CN1216269C - Self-separation method and device for spatial error of superprecise revolution reference - Google Patents

Abstract

The present invention belongs to the technical fields of the manufacture and the measurement of a precision instrument, particularly to an ultraprecise revolving fiducial space error self-separating method and a device. The method of the present invention separates the Z direction gradually sectional plane of the motion errors of the ultraprecise revolving fiducial space, satisfies the requirements of the motion error separation of the revolving fiducial (a main shaft) space of a high-precision cylindricity instrument, and reduces the turning errors of the space. The present invention also provides the error self-separating device for the ultraprecise revolving fiducial space. A roundness error separation system and a rotary main shaft system of the cylindricity instrument are organically integrated, and the present invention realizes the gradually sectional plane separation of the revolving motion errors of the rotary main shaft space of the cylindricity instrument by a revolving type single transposition minor angle error separation method of a working table. The errors of the rotary main shaft of measuring sectional planes are gradually separated within column measuring height ranges, and therefore, the present invention reduces the influence of the motion errors of the main shaft space of the cylindricity instrument on the measuring result.

Description

Ultra-precise revolving reference space error self-separation method and apparatus

Technical field

The invention belongs to exact instrument manufacturing and field of measuring technique, particularly a kind of ultra-precise revolving reference space error self-separation method and apparatus.

Background technology

The depth of parallelism between cylindricity measurement instrument spindle rotation error, vertical rail linearity, guide rail and the axis of rotation is the three mistake sources that constitute the cylindricity measurement instrument.In these three error sources, guide rail linearity can come correction-compensation by methods such as laser monitoring method, optical flat partition methods, the depth of parallelism can be revised in advance by reverse method or standard column anastrophe, and spindle rotation error does not find efficient ways to revise and compensate up to now yet.In fact, the turn error of cylindricity instrument main shaft has become the biggest obstacle that restriction cylindricity instrument measuring accuracy improves.

The cylindricity measurement instrument not only requires in the single cross section of rotary main shaft higher rotating accuracy is arranged, and requires its arbitrary section in axial (Z to) measuring height scope all higher rotating accuracy will be arranged.Owing to be subjected to the restriction of technological level, the rotating accuracy of present instrument main shaft can only reach (0.020+0.0003H) μ m, and (wherein H is a depth of section, unit is mm) temporary transient limit system manufacturing accuracy, this error is then bigger for the influence of ultraprecise cylindricity measurement instrument, as the cylindricity measurement uncertainty being required to reach the reference model cylindricity instrument of 0.1 μ m/100mm, this error occupies more than 50% of instrument overall uncertainty measuring error, reach 0.050 μ m/100mm, become the error source of ultraprecise cylindricity instrument maximum.Therefore, when improving the precision of ultraprecise cylindricity instrument revolution benchmark, except the basic manufacturing accuracy that improves revolution benchmark itself, also should adopt the method for error separating that its space turn error is separated.

Usually radially Error-motion in Rotation, (b) angular convolution commentaries on classics error motion, the motion of (c) axial error, four kinds of form superpositions of (d) twisting Error-motion in Rotation form the space turn error of instrument rotary main shaft by (a) shown in Figure 1, error motion form between each section of outline of space has not had linear similarity, as shown in Figure 2, be difficult to try to achieve the track profile in the 3rd cross section by the track profile in two cross sections by linear relationship.Therefore, research is adapted to the method and system that cylindricity measurement instrument revolution reference space error is separated in real time, will become the key of further raising cylindricity instrument surveying instrument precision.

At present, instrument spindle error isolation technics and systematic research all are to carry out at the single circle contour cross section of instrument main shaft, and its typical case is represented as the Taylor73 roundness measuring equipment measuring system with error separating function that Britain Tyler Corporations produces.Its structure as shown in Figure 3, error separating turntable 5 places on the roundness measuring instrument work top 6, work top 6 is positioned on the instrument base 10, measured workpiece (standard ball) 4 is positioned on the error separating turntable 5, during error separating, adjust error separating turntable 5 and measured workpiece 4, make error separating turntable 5 axiss of rotation, workpiece 4 axiss of rotation and roundness measuring equipment main shaft 1 axis of rotation on same axis, adjust spindle carrier 7 and sensor adjusting mechanism 2 and make sensor 3 be in suitable range ability.The error separating turntable 5 per 30 ° turn over a transposition, each transposition sensor 3 is finished a survey time in week, corotation 12 transpositions, finished for 12 survey time in week, through obtaining spindle rotation error and workpiece error after the multistep processes data processing, promptly realized of accurate the separating of roundness measuring equipment main shaft 1 turn error with workpiece 4 errors.

