of constant is " zero ", formula (1) and formula (3) therefore eliminate the straight line error motion of guide rail 10 impact on measurement naturally.

Obviously, at J location, obtain measured body 6 J-1 by the 4th sensor 4 and measure an order harmonic component R (z of cross sectional shape_J-1, 1) and measure, at measured body 6 J-1, the order harmonic component that the X-direction that cross section causes is beated with the error motion supported on axle system 7X directionSynthesisIn like manner, by the 5th sensor 5, it is thus achieved that J+1 measures an order harmonic component R (z of cross sectional shape_J+1, 1) and measure, at measured body 6 J+1, the order harmonic component that the X-direction that cross section causes is beated with the error motion supported on axle system 7X directionSynthesisIt addition, by first sensor the 1, second sensor 2 and the 3rd sensor 3, it is thus achieved that measured body 6 J measures cross section X-direction and beats an order harmonic component of separating resultingFormula (1) is subtracted formula (3) first formula, formula (3) second formula is subtracted formula (1), have

$\begin{array}{c}{\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)=R(z_J,1)-R(z_{J-1},1)+E_x^J(z_J,1)-E_x^J(z_{J-1},1)\\ T_5^J(z_{J+1},1)-{\hat{E}}_x(z_J,1)=R(z_{J+1},1)-R(z_J,1)+E_x^J(z_{J+1},1)-E_x^J(z_J,1)\end{array}---\left(4\right)$

In formula (4), R (z_J,1)-R(z_J-1, 1) and it is the measured body 6 J amount of change measuring that an order harmonic component of cross sectional shape measures an order harmonic component of cross sectional shape relative to J-1；R(z_J+1,1)-R(z_J, 1) and it is that the J+1 of measured body 6 measures an order harmonic component of cross sectional shape and measures the amount of change of an order harmonic component of cross sectional shape relative to J；Measuring on the axial location of cross section at measured body 6 J, the centre of gyration measuring cross section with J builds XOY coordinate system, 2 × R (z for zero_J, 1)/N be measured body 6 J measure cross section circle Geometric center coordinates；Therefore R (z can be used_J,1)-R(z_J-1, 1) and R (z_J+1,1)-R(z_J, 1) and it is characterized in J location measured body 6 J and the J-1 relative variability amount measuring the geometric center of cross section circle and J+1 and J measurement cross section circle respectively；WithThe X-direction error motion supporting axle system 7 when being measured body rotation in 6 one weeks measures an order harmonic component of the difference beated on cross sections at measured body 6 adjacent two." axle ties up to X and Y-direction has purely radial error motion x (θ), y (θ) and axial error motion z (θ) and the Obliquity error movement along X and Y-axis in definition according to international machinery production EASD CIRP shaft error motion", then:

Wherein, θ=i × δ；x^J(z_J, θ) andIt is characterized in J location and supports beat (purely radial error motion) and the Obliquity error movement along X-axis that axle system 7X direction Error-motion in Rotation causes on measured body 6 J measurement cross section.Obviously,WithIn eliminated the same section beated on two adjacent measurement cross sections of measured body 6 of X-direction Error-motion in Rotation supporting axle system 7, namely eliminate the purely radial error motion supporting axle system 7 in X-direction, therefore δ^JIt is characterized in when J location measured body 6 rotates a circle and supports axle system 7 Obliquity error movement in X direction in adjacent two order harmonic component estimated values measuring the difference beated caused on cross section.By formula (4), have

$\begin{array}{c}{\mathrm{\Θ}}_J=R(z_J,1)-R(z_{J-1},1)={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-{\mathrm{\δ}}^J\\ {\mathrm{\Θ}}_{J+1}=R(z_{J+1},1)-R(z_J,1)=T_5^J(z_{J+1},1)-{\hat{E}}_x(z_J,1)-{\mathrm{\δ}}^J\end{array}---\left(6\right)$

Θ in formula (6)_J+1Characterize J location measured body 6 J+1 and the J relative variation measuring the geometric center of cross section circle.

