CN1477369A - Method for utilizing time domain method to make difference measurement of accurate reconfiguration - Google Patents

Abstract

The method for making accurate restructure of difference measurement by using time domain is characterized by that according to the difference value obtained by measuring two different separation distances or shearing quanties of measured object, respectively using successive two-point method to evaluate two groups of different difference values, the number of evaluation curves obtained by every group is the ratio value of correspondent sensor separation distance or shearing quantity and sampling interval, then utilizing the interrelationship between two groups of the curves to calculate the influence of zero modulation error to the evaluation result so as to resolve the interrelationship between every curves in the two groups of curves, finally synthesizing these curves into an evaluation curve.

Description

Utilize time domain method to carry out the precise reconstruction method of difference measurement

Technical field:

The present invention relates to detect applied technical field, be specifically related to a kind of differential measurement values and come the detection method of the former measured parameter of reconstruct, comprise linearity, flatness, cylindricity, the detection of free form surface face shape and the wavefront reconstruction of lateral shearing interference of precision, ultraprecise surface of the work according to measured parameter.

Background technology

In ultraprecise processing, for linearity, cylindricity, flatness and the surface figure accuracy that detects the work piece surface, usually adopt many gauge heads scanning method, this method is installed in displacement gauge head (commonly used non-contact sensor such as current vortex or electric capacity etc.) or angle detector (as autocollimator etc.) on the slide carriage, tested profile moving linearly along workpiece, perhaps sensor is fixed, workpiece moves with slide carriage.When the workpiece profile error of measuring when needs and the rectilinear motion error of slide carriage are in same class, expect accurate workpiece profile parameter such as linearity, cylindricity, flatness and surface figure accuracy etc., just need to adopt the way of error separating.On-position measure such as workpiece is exactly directly to utilize machine slide to make the measuring method of scanning motion, and must separate the surface profile error of workpiece and the kinematic error of slide carriage this moment.The lateral shearing interference method is basic identical with many gauge head scanning ratio juris, all is based on the measurement of difference value, and the accurate reconstruct problem that has therefore solved based on difference has just solved many gauge heads scanning method and the problems of measurement of walking crosswise shearing interference method.

Surface figure accuracy reconstruct problem when detecting for linearity, cylindricity, flatness and employing displacement transducer, its the most basic problem is exactly the reconstruct problem that solves linearity, just can be summarised as linearity simply and walk crosswise two aspects of shear interference measurement based on the problems of measurement of difference value.

In order to detect the surface of the work profile accurately, people have begun the research of this respect very early, and until are also constantly proposing the whole bag of tricks in the hope of reconstruct surface of the work linearity profile accurately now.For the verticality measuring method of scanning feeler method, the difference according to adopting the sensor number is divided into one-point method and multipoint method (comprising two-point method, three point method even four-point method etc.).When measuring with one-point method, want error is separated, usually need workpiece is overturn or translation is done just can carry out behind twice scanning survey.The degree of consistency of the relative workpiece of sensor installation site is all influential to final evaluation result in the repeatable accuracy of slide carriage motion and twice measurement like this, and this influence can't be eliminated fully.So in ultra precise measurement, this method operability is bad.Different with inversion method or translation method, multipoint method uses more than one gauge head, carries out error separating, also can not carry out duplicate measurements to workpiece even therefore slide carriage motion repeatability is high.

Two-point method uses two gauge heads, is the simplest multipoint method.Respectively at the profile height of two spaced points detection measured surfaces, the difference output of adopting two gauge heads is with the translational error of eliminating the scanning slide carriage and the difference value that provides the profile height on measured workpiece surface with two gauge heads for this method.Three point method is used three displacement transducers, and a sensor that has more generally is used for eliminating the influence of slide carriage Run-out error.But, owing to can there be the zero error that is difficult to eliminate (being sensor moved and detected the surface of the work time institute perception amount of a desirable no straightness error on the guide rail of desirable no kinematic error difference) in the sensor actual installation, thereby can make difference value produce skew, special when workpiece size is longer, this zero error just becomes three point method and measures maximum error source.Adopt the differential laser autocollimator method of two angle gauge heads and the mixing method that adopts two displacement transducers and an angular transducer, all have same problem.