Above-mentioned circle contour error separating technology and system still can not effectively separate the space turn error of cylindricity measurement instrument.As shown in Figure 4, its reason is as follows: 1) error separating turntable 5 and cylindricity measurement instrument revolution baseline system 12 is independently of one another, when needing to separate revolution reference space kinematic error, the error separating system that constitutes is difficult to become one with the revolution benchmark set, because the influence of error separating turntable pilot 11, detachment process certainly will need people's intervention, causes complex structure, disengaging time is long, and the error link increases; When 2) existing error separation method such as multistep processes (12 transpositions commonly used), reverse method etc. are carried out space turn error separation, the detachment process complexity, disengaging time is long, and all kinds of drifts of introducing are bigger; 3) error separating turntable 5 is raised h with measured workpiece 4, has increased chain tape, has sacrificed the original precision of revolution benchmark, increases as axial dimension, and angular convolution changes that error is multiplied etc.; 4) adjust difficulty, each measurement all need be adjusted error separating turntable 5 and measured workpiece 4, the axis of rotation, workpiece 4 axiss of rotation and cylindricity instrument main shaft gyration benchmark 15 axiss of rotation that make error separating turntable 5 have also proposed very high requirement to the manufacturing accuracy of error separating turntable on same axis.

Summary of the invention

In order to overcome the weak point of above-mentioned prior art, to satisfy the demand of high precision cylindricity instrument revolution benchmark (main shaft) spatial movement error separating, the present invention proposes to make it reach the purpose that reduces the space turn error by ultra-precise revolving reference space kinematic error being carried out Z to the method for separating by the cross section.

The present invention also provides a kind of ultra-precise revolving reference space error self-separation device, it organically integrates deviation from circular from piece-rate system and cylindricity instrument rotary main shaft system, utilize single transposition small angle error separation method of work table rotation formula, to realize separating to cylindricity instrument rotary main shaft space gyration error by the cross section, promptly in the cylindrical measurement altitude range, one by one each rotary main shaft error of measuring the cross section is separated, reach then and reduce of the influence of cylindricity instrument main shaft spatial movement error measurement result.

Technical solution of the present invention is: a kind of ultra-precise revolving reference space error self-separation method, and this method may further comprise the steps:

1. measure the cross section and measure for selected M, initial index position is in the workpiece of a position, and Z is to measuring vertically, and the composition error value that obtains the circle contour value successively is { V _A0(n), V _A1(n) ... V _Ai(n) ... V _{A (M-1)}(n) };

2. rotation error separates turntable, drive workpiece and turn over angle [alpha] arrival index position b, to being positioned at the workpiece of initial index position b, to measuring successively, obtaining its composition error value and be followed successively by { V again with strict M the corresponding circle contour value of measuring on the cross section of position a along Z _B0(n+n _α), V _B1(n+n _α) ... V _Bi(n+n _α) ... V _{B (M-1)}(n+n _α);

3. utilize harmonic analysis method and single position shifter error separation method to transposition angle α, { V _A0(n), V _A1(n) ... V _Ai(n) ... V _{A (M-1)}And { V (n) } _B0(n+n _α), V _B1(n+n _α) ... V _Bi(n+n _α) ... V _{B (M-1)}(n+n _α) carry out data processing and error separating after, obtain Z to the rejecting of M measuring height position the roundness error of workpiece { S of spindle rotation error ₀(n), S ₁(n) ... S _i(n) ... S _M-1And the workpiece radius difference { R between M respective cross-section height (n) } ₀(n), R ₁(n) ... R _i(n) ... R _M-1(n) };

4. with S _i(n) and R _i(n) carry out the cylindricity evaluation in the substitution cylindricity measurement assessment system, obtained rejecting the cylindricity value of the workpiece of cylindricity instrument space turn error.

A kind of ultra-precise revolving reference space error self-separation device, comprise Z guide track system 8 and another Z guide track system 9, circle contour survey sensor 3, worktable 13, error separating turntable 14, instrument rotary main shaft 15, motor driven systems 18, scrambler 19, pedestal 10, this device also comprises low-angle transposition angle generation systems 20, conducting slip ring 17, instrument rotary main shaft 15 constitutes the revolution benchmark of air supporting rotary axis system A as cylindricity instrument with axle sleeve 16, error separating turntable 14 has constituted air supporting rotary axis system B again as special axle sleeve and rotary main shaft 15, the shared same rotary main shaft 15 of air supporting rotary axis system A and air supporting rotary axis system B, it is air supporting rotary axis system B that air supporting rotary axis system A drives error separating turntable 14, rotary table 13 and tested cylindrical workpiece 4 turn round together, error separating turntable 14 drives worktable 13 again and turns round with tested cylindrical workpiece 4 relative air supporting rotary axis system A, Z guide track system 8 drives sensor 3 and moves along the Z direction, reaches the measuring height of the optional cross section i of measurement; When carrying out error separating, the rotation of the required relative air supporting rotary axis system A of error separating is finished in error separating turntable 14 air feed and work; When need not error separating, error separating turntable 14 is died, and it unites two into one with rotary main shaft 15 under the effect of gravity, is equal to the cylindricity measurement instrument of error free piece-rate system.