To J+1 location, the axial location overlap in cross section is measured with measured body 6 J, J+1 and J+2 respectively in cross section, measurement bay 8 left, center, right, therefore the 4th sensor 4, first, two and three sensors 1～3 and the 5th sensing 5 gather J, J+1 and J+2 on measured body 6 respectively and measure a weekly data in cross section, identical with the measurement process of J location, similar formula (6), has:

$\begin{array}{c}{\mathrm{\Θ}}_{J+1}=R(z_{J+1},1)-R(z_J,1)={\hat{E}}_x(z_{J+1},1)-T_4^{J+1}(z_J,1)-{\mathrm{\δ}}^{J+1}\\ {\mathrm{\Θ}}_{J+2}=R(z_{J+2},1)-R(z_{J+1},1)=T_5^{J+1}(z_{J+2},1)-{\hat{E}}_x(z_{J+1},1)-{\mathrm{\δ}}^{J+1}\end{array}---\left(7\right)$

In like manner, Θ in formula (7)_J+1Being characterized in J+1 location, measured body 6 J+1 and J measures the relative variation of the geometric center of cross section circle.Obviously, no matter on any location, measured body 6, the adjacent two relative changes measuring the geometric center of cross section circle should be consistent, and namely the second formula of formula (6) should be equal with the first formula of formula (7), so that

${\mathrm{\δ}}^{J+1}={\hat{E}}_x(z_{J+1},1)-T_4^{J+1}(z_J,1)-\[T_5^J(z_{J+1},1)-{\hat{E}}_x(z_J,1)\]+{\mathrm{\δ}}^J---\left(8\right)$

In formula (8), δ^J+1It is at J+1 location, supports axle system 7 Obliquity error movement in X direction when measured body 6 rotates a circle in adjacent two order harmonic component estimated values measuring the difference beated caused on cross section.Thus can plan a kind of recurrence relation:

M the order harmonic component measuring cross sectional shape on step 3, calculating measured body 6:

Step 3.1, initialization J=1；

Step 3.2, rotating a circle by supporting axle system 7 drive measured body 6, causing adjacent two the order harmonic component estimated values measuring the difference beated on cross sections of J location to be δ if supporting axle system 7 Obliquity error movement in X direction¹=C (zero or small plural number)；

Step 3.3, utilize formula (9) to extract J on measured body 6 to measure the relative variation Θ of cross sectional shape and an order harmonic component of J-1 measurement cross sectional shape_J:

${\mathrm{\Θ}}_J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-C---\left(9\right)$

I.e. Θ_JCharacterize J on measured body 6 and measure the relative variation that the geometric center of cross section circle measures the geometric center of cross section circle with J-1.

Step 3.4, set J-1 on measured body 6 and measure an order harmonic component of cross sectional shape as R (z_J-1, 1) and=B (zero or small plural number), utilize formula (10) to calculate J on measured body 6 and measure an order harmonic component R (z of cross sectional shape_J, 1):

R(z_J, 1) and=R (z_J-1,1)+Θ_J=B+ Θ_J(10)

This, R (z_J, 1) and characterize the geometric center of J measurement cross section circle on measured body 6.It should be noted that the measured body 6 reconstructed is overall, and small translation and deflection occur B and C by making, and do not affect the reconstruct of tested cylinder entirety profile.

Step 3.5, J+1 is assigned to J, and judges whether J > M sets up, if setting up, then it represents that complete the calculating of an order harmonic component of M measurement cross sectional shape；Otherwise, step 3.6 is performed；

Step 3.6, rotate a circle by supporting axle system 7 drive measured body 6；Formula (3) is utilized to calculate the estimated value δ supporting axle system 7 Obliquity error movement in X direction in adjacent two order harmonic component measuring the difference that cross section causes to beat of measured body (6)^J:

${\mathrm{\δ}}^J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-\[T_5^{J-1}(z_J,1)-{\hat{E}}_x(z_{J-1},1)\]+{\mathrm{\δ}}^{J-1}---\left(11\right)$

Step 3.7, utilize formula (12) to extract J on measured body 6 to measure the relative variation Θ that cross sectional shape measures an order harmonic component of cross sectional shape with J-1_J:

${\mathrm{\Θ}}_J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-{\mathrm{\δ}}^J---\left(12\right)$

I.e. Θ_JCharacterize measured body 6 J and measure the relative variation that the geometric center of cross section circle measures the geometric center of cross section circle with J-1.

Step 3.8, utilize formula (13) to calculate J on measured body 6 to measure an order harmonic component R (z of cross sectional shape_J, 1):

$R(z_J,1)=R(z_{J-1},1)+{\mathrm{\Θ}}_J=B+\underset{j=1}{\overset{J}{\Σ}}{\mathrm{\Θ}}_j---\left(13\right)$

This, R (z_J, 1) and characterize the geometric center of J measurement cross section circle on measured body 6.