According to the difference of error separating method, the scanning feeler method can be divided into time domain method and frequency domain method again.Existing time domain method has one by one method, broad sense method, combined method etc.Two-point method (STP) is used for the linearity of measuring workpieces and guide rail movement one by one, the spacing distance of the each feeding sensor of slide carriage, and promptly sampling interval equals transducer spacing, and single pass can be finished measurement.Again the characteristic of this method was studied afterwards, and it is expanded to one by one three point method (STRP), it not only can be isolated the straight-line translational error of slide carriage but also can isolate Run-out error.Two-point method can accurately be determined the relative height of discrete point when sampling interval equals transducer spacing one by one, but data point is difficult to accurately give expression to the tested surface profile very little in this case.On the other hand, when sampling interval during less than transducer spacing, many discrete curves that obtain by the skew starting point are because not matching between the data set also can produce wrong result.Broad sense two-point method (GTP) is by spaced far is carried out integration less than the sampled data of transducer spacing, thereby might obtain about the detailed profile information of space wavelength.Its shortcoming is the cycle to be equaled sensor frequency and harmonic component thereof at interval lost, and can bring unacceptable error under specific situation.Combination two-point method (CTP) is used for the surface measurements profile, and it combines broad sense two-point method and two-point method one by one measures the profile that comprises high fdrequency component, and its space wavelength is less than the interval of sensor.Combination two-point method (CTP) is extended for combination three point method (CTRP) again can not only give expression to the profile that comprises high fdrequency component, and the z on the direction of scanning can be eliminated to error and Run-out error.But set of applications is legal when carrying out error separating, must select for use one section level and smooth standard area to make least square fitting and just can obtain higher evaluation precision.On the basis of two-point method, developed a kind of precision measuring method of three point method (FSTRP) one by one again, this method adopts three sensors making the non-equidistance layout to measure, ignore the influence of slide carriage Run-out error, can obtain two appraisal curves by two-point method respectively, two curves should overlap at the common multiple point place of two spacings, suppose that the difference between two curve each points is linear, again by the method for interpolation try to achieve " encryption " the workpiece linearity.Because this method is responsive to The noise, develops into improved accurate three point method on this basis again, promptly carries out match with least square method on one section smooth region selecting, can suppress noise preferably.The three point method sampling number is limited one by one in order to solve, the problem of incompatibility casual labourer's part, high-acruracy survey, the someone has proposed four-point method and has measured linearity again, first three sensor is equidistantly arranged when adopting this method, the 4th the many skews of sensor one sampling interval is apart from layout, by presetting suitable initial value and process recursive operation restructural workpiece linearity.Afterwards this method was applied to again in the time domain two-point method, can avoids the distortion that causes the high-order harmonic wave component to cause owing to surperficial noncontinuity.The many gauge heads systematic survey right cylinder linearity method that proposes adopts two groups of totally six gauge heads at present, utilize the principle of three point method to measure equally, for avoiding the influence of zero error, this method will be carried out twice measurement by the upset workpiece, therefore cost dearly and practicality not strong.

Find out from above, people to the measuring method of linearity particularly its algorithm carry out more and more deep research, in the hope of on enough little sampling interval point, reconstructing the linearity profile of workpiece accurately, but existing these algorithms all can't reach this purpose, promptly can't accurately reconstruct to gear shaper without theoretical errors the linearity of any workpiece on less than the enough little sampling interval each point of transducer spacing.

And for the lateral shearing interference method, because it has simple and stable structure, do not need characteristics such as high precision reference surface, so being widely used in high-precision optical surface face shape detects, the particularly detection of free form surface such as aspheric surface, but simultaneously, to the reconstruct based on difference but is a very complicated problems, people have developed multiple computing method over more than 20 year, previous method is based on the reconstruct of consecutive point difference value, up to the reconstructing method that just propose to adapt to big shearing displacement in recent years, make nearest research cause interest widely to lateral shearing interference, but all there is certain limitation in all these methods, suppose that the wavefront that is studied has certain " priori " knowledge such as slickness etc., adopt the little shearing displacement that equals the measurement point interval to measure (sensitivity of Jian Ceing at this moment will be affected), even can only obtain separating of approaching.

Summary of the invention:

Technical matters to be solved by this invention is the defective that overcomes prior art, on basis based on the measured parameter difference value, problem at existing difference reconfiguration technique exists does not need any " priori " knowledge, just can accurately reconstruct to gear shaper without theoretical errors measured parameter generally speaking.

The present invention solves the problems of the technologies described above by following technical scheme.It is characterized in that it is the difference value that records according to two different spacing on the measurand or shearing displacement, then two groups of different difference values are estimated with two-point method one by one respectively, the number of every group of appraisal curve that obtains is the ratio of corresponding transducer spacing or shearing displacement and sampling interval, utilize the mutual relationship between this two sets of curves again, calculate the influence of zero error to evaluation result, obtain in two sets of curves mutual relationship between every curve, at last these curves are synthesized an appraisal curve, thereby realize the accurate reconstruct of measured parameter.The present invention includes following step: sampling interval Δ that (1) selection is certain and transducer spacing r Δ, v Δ; (2) measurand is measured; (3) calculate the difference value of measuring; (4) two groups of different difference values are estimated with two-point method one by one respectively, try to achieve two groups of each r, v bar curve: (5) calculate the difference of zero error and the ratio of transducer spacing or shearing displacement: (6) eliminate the influence of zero error, and try to achieve a certain transducer spacing appraisal curve each point tram relation when surveying; (7) ask the appraisal curve of measured parameter; (8) remove the linear deflection amount of appraisal curve, try to achieve final appraisal curve.