The present invention has following characteristics and good result:

The present invention organically integrates deviation from circular from piece-rate system and these two separate systems of script of cylindricity instrument main shaft gyration system, its function is merged mutually with structure, the ultraprecise cylindricity measurement instrument of setting up according to this technology, need not any add-on device, just can separate voluntarily its space turn error, this is one of innovative point of difference prior art;

Error separating method adopts the single position shifter error separation method based on frequency analysis, separates turntable during error separating and only need finish the specific low-angle transposition of single, can finish the error separating in this cross section, this be the difference prior art innovative point two;

Measurement mechanism after structure merges when needing error separating, separates turntable work, can finish the required rotation of error separating.When need not error separating, the error separating turntable is stopped the supple of gas or steam, and it unites two into one with rotary axis system under the effect of gravity, is equal to the cylindricity measurement instrument of error free piece-rate system, this be the difference prior art innovative point three.

After adopting above-mentioned technology, measurement mechanism has following distinguishing feature:

1) can separate ultra-precise revolving reference space turn error voluntarily, when having avoided original cylindricity measurement instrument to separate revolution reference space kinematic error, exist the error separating system to be difficult to be integral complex structure, the shortcoming that the error link increases with the revolution benchmark set;

2) significantly shortened the axial dimension of cylindricity instrument revolution reference space error separating system, when having avoided original cylindricity measurement instrument to separate revolution reference space kinematic error, exist the system's revolution standard apparatus axial dimension that constitutes to increase, measure chain length, sacrificed the original precision of revolution benchmark, angular convolution changes fatal shortcomings such as error is multiplied.

3) based on the employing of single position shifter error separation method of frequency analysis, when avoiding existing error separation method such as multistep processes, reverse method etc. to carry out space turn error separation, the detachment process complexity, disengaging time is long, the deficiencies that all kinds of drifts of introducing are bigger etc. have been simplified error separating device and error separating process simultaneously greatly.

Description of drawings

Fig. 1 is existing spindle rotation error typical motion form synoptic diagram

Fig. 2 is existing space revolution benchmark kinematic error forms of motion synoptic diagram

Fig. 3 is existing roundness measuring equipment error separating system schematic

Fig. 4 is existing cylindricity instrument error separating system schematic

Fig. 5 is the structural representation of apparatus of the present invention

Fig. 6 is single transposition space error separation principle figure of the present invention

Fig. 7 is the structural representation of an embodiment of apparatus of the present invention

The data and curves of measured workpiece before Fig. 8 separates

Fig. 9 separates the data and curves of front axle

Figure 10 separates the data and curves of back measured workpiece

Figure 11 separates the data and curves comparison diagram of forward and backward measured workpiece

Among the figure, 1 roundness measuring equipment main shaft, 2 sensor adjusting mechanisms, 3 sensors, 4 measured workpieces, 5 error separating turntables, 6 roundness measuring instrument work tops, 7 spindle carriers, 8 and 9 Z guide track systems, 10 pedestals, 11 error separating turntable pilots, 12 cylindricity measurement instruments revolution baseline system, 13 worktable, 14 error separating turntables, 15 instrument rotary main shafts, 16 axle sleeves, 17 conducting slip rings, 18 motor driven systems, 19 scramblers, 20, low-angle transposition angle generation systems, the initial position of 21 measured workpieces, the initial zero-bit of 22 apparatus measures, 23 closing force generators, 24 screw-type PZT, 25, low-angle transposition angle detection system

Embodiment

The structure of ultra-precise revolving reference space error self-separation device of the present invention and principle of work reach accompanying drawing in conjunction with the embodiments and are described in detail as follows:

The structural representation of ultra-precise revolving reference space error self-separation device one embodiment of the present invention.As shown in Figure 7, comprising: formations such as the B end of the air-bearing shafts system of circle contour survey sensor 3, tested cylinder 4, rotary table 13, error separating turntable 14, error separating turntable, low-angle transposition angle generation systems 20, instrument rotary main shaft 15, low-angle transposition angle detection system 25 (reflective fan-shaped grating commonly used and combined photo receiver), conducting slip ring 17, motor driven systems 18, angle measurement scrambler 19, pedestal 10, closing force generator 23, screw-type PZT 24.Measured workpiece is positioned on the rotary table 13, and rotary table 13 is supported by error separating turntable 14, and the air supporting rotary axis system that instrument rotary main shaft 15 and axle sleeve 16 constitute is as original revolution benchmark A; The error separating turntable is again that secondary air-bearing shafts is the special axle sleeve of B simultaneously, and they have constituted the error separating system.Error separating turntable main shaft is mutually compound with the function of instrument revolution benchmark main shaft upper end locating shaft (B axle), realize dual-use function by the B axle, and play the effect of following several respects:

1) (former error separating turntable structure is very complicated with complication system, size is also very big) change single system into, constitute a global facility, axial dimension is greatly reduced, the Space Angle turn error of instrument rotary main shaft A is increased, chain tape shortens dramatically, and error loop is reduced few, has significantly reduced the system mechanics drift;

2) because B axle good manufacturability, the coaxiality error of the relative A axle of B axle reduces, the verticality of the relative A axle of B axle thrust surface also reduces, and error separating turntable precision is obviously improved, and its result has avoided the coaxial centering between instrument revolution reference center's line and the error separating system centre line;

3) when carrying out error separating, air-bearing shafts is B air feed and work, when the error separating system turns over corresponding angle, can pursue the separation voluntarily of space, cross section turn error etc.When need not to carry out error separating, air-bearing shafts is that B stops the supple of gas or steam, and the error separating turntable unites two into one with rotary axis system A under the effect of gravity, is equal to the cylindricity measurement instrument of error free piece-rate system.

The rotary axis system A that instrument rotary main shaft and axle sleeve constitute among the present invention can also be the axle system of other form, as forms such as hydraulic pressure, close posts except being the air-bearing shafts system.

The rotary axis system B that the error separating turntable constitutes as special axle sleeve and rotary main shaft can also be the axle system of other form, as forms such as hydraulic pressure, close posts except being the air-bearing shafts system.

For realizing the required low-angle high precision transposition of error separating, transposition angle generating mechanism is designed to tangent mechanism, driving mechanism adopt that U.S. NEWFOCUS company produces on a large scale, the spiral micro-displacement driver of high stability (Picomotor), outer extension mechanism along the error separating turntable drives, its drive displacement resolving power reaches 10nm, driving force reaches 20N, and the transposition angle can accurately be detected by being installed in the outer high precision fan-shaped grating that extends mechanism's diameter.For reducing the corner backhaul, lay the closing force generator in the direction relative with driver.

In the tripping device, the error separating turntable both can rotate with main shaft, can drive workpiece again and carry out rotation.When manufacturing and designing, make error separating turntable rotation axis of rotation and cylindricity measurement instrument main shaft gyration axis coaxle.During separation, measured workpiece is positioned on the worktable, adjusts worktable and make measured workpiece centre of gyration line and cylindricity measurement instrument main shaft gyration center line almost coaxial.As shown in Figure 6, move up and down sensor, arrive and measure cross section 0, rotary work-table, sensor records the cross section data of 0 first survey time, the error separating turntable drives worktable and the relative instrument main shaft of measured workpiece turns over specific angle, and sensor records another drive test amount data of measuring cross section 0 after the transposition of measured workpiece single.According to single transposition space error partition method the turn error of cylindricity measurement instrument rotary main shaft is separated from measurement result, obtained the circle contour measuring error of measured workpiece.And the like, utilize this error separating device in the cylindricity measurement instrument, can reach the separation of spatial movement error then with from measurement result, separating for arbitrarily the instrument space spindle rotation error of uniform section, finally improve the measuring accuracy of instrument.

Adopt foregoing invention, utilize the redundancy feature of former revolution benchmark and error separating internal system part, the parts that will have a correlation function are simplified with function and are sorted out, most of major function all is compound on some core components such as main shaft, thereby has constituted the monoblock type ultra-precise revolving reference space error self-separation device that the space turn error can separate voluntarily.This device is simplified the system architecture of cylindricity measurement instrument significantly, has reduced the bad joint of error, has shortened chain tape, and lay the foundation the separating in real time, efficiently with accurately of spatial movement error of turning round benchmark for the cylindricity measurement instrument.The inventive method not only is used for ultraprecise cylindricity measurement instrument with device, also can be used for setting up high-precision revolution benchmark simultaneously.