Step 3.9, return step 3.5 perform；

M the order harmonics measuring cross sectional shape on step 4, extraction measured body 6；

Step 4.1, with on measured body 6 J measure cross sectional shape an order harmonic component R (z_J, 1), and utilize formula (14) to build sequence Γ (z_J, k):

$\mathrm{\Γ}(z_J,k)=\left\{\begin{array}{cc}R(z_J,1)& k=1\\ 0& k=0,2,3,...N-2\\ \stackrel{\‾}{R}(z_J,1)& k=N-1\end{array}\right.,J=1,2,...,M---\left(14\right)$

In formula (6),Represent R (z_J, 1) conjugation；

Step 4.2, utilize formula (15) to sequence Γ (z_J, k) carry out inverse discrete Fourier transform, thus extracting measured body (6) J to measure an order harmonics r of cross sectional shape₁(z_J, i):

r₁(z_J, i)=IDFT [Γ (z_J, 1)] J=1,2 ..., M (15)

Step 5, utilize formula (16) reconstruct measured body 6 cylinder profile r (z_J, i) i=0,1 ..., N-1:

r(z_J, i)=r₀(z_J)+r₁(z_J,i)+r₂(z_J, i) J=1,2 ..., M (16)

The present invention is that " axle ties up to X to the definition according to international machinery production EASD CIRP shaft error motion and Y-direction has purely radial error motion x (θ), y (θ) and axial error motion z (θ) and the Obliquity error movement along X and Y-axis" and propose.If known a priori supports the value of beating caused in the X-direction error motion of axle system 7 along the Obliquity error movement of X-axisError motion x purely radial with X-direction^J(z_J, θ) and to compare be small quantity, sees formula (5), it is negligible, then can cancel the right measurement cross section of measurement bay 8 removal sensor 5 (see Fig. 1～Fig. 3), make measurement bay 8 become double sections parallel schema, and ignore step 3.6, and by δ^JAssignment is " zero ", the present invention propose technical scheme can be completely separating equally measurement process center shafting Radial mixing motion and guide rail straight line error motion, with this reduce due to multisensor characteristic discordance on measure reconstruction accuracy impact.

Claims (1)

1. the large cylindrical profile on-line measurement reconstructing method based on parallel error separation method, being be applied to be moved in X-Z direction by Z guide rail (10) and X guide rail (9) common support measurement bay (8), support axle system (7) support and drive measured body (6) to rotate in the measurement system formed, described Z guide rail (10) is axially in parallel with described measured body (6)；And the moving step pitch that support measurement bay (8) is along the Z direction is d；It is characterized in that described on-line measurement reconstructing method is to carry out as follows:

Step 1, data acquisition:

Step 1.1, arranging cross section, three, left, center, right on measurement bay (8), described three cross section orthogonal are in described Z guide rail (10) moving direction, and the distance between three cross sections is d；Middle section configures three sensors according to 3 roundness error separation measuring methods, including: first sensor (1), the second sensor (2) and the 3rd sensor (3)；

Step 1.2, on left cross section and right section, it is each configured with the 4th sensor (4) and the 5th sensor (5) in X direction；

Step 1.3, described measured body (6) divide M vertically and measures cross section；Each distance measured between cross section is d；Definition location J；J=1,2 ..., M；

Step 1.4, initialization J=1；

Step 1.5, traverse measurement frame (8), make the upper middle section of described measurement bay (8) be positioned at measured body (6) J and measure on cross section；

Step 1.6, described measured body (6) is driven to rotate a circle by supporting axle system (7) so that described first sensor (1), the second sensor (2) and the 3rd sensor (3) can gather the measurement data of a week on described measured body (6) J measurement cross section；Described 4th sensor (4) gathers described measured body (6) J-1 and measures the measurement data of a week on cross section；Described 5th sensor (5) gathers described measured body (6) J+1 and measures the measurement data of a week on cross section；Thus completing the measurement of J location, it is thus achieved that the measurement data of J location；The measurement data of described J location includes: the right section data of the middle section data of J location, the left cross-section data of J location and J location；

Step 1.7, J+1 is assigned to J, and judges whether J > M sets up, if setting up, then it represents that complete the measurement of M location；Obtain the measurement data of M location；Otherwise, return step 1.5 order to perform；

Step 2, data prediction:

Step 2.1, middle section data according to J location, utilize 3 leading roundness fault separating methods of frequency domain to extract described measured body (6) J and measure the circularity r on cross section₂(z_J, i) with radius relative value r₀(z_J)；Obtain described measured body (6) J simultaneously and measure the order harmonic component that cross section X-direction is beated in separating resultingz_J=J × d represents that described measured body (6) J measures the axial location in cross section；I represents the period of any sensor sampling in a week；I=0,1 ... N-1；N represents counting of any sensor sampling in a week, and the angular spacing of sampling is δ=2 π/N；

Step 2.2, respectively left cross-section data and right section data to J location carry out discrete Fourier transform, obtain an order harmonic component of transformation resultsWith

Step 3, calculate an order harmonic component of upper M the measurement cross sectional shape of described measured body (6):

Step 3.1, initialization J=1；

Step 3.2, described measured body (6) is driven to rotate a circle by supporting axle system (7), if the estimated value of adjacent two order harmonic component measuring the difference beated on cross sections of the measured body (6) that causes of the Obliquity error movement that described support axle system (7) is in X direction is δ¹=C；

Step 3.3, formula (1) is utilized to extract described measured body (6) the J relative variation Θ measuring an order harmonic component of cross sectional shape and J-1 measurement cross sectional shape_J:

${\mathrm{\Θ}}_J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-C---\left(1\right)$

Step 3.4, set described measured body (6) J-1 and measure an order harmonic component of cross sectional shape as R (z_J-1, 1) and=B, utilize formula (2) to calculate described measured body (6) J and measure an order harmonic component R (z of cross sectional shape_J, 1):

R(z_J, 1) and=R (z_J-1,1)+Θ_J=B+ Θ_J(2)

Step 3.5, J+1 is assigned to J, and judges whether J > M sets up, if setting up, then it represents that completed the calculating of an order harmonic component of M measurement cross sectional shape；Otherwise, step 3.6 is performed；

Step 3.6, described measured body (6) is driven to rotate a circle by described support axle system (7)；Formula (3) is utilized to calculate described support axle system (7) the Obliquity error movement in X direction estimated value δ in adjacent two order harmonic component measuring the difference that cross section causes to beat of J location^J:

${\mathrm{\δ}}^J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-\[T_5^{J-1}(z_J,1)-{\hat{E}}_x(z_{J-1},1)\]+{\mathrm{\δ}}^{J-1}---\left(3\right)$

Step 3.7, utilize formula (4) to extract measured body (6) J to measure the relative variation Θ that cross sectional shape and J-1 measure an order harmonic component of cross sectional shape_J:

${\mathrm{\Θ}}_J={\hat{E}}_x(z_J,1)-T_4^J(z_{J-1},1)-{\mathrm{\δ}}^J---\left(4\right)$

Step 3.8, utilize formula (5) calculate described measured body (6) J measure cross sectional shape an order harmonic component R (z_J, 1):

$R(z_J,1)=R(z_{J-1},1)+{\mathrm{\Θ}}_J=B+\underset{j=1}{\overset{J}{\Σ}}{\mathrm{\Θ}}_j---\left(5\right)$

Step 3.9, return step 3.5 perform；

Step 4, extract an order harmonics of upper M the measurement cross sectional shape of described measured body (6):

Step 4.1, with measured body (6) J measure cross sectional shape an order harmonic component R (z_J, 1), and utilize formula (6) to build sequence Γ (z_J, k):

$\mathrm{\Γ}(z_J,k)=\left\{\begin{array}{cc}R\left(z_J,1\right)& k=1\\ 0& k=0,2,3,...N-2\\ \stackrel{\‾}{R}\left(z_J,1\right)& k=N-1\end{array}\right.,J=1,2,...,M---\left(6\right)$

In formula (6),Represent R (z_J, 1) conjugation；

Step 4.2, utilize formula (7) to described sequence Γ (z_J, k) carry out inverse discrete Fourier transform, thus extracting described measured body (6) J to measure an order harmonics r of cross sectional shape₁(z_J, i):

r₁(z_J, i)=IDFT [Γ (z_J, 1)] J=1,2 ..., M (7)

Step 5, formula (8) is utilized to reconstruct the cylinder profile r (z of described measured body (6)_J, i):

r(z_J, i)=r₀(z_J)+r₁(z_J,i)+r₂(z_J, i) J=1,2 ..., M (8).