The present invention has following technique effect:

1, applicable to two-point method or three point method the workpiece linearity is estimated, and the various shear interferences measurements that are applicable to variable shearing displacement, comprise and estimate cylindricity, flatness and surface figure accuracy.Therefore do not need to adopt complicated apparatus.

2, can adopt big transducer spacing or shearing displacement.For the evaluation of linearity, cylindricity, flatness etc., because the influence of sensor physical dimension, cause the transducer spacing can not be too little, when estimating as only using one by one method, then spacing is big more, and the spacing distance of estimating point is also big more, to same measurand, then estimate and count fewly more, therefore be difficult to estimate ideally measurand more.For the lateral shearing interference method, too small shearing displacement can cause sensitivity to reduce, and can influence evaluation effect equally.And the method for the present invention of sampling does not then need to adopt little transducer spacing or shearing displacement.

3,, need not suppose that promptly measured parameter has slickness or periodicity etc., so can be suitable for general measurand without any need for " priori " knowledge.

4, can try to achieve the exact evaluation of measurand but not the resulting approximate or evaluation that approaches of existing method.

5, owing to accurately calculated of the influence of sensor zero error, therefore when sensor installation, needn't return to zero accurately or zero error accurately be measured evaluation result.Therefore the present invention has improved detection efficiency greatly and has reduced cost.

6, workpiece size less than or still can carry out accurate reconstruct during greater than the integral multiple of transducer spacing or shearing displacement.

Description of drawings:

Fig. 1 is a measuring process synoptic diagram of the present invention;

Fig. 2 is the process flow diagram of exact evaluation of the present invention.

Embodiment:

The present invention is the difference value that records according to two different spacing on the measurand or shearing displacement, by the accurate reconstruct measured parameter of time domain method.It is at first estimated with two-point method one by one respectively two groups of different difference values, the number of every group of appraisal curve that obtains is the ratio of corresponding transducer spacing or shearing displacement sampling interval, utilize the mutual relationship between this two sets of curves then, calculate the influence of zero error to evaluation result, obtain in two sets of curves mutual relationship between every curve, at last with the synthetic appraisal curve of these curves.The generalized case that this method itself goes for the measured piece size when not being the long-pending integral multiple of two kinds of transducer spacings or shearing displacement, being not equal to integral multiple, measured parameter that transducer spacing or shearing displacement, measured piece size need not equal transducer spacing or shearing displacement as sampling interval is cycle, non-periodic, smooth and non-situation such as smooth, makes precise reconstruction method can really be applied to practice.

As shown in Figure 1, establish sensor and be respectively s at interval ₁And s ₂, sensor mount 4 moves on guide rail 5, and workpiece 6 surperficial linearitys are Ms (x), and workpiece calibration length is p, and total measure dot number is N on the workpiece, and sampling interval is Δ=p/N, and the zero error of sensor is respectively e ₁, e ₂Because there is zero error in sensor, the relative primary curve of surface of the work linearity curve that the historical facts or anecdotes border is measured has produced skew.If two zero errors equate with sensor ratio at interval, i.e. e ₁/ s ₁=e ₂/ s ₂, then Pian Yi result can not bring influence to the evaluation of linearity, but above-mentioned equation is difficult to set up in the actual measurement, i.e. e ₁/ s ₁≠ e ₂/ s ₂, also be difficult to accurately record e ₁And e ₂, but want reconstruct workpiece linearity exactly, then need to know between the two relation or its difference at least.Do twice measurement or adopt three sensors to make the synoptic diagram of one-shot measurement for two sensors of employing (this moment is without sensor 3) among Fig. 1.In the practice, desirable s ₁=A, and s ₂Can get s as required ₂=B, or s ₂=C, the zero error e of sensor ₁=e _A, e ₂=e _BOr e ₂=e _CNote when adopting three sensors, as get s ₂During=B, the initial detection position of slide carriage is the starting point of sensor 2 at workpiece, and 1 pair of sky of sensor this moment moves S up to slide carriage ₁The time sensor 1 just begin image data.Work as s ₂During=C, then the initial detection position of slide carriage is the starting point 7 of sensor 1 at workpiece, and the final position of slide carriage motion is that sensor 2 moves to workpiece terminating point 8, image data not then when sensor 3 exceeds the tested zone of workpiece.