As shown in Figure 6,21 is the initial position a of measured workpiece, and 3 is sensor, and 22 is the initial zero-bit of apparatus measures.When sensor 3 is in (i+1) individual measurement cross section of tested cylindrical workpiece 4 as shown in Figure 5, and tested cylindrical workpiece 4 is when being positioned at index position a shown in Fig. 6 (a), and the error of establishing cylindrical workpiece is S _i(θ), instrument rotary main shaft error is e _i(θ), the comprehensive contour signal that records of sensor is V _Ai(θ); When cylindrical workpiece 4 turned over the α angle and arrives position b as Fig. 6 (b) shown in respect to rotary main shaft 15 with error separating turntable 14, variation had taken place in the phase place of its all subharmonic, and its value is S _i(θ+α), and the phase invariant of air supporting rotary axis system A error percentage, its value still is e _i(θ), the comprehensive contour signal that records of this transposition upper sensor is V _Bi(θ).

The ultimate principle of separating is as follows: the initial position a place that tested cylindrical workpiece is placed worktable, along Z to movable sensor 3, make it to be in 0 of workpiece 4 and measure the sectional position, rotating air supporting rotary axis system A makes cylindrical workpiece 4 rotate with worktable 13 and error separating turntable 14, at this moment, the composition error that records of sensor 4 is V _A0(θ), then along Z guide track system 9 movable sensors 3, measure cross section 1 at selected workpiece 4 respectively ... i ... M-1 measures, record successively cross section 0 ... i ... the composition error of M-1 is { V _Ai(θ) } (i=0 ... k ... M-1).

If the direction of compression sensor gauge head is the sensor forward, then measuring workpieces shape and instrument rotary main shaft shape are respectively S to the direction of outer lug _i(θ) and e _iForward (θ), because workpiece is positioned on the instrument rotary table, e then _i(θ) and V _AiDirection (θ) all the time in the same way, then to any measurement cross section (i+1), the comprehensive contour signal V that sensor records _Ai(θ) be:

V _ai(θ)＝S _i(θ)+e _i(θ)cosθ (1)

After finishing the measurement of a transposition, carry out the measurement of b transposition again, be after rotation error separation turntable makes workpiece turn over the position of arrival shown in Fig. 6 (b), α angle, measuring the sectional position selectes and strict corresponding position, a transposition measurement sectional position successively, in like manner, sensor can record successively cross section 0,1 ... i ... composition error { the V of M-1 _Bi(θ) } (i=0 ... k ... M-1).To measuring cross section (i+1), the comprehensive contour signal V that sensor records _Bi(θ) also be:

V _bi(θ)＝S _i(θ+α)+e _i(θ)cosθ (2)

With the S in (1) and (2) _i(θ), e _i(θ) and S _i(θ+α) in time domain, expand into one week of instrument main shaft gyration be the function of first-harmonic, its fourier progression expanding method formula is:

$S_i\left(\mathrm{\&theta;}\right)={\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">S</figure-callout>}}_i+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}(a_{\mathrm{ik}}\cos \mathrm{k\&theta;}+b_{\mathrm{ik}}\sin \mathrm{k\&theta;})---\left(3\right)$

$e_i\left(\mathrm{\&theta;}\right)=e_{i0}+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}(c_{\mathrm{ik}}\cos \mathrm{k\&theta;}+d_{\mathrm{ik}}\sin \mathrm{k\&theta;})---\left(4\right)$

$S_i(\mathrm{\&theta;}+\mathrm{\&alpha;})={\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">S</figure-callout>}}_i^0+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}(a_{\mathrm{ik}}\cos k{(\mathrm{\&theta;}+\mathrm{\&alpha;})+b}_{\mathrm{ik}}\sin k(\mathrm{\&theta;}+\mathrm{\&alpha;}))---\left(5\right)$

$={\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">S</figure-callout>}}_i^0+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}((a_{\mathrm{ik}}\cos \mathrm{k\&alpha;}+b_{\mathrm{ik}}\sin \mathrm{k\&alpha;})\cos \mathrm{k\&theta;}+(b_{\mathrm{ik}}\cos \mathrm{k\&alpha;}-a_{\mathrm{ik}}\sin \mathrm{k\&alpha;})\sin \mathrm{k\&theta;})$

In the formula: S _I0, S ' _I0, e _I0, a _Ik, b _Ik, c _IkAnd d _IkBe the fourier progression expanding method coefficient.