Because the existence of zero error, the appraisal curve that makes two shearing displacements measure has different linear deflection, and as not eliminating the influence of zero error, then final evaluation result can produce mistake equally.Existing all verticality measuring methods both at home and abroad and the report that just calculates the influence of zero error based on the difference value that does not all only adopt two transducer spacings or shearing displacement to record in the restructing algorithm of difference, cylindrical workpiece upset measured the influence of zero error is calculated and adopt six sensors to be divided into two groups, this method operability in practice is not strong, if and for the linearity that is not cylindrical non-rotating symmetrical workpiece, just then its method is difficult to carry out.

As shown in Figure 2, the present invention anatomize two shearing displacements record the data mutual relationship get basic on, the influence of zero error is accurately calculated, concrete computing method are provided below.

If the linearity of workpiece is without loss of generality with function f (x) expression, make f (0)=0 (then can obtain) by translation as non-vanishing.Select suitable relatively prime integer r, v, get two sensor spans and be respectively s ₁=v Δ, s ₂=r Δ, sampling is always counted and is respectively when adopting two kinds of different transducer spacings $n_{s_1}=(r-1)v,$ $n_{s_2}=(v-1)r.$ Discuss in two kinds of situation, a kind of is as workpiece length overall p=s ₁S ₂The time special circumstances ,-kind be as workpiece length overall p ≠ s ₁S ₂The time generalized case.Below for sake of convenience, get Δ=1, p=N then, s ₁=v, s ₂=r, and hypothesis v＜r.

One, as workpiece length overall p=s ₁S ₂The time special circumstances

Step 1: establish p=s ₁S ₂, this moment, total measure dot number was N=rv, the convenience for expressing makes f (m)=f (x _m), m=0, K, N-1;

Step 2: measurand is measured;

Step 3: calculate difference value: Δ f (x)=f (x+s)-f (x), promptly $\mathrm{\Δ}{f}_{j,\mathrm{\σ}}\left(\mathrm{\α}\right)=f_{j,\mathrm{\σ}}(\mathrm{\α}+s_j)-f_{j,\mathrm{\σ}}\left(\mathrm{\α}\right),---\mathrm{\α}=0,K,n_{s_j}-1,j=\mathrm{1,2}$

Step 4: when adopting one by one two-point method to estimate, can obtain s respectively ₁, s ₂The bar curve, because the mutual relationship between these curves is can not determine out in the two-point method measurement, thus be zero at the first point of estimating these curves in season, thereby in twice measurement, our the actual result who records is as follows: $f\left(m\right)+\frac{e_j}{s_j}(m-r_j)-f\left(r_j\right)=G_j(r_j+1,t_j+1),j=\mathrm{1,2},m=0,K,N-1---\left(1\right)$

Separately write as following formula:

Transducer spacing is s ₁The time: $f\left(n\right)+\frac{e_1}{s_1}(n-r_1)-f\left(r_1\right)=G_1(r_1+1,t_1+1)---\left(2\right)$

Transducer spacing is s ₂The time: $f\left(n\right)+\frac{e_2}{s_2}(n-r_2)-f\left(r_2\right)=G_2(r_2+1,t_2+1)---\left(3\right)$

In the formula, n=0,1, Λ, N-1, r ₁=rem (n, s ₁), r ₂=rem (n, s ₂), t ₁=fix (n/s ₁), t ₂=fix (n/s ₂).Symbol rem (x, y) the remainder part after two number x, y are divided exactly is asked in expression, and the maximum integer that is not more than x is asked in fix (x) expression.Obvious r _j=n-t _jS _j, and 0≤r _j≤ s _j, j=1,2.Above the right-hand member of (2) (3) two formula equal signs be the array of depositing the appraisal curve data, the data of the curve that each behavior obtains with two-point method one by one in the array, array index is since 1.

Step 5: calculate e ₁/ s ₁-e ₂/ s ₂Value.

(1) works as n=k ₁S ₁, k ₁=0, Λ, N/s ₁-1 o'clock, have: $f(k_1\·s_1)+\frac{e_1}{s_1}(k_1\·s_1)=G_1(1,k_1+1)---\left(4\right)$ $f(k_1\·s_1)+\frac{e_2}{s_2}(k_1\·s_1-r_2)-f\left(r_2\right)=G_2(r_2+1,t_2+1)---\left(5\right)$ (4) the linearity evaluating data of (5) formula right-hand member for using one by one two-point method to obtain is known quantity.(4) (5) two formulas are subtracted each other and can be got: $\frac{e_1}{s_1}(k_1\·s_1)-\frac{e_2}{s_2}(k_1\·s_1-r_2)+f\left(r_2\right)=G_1(1,k_1+1)-G_2(r_2+1,t_2+1)=A_1---\left(6\right)$ (2) work as n=k ₂S ₂, k ₂=0, Λ, N/s ₂-1 o'clock, have: $f(k_2\·s_2)+\frac{e_2}{s_2}(k_2\·s_2)=G_2(1,k_2+1)---\left(7\right)$ $f(k_2\·s_2)+\frac{e_1}{s_1}(k_2\·s_2-r_1)-f\left(r_1\right)=G_1(r_1+1,t_1+1)---\left(8\right)$

Equally, the linearity evaluating data of (7) (8) formula right-hand member for using one by one two-point method to obtain is known quantity.(7) (8) two formulas are subtracted each other and can be got: $\frac{e_2}{s_2}(k_2\·s_2)-\frac{e_1}{s_1}(k_2\·s_2-r_1)+f\left(r_1\right)=G_2(1,k_2+1)-G_1(r_1+1,t_1+1)=A_2---\left(9\right)$

(6) (9) two formulas of investigation are worked as r ₁=r ₂During=r, two formulas are subtracted each other, and can get: $\frac{e_1}{s_1}(k_1{s}_1+k_2{s}_2-r)-\frac{e_2}{s_2}(k_1{s}_1+k_2{s}_2-r)=A_1-A_2---\left(10\right)$

Thereby by (10) Shi Kede: $\frac{e_1}{s_1}-\frac{e_2}{s_2}=\frac{A_1-A_2}{k_1{s}_1+k_2{s}_2-r}---\left(11\right)$

Obviously, we know, can try to achieve e by v-1 equation at least ₁/ s ₁-e ₂/ s ₂Value in actual measurement, can be weighted all these values on average to reduce The noise.

Step 6: with s ₁Or s ₂The bar curve synthesizes a curve, i.e. reconstruct workpiece linearity profile on the each point of sampling interval.Below as an illustration with the former:

With G ₁(1, j ₁) curve is standard, other curve promoted corresponding difference respectively can fit to a curve, this difference is by G ₂(1, j ₂) come to determine j wherein ₁=1, Λ, N/s ₁, j ₂=1, Λ, N/s ₂Make r=rem ((j ₂-1) s ₂, s ₁), t=fix ((j ₂-1) s ₂/ s ₁), the appraisal curve group after then promoting is: ${\tilde{G}}_1((r+1),:)=G_1(r+1,:)+(G_2(1,j_2)-G_1(r+1,t+1))+(\frac{e_1}{s_1}-\frac{e_2}{s_2})(j_2-1)\·s_2---\left(12\right)$

This moment, evaluation function was: ${\tilde{f}}_1\left(n\right)={\tilde{G}}_1(i,j)---\left(13\right)$

In the formula, n=i+ (j-1) s ₁, i=1, Λ, s ₁, j=1, Λ, N/s ₁

We are with P equally ₂(1, j ₂) curve is standard, other curve is promoted corresponding difference respectively also can fit to a curve: ${\tilde{f}}_2\left(n\right)={\tilde{G}}_2(i,j)---\left(14\right)$

In the formula, n=i+ (j-1) s ₂, i=1, Λ, s ₂, j=1, Λ, N/s ₂

Step 7: select suitable weighting coefficient w ₁(n) and w ₂(n) (n=0,1, Λ, N-1).For simplicity, get w ₁(n)=0.5, w ₂(n)=0.5.

Step 8: try to achieve final evaluation function $\tilde{f}\left(n\right)=\frac{w_1\left(n\right){\tilde{f}}_1\left(n\right)+w_2\left(n\right)({\tilde{f}}_2\left(n\right)+(\frac{e_1}{s_1}-\frac{e_2}{s_2})\·n)}{w_1\left(n\right)+w_2\left(n\right)}---\left(15\right)$

Step 9: remove linear trend, try to achieve final evaluation function.

Two, as p ≠ s ₁S ₂The time generalized case

Generalized case is p ≠ s ₁S ₂, and signal f (x) do not satisfy f (p)=f (0), and still can handle by above way this moment.Again in two kinds of situation:

1, as p＞p ', i.e. the length p＞s of the workpiece of surveying ₁S ₂, then p can be divided into two sections and handle, first segment length is p '=s ₁S ₂, 0≤x＜p ', second segment length also are p '=s ₁S ₂And p-p '≤x＜p obtains the linearity appraisal curve respectively as stated above twice, because what have that p-p '≤x＜p ' zone surveys in these two curves is the same part of workpiece, thus this section curve is shifted with overlapping, thus can obtain exact evaluation result on the whole work-piece length.