Formula (1) and formula (2) subtracted each other:

$r_i\left(\mathrm{\&theta;}\right)=V_{\mathrm{ai}}\left(\mathrm{\&theta;}\right)-V_{\mathrm{bi}}\left(\mathrm{\&theta;}\right)=S_i\left(\mathrm{\&theta;}\right)-S_i(\mathrm{\&theta;}+\mathrm{\&alpha;})$

$={\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">S</figure-callout>}}_i^0+\underset{k=1}{\overset{N-1}{\mathrm{\&Sigma;}}}((a_{\mathrm{ik}}(1-\cos \mathrm{k\&alpha;})-b_{\mathrm{ik}}\sin \mathrm{k\&alpha;})\cos \mathrm{k\&theta;}+(a_{\mathrm{ik}}\sin \mathrm{k\&alpha;}+b_{\mathrm{ik}}(1-\cos \mathrm{k\&alpha;}))\sin \mathrm{k\&theta;})---\left(6\right)$

In the formula: S ₀", a _k, and b _kBe the fourier progression expanding method coefficient.

Following formula is handled through N point sampling discretize, and only got 0 to the N-1 subharmonic, the angle of the n time sampled point is 2n π/N, and then its discretize formula is:

$r_i\left(n\right)={\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{\&prime;\&prime;}+\underset{k=1}{\overset{N-1}{\mathrm{\&Sigma;}}}((a_{\mathrm{ik}}(1-\cos \mathrm{k\&alpha;})-b_{\mathrm{ik}}\sin \mathrm{k\&alpha;})\cos (2\mathrm{n\&pi;k}/N)---\left(7\right)$

$+(a_{\mathrm{ik}}\sin \mathrm{k\&alpha;}+b_{\mathrm{ik}}(1-\cos \mathrm{k\&alpha;}))\sin (2\mathrm{n\&pi;k}/N))$

Following formula r _i(n) also deployable is the fourier series form:

$r_i\left(n\right)={\mathrm{<figure-callout\; id="0"\; label="r\; i"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">r</figure-callout>}}_i+\underset{k=1}{\overset{N-1}{\mathrm{\&Sigma;}}}(e_{\mathrm{ik}}\cos (2\mathrm{n\&pi;k}/N)+f_{\mathrm{ik}}\sin (2\mathrm{n\&pi;k}/N))---\left(8\right)$

In the formula $r_i$ $0_{}=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{r}_i\left(n\right)---\left(9\right)$

$e_{\mathrm{ik}}=\frac{2}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{r}_i\left(n\right)\cos (2\mathrm{n\&pi;k}/N)---\left(10\right)$

$f_{\mathrm{ik}}=\frac{2}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{r}_i\left(n\right)\sin (2\mathrm{n\&pi;k}/N)---\left(11\right)$

The harmonic components of k in comparison expression (7) and (8) 〉=2 can get:

$\left\{\begin{array}{c}{e}_{\mathrm{ik}}=a_{\mathrm{ik}}(1-\cos \mathrm{k\&alpha;})-b_{\mathrm{ik}}\sin \mathrm{k\&alpha;}\\ f_{\mathrm{ik}}=a_{\mathrm{ik}}\sin \mathrm{k\&alpha;}+b_{\mathrm{ik}}(1-\cos \mathrm{k\&alpha;})\end{array}\right.---\left(12\right)$

Find the solution following formula:

$\left\{\begin{array}{c}{a}_{\mathrm{ik}}=\frac{1}{2}{e}_{\mathrm{ik}}+\frac{\sin \mathrm{k\&alpha;}}{2(1-\cos \mathrm{k\&alpha;})}{f}_{\mathrm{ik}}\\ b_{\mathrm{ik}}=-\frac{\sin \mathrm{k\&alpha;}}{2(1-\cos \mathrm{k\&alpha;})}{e}_{\mathrm{ik}}+\frac{1}{2}{f}_{\mathrm{ik}}\end{array}\right.---\left(13\right)$

Obtain the harmonic constant a of any k subharmonic _k, b _kAfter, again according to formula (3) and carry out discretize and handle and can obtain the time domain discrete value S of cylindrical workpiece at the deviation from circular from (i+1) cross section _i(n):

$S_i\left(n\right)={\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20041000119300172.png,C20041000119300181.png"\; state="\{\{state\}\}">S</figure-callout>}}_i+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}((\frac{1}{2}{e}_{\mathrm{ik}}+\frac{\sin \mathrm{k\&alpha;}}{2(1-\cos \mathrm{k\&alpha;})}{f}_{\mathrm{ik}})\cos (2\mathrm{n\&pi;k}/N)+(\frac{\sin \mathrm{k\&alpha;}}{2(1-\cos \mathrm{k\&alpha;})}{e}_{\mathrm{ik}}+\frac{1}{2}{f}_{\mathrm{ik}})\sin (2\mathrm{n\&pi;k}/N))---\left(14\right)$