2, as p＜p ', i.e. the length p＜s of the workpiece of surveying ₁S ₂, be not less than a certain minimum value p at Workpiece length _MinIn time, still can accurately come out the reconstruct of workpiece linearity.This moment, the minimum length of workpiece must meet some requirements, and this condition requirement at least can be with e ₁/ s ₁-e ₂/ s ₂Calculate, this condition is r ₁=r ₂, r wherein ₁=rem (n, s ₁), r ₂=rem (m, s ₂), n=k ₁S ₁, m=k ₂S ₂, try to achieve at this moment minimum n _MinAnd m _Min, so the accurate reconstruct length of I of workpiece is p _Min=max (n _Min, m _Min).

We suppose that minimum sampling interval is a Δ _Min, the minimum value of transducer spacing or shearing displacement is s _1min=v Δ _Min, relatively prime for guaranteeing two kinds of transducer spacings or shearing displacement, can detect minimum Workpiece length simultaneously again, then getting another transducer spacing or shearing displacement is s _2min=(v+1) Δ _MinThis moment is if Workpiece length is p 〉=s _1minS _2min, then can adopt preceding method to carry out accurate reconstruct.Following method proposes based on this thought, and concrete steps are as follows:

Step 1: select proper sampling interval Δ and transducer spacing r Δ, v Δ

Step 2: the workpiece shortest length that calculates the accurate reconstruct of energy this moment

When adopting the programming of Matlab tool software, its program structure is as follows:

Nf=v*r; N1=Nf-s1; The % search area

for?i＝1：(Nf/s1-1)

r1＝rem(i*s1，s2)；

for?j＝1：(Nf/s2-1)

r2＝rem(j*s2，s1)；

if?r1＝r2

N=max (i*s1, j*s2); The reconfigurable shortest length of % workpiece

if?N＞＝N1

N＝N1；

end

N1＝N；

end

end

end

Step 3: whether judge the measured workpiece physical length greater than this shortest length, as not being then accurately reconstruct;

Step 4: measurand is measured;

Step 5: calculate difference value;

Step 6: the expression way in this step and aforesaid method change to some extent.The previous method result that to be the data that obtain when two kinds of transducer spacings or shearing displacement are measured estimate with two-point method one by one is divided into two groups and comprises s respectively ₁And s ₂Bar appraisal curve, the starting point of every appraisal curve are zero.Present method is at first just with the s in each group ₁And s ₂The bar appraisal curve is combined into an appraisal curve, and step then then is to determine the mutual relationship of the each point on the appraisal curve, respectively these points is put on its right position.If the workpiece linearity represents that with function f (x) transducer spacing or shearing displacement are s ₁And s ₂The time the initial evaluation curve use respectively With Expression, the evaluation function that obtains is at last used

Expression.It is as follows that all curves in each group are combined into a curve representation:

When transducer spacing or shearing displacement are s ₁The time, the initial evaluation curve is ${\tilde{f}}_1\left(i\right)=0,i=\mathrm{0,1},\mathrm{\Λ},s_1-1----\left(17\right)$ ${\tilde{f}}_1\left(i\right)={\tilde{f}}_1(j-s_1)+\mathrm{\Δ}{f}_1(i-s_1),i=s_1,s_1+1,\mathrm{\Λ},N---\left(18\right)$

Equally, when transducer spacing or shearing displacement be s ₂The time, the initial evaluation curve is ${\tilde{f}}_2\left(i\right)=0,i=\mathrm{0,1},\mathrm{\Λ},s_2-1---\left(19\right)$ ${\tilde{f}}_2\left(i\right)={\tilde{f}}_2(i-s_2)+\mathrm{\Δ}{f}_2(i-s_2),i=s_2,s_2+1,\mathrm{\Λ},N---\left(20\right)$

Step 7: calculate e ₁/ s ₁-e ₂/ s ₂:

Work as i=k ₁s ₁The time, $f\left(k_1{s}_1\right)+\frac{e_1}{s_1}\·k_1{s}_1={\tilde{f}}_1\left(k_1{s}_1\right)---\left(21\right)$ $f\left(k_1{s}_1\right)+\frac{e_2}{s_2}\·(k_1{s}_1-r_2)-f\left(r_2\right)={\tilde{f}}_2\left(k_1{s}_1\right)---\left(22\right)$

R in the formula ₂=rem (i, s ₂)=rem (k ₁s ₁, s ₂)

Work as i=k ₂s ₂The time, $f\left(k_2{s}_2\right)+\frac{e_2}{s_2}\·k_2{s}_2={\tilde{f}}_2\left(k_2{s}_2\right)---\left(23\right)$ $f\left(k_2{s}_2\right)+\frac{e_1}{s_1}\·(k_2{s}_2-r_1)-f\left(r_1\right)={\tilde{f}}_1\left(k_2{s}_2\right)---\left(24\right)$

R in the formula ₁=rem (i, s ₁)=rem (k ₂s ₂, s ₁).

Can get by (21), (22): $\frac{e_1}{s_1}{k}_1{s}_1-\frac{e_2}{s_2}(k_1{s}_1-r_2)+f\left(r_2\right)={\tilde{f}}_1\left(k_1{s}_1\right)-{\tilde{f}}_2\left(k_1{s}_1\right)=B_1---\left(25\right)$

Can get by (23), (24): $\frac{e_2}{s_2}{k}_2{s}_2-\frac{e_1}{s_1}(k_2{s}_2-r_1)+f\left(r_1\right)={\tilde{f}}_2\left(k_2{s}_2\right)-{\tilde{f}}_1\left(k_2{s}_2\right)=B_2---\left(26\right)$

Work as r ₁=r ₂=r _mThe time, can get by (25), (26): $\frac{e_1}{s_1}-\frac{e_2}{s_2}=\frac{B_1-B_2}{k_1{s}_1+k_2{s}_2-r}---\left(27\right)$

Step 8: the position relation of determining measured parameter each point when a certain transducer spacing or shearing displacement;

Step 9: the appraisal curve that constitutes measured parameter

$\tilde{f}\left(i\right)={\tilde{f}}_1\left(i\right),i=0:s_1:N---\left(28\right)$

Annotate: i=0: s ₁: N represents i ∈ [0, N], and i=0, s ₁, 2s ₁, Λ, down together.

In like manner: $\tilde{f}\left(j\right)={\tilde{f}}_2\left(j\right)+(e_1/s_1-e_2/s_2)\·j,j=0:s_2:N---\left(29\right)$

Order $\mathrm{\δ}=\tilde{f}\left(j\right)-{\tilde{f}}_1\left(j\right),$ Then $\tilde{f}\left(k\right)={\tilde{f}}_1\left(k\right)+\mathrm{\δ},k=r{:s}_1:N---30$

R=rem (j, s wherein ₁).

Can try to achieve i=(0: s by above step ₁: N), (1: s ₁: N), Λ, (r _m: s ₁: in the time of N)

Value.Also need try every possible means in addition reconstruct all the other as i=(r _m+ 1: s ₁: N), (r _m+ 2: s ₁: N), Λ, (s ₁-1: s ₁: in the time of N)

Value.Then need utilize transducer spacing or shearing displacement to be s this moment ₂The time the initial evaluation curve We know, by above step mule tried to achieve first section of appraisal curve ([0, s ₁-1] part) promptly [0, r _m] time

Value.So utilize the initial evaluation curve

Work as n=r _m-1: s ₂: N or n=r _m: s ₂: during N

Value is: $\tilde{f}\left(n\right)={\tilde{f}}_2\left(n\right)+f(r_m-1)+(e_1/s_1-e_2/s_2)\·(n-r_m+1)---\left(31\right)$ Or $\tilde{f}\left(n\right)={\tilde{f}}_2\left(n\right)+f\left(r_m\right)+(e_1/s_1-e_2/s_2)\·(n-r_m)---\left(32\right)$

Ask r '=rem (n, s ₁), Ci Shi r '=(Λ, r then _m+ 1, r _m+ 2, Λ, s ₁-1), thus just can reconstruct as i=(r _m+ 1: s ₁: N), (r _m+ 2: s ₁: N), Λ, (s ₁-1: s ₁: in the time of N) Value.

Following Matlab program can continue the appraisal curve on these aspects of accurate reconstruct

Value.

for?i＝rm∶s2∶N-1

fxe(i+1)＝fxe2(i+1)+fxe(rm+1)+dt*(i-rm)；

if(i~＝rm)&(i~＝N)

dat＝fxe(i+1)-fxe1(i+1)；

for?j＝rem(i，s1)∶s1∶N-1

fxe(j+1)＝fxe1(j+1)+dat；

end

end

end

Rm is r in the program _m=max (rem (j, s ₁)) value, dt is e ₁/ s ₁-e ₂/ s ₂Value, fxe () is an appraisal curve Array, fxe1 () is the initial evaluation curve

Array.

Step 10: remove linear trend, try to achieve final evaluation function.

So far, final appraisal curve The value that there is an i ∈ [0, N] in last institute all reconstruct come out.

Be noted that in addition, detect the linearity of workpiece at above employing displacement transducer, cylindricity, when flatness and surface figure accuracy, the deflection angle of relative workpiece was to the influence of evaluation result when we had all ignored the slide carriage motion, this influence is very little because in experimenting, we find out that, can ignore, when if the influence of this deflection angle can not be ignored, we then can be provided with an angular transducer (as autocollimator etc.) the deflection angle ri of detecting sensor erecting frame (i=0 wherein in real time on slide carriage, N-s, s is a shearing displacement), in corresponding difference value, deduct stg (r then _i), promptly Δ f ' (i)=Δ f (i)-stg (r _i), (i) replace corresponding Δ f (i) with Δ f ', get final product by method calculating of the present invention again.