When measuring circularity, fundametal compoment in the harmonic component and first harmonic component (k=0,1) all do not belong to the category of circularity.Therefore, S _i(n) can revise as follows:

${S^{\&prime;\&prime;}}_i\left(n\right)=\underset{k=2}{\overset{N-1}{\mathrm{\&Sigma;}}}((a_{\mathrm{ik}}\cos (2\mathrm{n\&pi;k}/N)+b_{\mathrm{ik}}\sin (2\mathrm{n\&pi;k}/N))---\left(15\right)$

S _i(n) be the deviation from circular from of the workpiece of having rejected (i+1) depth of section place cylindricity instrument spindle rotation error.

With V _Ai(θ) and V _Bi(θ) handle through discretize, get final product the relative radius difference R of respective cross-section height _i(n):

$R_i\left(n\right)=\frac{1}{2}[\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{V}_{\mathrm{ai}}\left(n\right)+\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{V}_{\mathrm{bi}}\left(n\right)]---\left(16\right)$

Like this, utilize harmonic analysis method and single position shifter error separation method to measure the two routine integrated data { V that record on the cross section to transposition angle α, M _A0(θ), V _A1(θ) ... V _Ai(θ) ... V _{A (M-1)}(θ) } and { V _B0(θ), V _B1(θ) ... V _Bi(θ) ... V _{B (M-1)}(θ) } carry out data processing and error separating after, obtain Z to the rejecting of M measuring height position the roundness error of workpiece of spindle rotation error S " _i(n) } (i=0,1 ... i ... M-1; N=0,1 ... k ... N-1) and the workpiece radius difference { R between M respective cross-section height _i(n) } (i=0,1 ... i ... M-1; N=0,1 ... k ... N-1).

Will S " _i(n) } and S " _i(n) } carry out the cylindricity evaluation in the substitution cylindricity measurement assessment system, can obtain rejecting the cylindricity value of the workpiece of cylindricity instrument space turn error.

The checking of the single transposition space error of the present invention separation method separating effect

For verifying the validity and the correctness of single transposition space error separation method, take following verification method: select the data of two groups of actual measurements, one group as main shaft data { Z _i(n) } (i=0,1 ... i ... M-1; N=0,1 ... k ... N-1), another group is as workpiece data { G _i(n) } (i=0,1 ... i ... M-1; N=0,1 ... k ... N-1), at first with the corresponding addition of above-mentioned two groups of data, obtain the integrated data { V of first survey time _Ai(n) } (i=0,1 ... i ... M-1; N=0,1 ... k ... N-1) be:

Then, with workpiece data { G _i(n) } an equal translation n1 data point is again with workpiece data { G _i(n) } addition obtains the integrated data { V of second survey time _Bi(n) } (i=0,1 ... i ... M-1; N=0,1 ... k ... N-1) be:

With { V _Ai(n) }, { V _BiAnd n (n) } ₁Carry out data processing, the workpiece data { S after obtaining separating in the turn error separation method of the single transposition of substitution space _iAnd main shaft data { e (n) } _i(n) }.Data { G before relatively cylindrical workpiece makes up _i(n) } with combination back and separate the data { S that obtains _i(n) } difference is verified the separating effect of single transposition space turn error separation method.Two cylindrical workpieces are placed respectively on the cylindricity measurement instrument measure, choose sampled point N=512 weekly, the single cross section at (i+1) depth of section place, the circle contour data developed curve of two workpiece is respectively as Fig. 8 and shown in Figure 9.With the data of Fig. 8 data { G as tested cylindrical workpiece _i(n) } (n=0,1 ... k ... 511), the data of Fig. 9 are as the data { Z of instrument shaft system _i(n) } (n=0,1 ... k ... 511).

At first with data { G _i(n) } with { Z _i(n) } corresponding addition constitutes integrated data { V _Ai(n) }; Again with data { G _i(n) } 5 sampled points of translation, data { G after the translation _i(n+5) }, with { G _i(n+5) } with data { Z _i(n) } addition constitutes integrated data { V _Bi(n) }.

According to integrated data { V _Ai(n) }, { V _BiAnd transposition angle α (α=360 * 5/512-3.516 °) (n) }, adopt single position shifter error partition method that it is separated, obtain data { S _i(n) }, its data and curves as shown in figure 10.Figure 11 has provided workpiece data { G _i(n) } curve and data { S _i(n) } comparison diagram of curve, for ease of relatively, among Figure 11 with data { G _i(n) } the curve translation 0.2 μ m that makes progress, therefrom { G as can be seen _i(n) } curve and { S _i(n) } only there is small difference in curve, but the roundness evaluation value is 1.729 μ m, and this mainly is because data difference is little little to whole roundness evaluation influence.This shows,,, also can separate fully it even the actual data harmonic wave that records is very abundant as long as the transposition angle error is very little.

Below in conjunction with the accompanying drawings the specific embodiment of the present invention is described; but these explanations can not be understood that to have limited scope of the present invention; protection scope of the present invention is limited by the claims of enclosing, and any change of carrying out on claim of the present invention basis all is protection scope of the present invention.

Claims (7)

1, a kind of ultra-precise revolving reference space error self-separation method is characterized in that this method may further comprise the steps:

1. measure the cross section and measure for selected M, initial index position is in the workpiece of a position, and Z is to measuring vertically, and the composition error value that obtains the circle contour value successively is { V _A0(n), V _A1(n) ... V _Ai(n) ... V _{A (M-1)}(n) };

2. rotation error separates turntable, drive workpiece and turn over angle [alpha] arrival index position b, to being positioned at the workpiece of initial index position b, to measuring successively, obtaining its composition error value and be followed successively by { V again with strict M the corresponding circle contour value of measuring on the cross section of position a along Z _B0(n+n _α), V _B1(n+n _α) ... V _Bi(n+n _α) ... V _{B (M-1)}(n+n _α);

3. utilize harmonic analysis method and single position shifter error separation method to transposition angle α, { V _A0(n), V _A1(n) ... V _Ai(n) ... V _{A (M-1)}And { V (n) } _B0(n+n _α), V _B1(n+n _α) ... V _Bi(n+n _α) ... V _{B (M-1)}(n+n _α) carry out data processing and error separating after, obtain Z to the rejecting of M measuring height position the roundness error of workpiece { S of spindle rotation error ₀(n), S ₁(n) ... S _i(n) ... S _M-1And the workpiece radius difference { R between M respective cross-section height (n) } ₀(n), R ₁(n) ... R _i(n) ... R _M-1(n) };

4. with S _i(n) and R _i(n) carry out the cylindricity evaluation in the substitution cylindricity measurement assessment system, obtained rejecting the cylindricity value of the workpiece of cylindricity instrument space turn error.

2, a kind of ultra-precise revolving reference space error self-separation device, comprise a Z guide track system (8) and another Z guide track system (9), circle contour survey sensor (3), worktable (13), error separating turntable (14), instrument rotary main shaft (15), motor driven systems (18), scrambler (19), pedestal (10), it is characterized in that this device also comprises low-angle transposition angle generation systems (20), conducting slip ring (17), instrument rotary main shaft (15) constitutes the revolution benchmark of air supporting rotary axis system A as cylindricity instrument with axle sleeve (16), error separating turntable (14) has constituted air supporting rotary axis system B again as special axle sleeve and rotary main shaft (15), the shared same rotary main shaft of air supporting rotary axis system A and air supporting rotary axis system B (15), it is air supporting rotary axis system B that air supporting rotary axis system A drives error separating turntable (14), rotary table (13) and tested cylindrical workpiece (4) turn round together, error separating turntable (14) drives worktable (13) again and turns round with the relative air supporting rotary axis system of tested cylindrical workpiece (4) A, Z guide track system (8) drives sensor (3) and moves along the Z direction, reaches the measuring height of the optional cross section i of measurement; When carrying out error separating, the rotation of the required relative air supporting rotary axis system A of error separating is finished in error separating turntable (14) air feed and work; When need not error separating, error separating turntable (14) is died, and it unites two into one with rotary main shaft (15) under the effect of gravity, is equal to the cylindricity measurement instrument of error free piece-rate system.

3, according to claim 2 described ultra-precise revolving reference space error self-separation devices, it is characterized in that also comprising low-angle detection system (25).

4, according to claim 2 described ultra-precise revolving reference space error self-separation devices, it is characterized in that transposition angle generation systems (20) is a tangent mechanism.

5, according to claim 2 described ultra-precise revolving reference space error self-separation devices, it is characterized in that also comprising closing force generator (23).

6, according to claim 2 described ultra-precise revolving reference space error self-separation devices, it is characterized in that rotary axis system A is hydraulic pressure or close cylindricality formula.

7,, it is characterized in that rotary axis system B is hydraulic pressure or close cylindricality formula according to claim 2 described ultraprecise cylindricity instrument space turn error tripping devices.

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