Claims (3)

1, a kind of precise reconstruction method that utilizes time domain method to carry out difference measurement, it is characterized in that it is the difference value that records according to two different spacing on the measurand or shearing displacement, then two groups of different difference values are estimated with two-point method one by one respectively, the number of every group of appraisal curve that obtains is the ratio of corresponding transducer spacing or shearing displacement and sampling interval, utilize the mutual relationship between this two sets of curves again, calculate the influence of zero error to evaluation result, obtain in two sets of curves mutual relationship between every curve, at last these curves are synthesized an appraisal curve, thereby realize the accurate reconstruct of measured parameter.

2, the precise reconstruction method that utilizes time domain method to carry out difference measurement according to claim 1 is characterized in that comprising the steps: when the workpiece length overall equals the product at two sensors interval

(1) select certain sampling interval Δ and transducer spacing r Δ, v Δ, the surface of the work measured parameter is represented with function f (x):

f(m)＝f(x _m)，m＝0，K，N-1

(2) measurand is measured:

(3) calculate the difference value of measuring: $\mathrm{\Δ}{f}_{j,\mathrm{\σ}}\left(\mathrm{\α}\right)=f_{j,\mathrm{\σ}}(\mathrm{\α}+s_j)-f_{j,\mathrm{\σ}}\left(\mathrm{\α}\right),---\mathrm{\α}=0,K,n_{s_j}-1,j=\mathrm{1,2}$

(4) two groups of different difference values are estimated with two-point method one by one respectively, are tried to achieve two groups of each r, v bar curve:

Transducer spacing is s ₁The time: $f\left(n\right)+\frac{e_1}{s_1}(n-r_1)-f\left(r_1\right)=G_1(r_1+1,t_1+1)$

Transducer spacing is s ₂The time: $f\left(n\right)+\frac{e_2}{s_2}(n-r_2)-f\left(r_2\right)=G_2(r_2+1,t_2+1)$

(5) calculate the difference of zero error and the ratio of transducer spacing or shearing displacement: $\frac{e_1}{s_1}-\frac{e_2}{s_2}=\frac{A_1-A_2}{k_1{s}_1+k_2{s}_2-r}$

Wherein: A ₁=G ₁(1, k ₁+ 1)-G ₂(r+1, t ₂+ 1), A ₂=G ₂(1, k ₂+ 1)-G ₁(r+1, t ₁+ 1)

(6) eliminate the influence of zero error, and try to achieve a certain transducer spacing appraisal curve each point tram relation when surveying: ${\tilde{f}}_1\left(n\right)={\tilde{G}}_1(i,j)$ Or ${\tilde{f}}_2\left(n\right)={\tilde{G}}_2(i,j)$

(7) try to achieve the appraisal curve of measured parameter: $\tilde{f}\left(n\right)=\frac{w_1\left(n\right){\tilde{f}}_1\left(n\right)+w_2\left(n\right)({\stackrel{\stackrel{.}{~}}{f}}_2\left(n\right)+(\frac{e_1}{s_1}-\frac{e_2}{s_2})\·n)}{w_1\left(n\right)+w_2\left(n\right)}$

(8) remove the linear deflection amount of appraisal curve, try to achieve final appraisal curve.

3, the precise reconstruction method that utilizes time domain method to carry out difference measurement according to claim 1 is characterized in that it comprises the steps: when the workpiece length overall is not equal to the product at two sensors interval

(1) select certain sampling interval Δ and transducer spacing r Δ, v Δ, the surface of the work measured parameter is represented with function f (x):

f(m)＝f(x _m)，m＝0，K，N-1

(2) measurand is measured;

(3) calculate the difference value of measuring: $\mathrm{\Δ}{f}_{j,\mathrm{\σ}}\left(\mathrm{\α}\right)=f_{j,\mathrm{\σ}}(\mathrm{\α}+s_j)-f_{j,\mathrm{\σ}}\left(\mathrm{\α}\right),---\mathrm{\α}=0,K,n_{s_i}-1,j=\mathrm{1,2}$

(4) two groups of different difference values are estimated with two-point method one by one respectively, are tried to achieve two groups of each r, v bar curve:

Transducer spacing is s ₁The time: $f\left(n\right)+\frac{e_1}{s_1}(n-r_1)-f\left(r_1\right)=G_1(r_1+1,t_1+1)$

Transducer spacing is s ₂The time: $f\left(n\right)+\frac{e_2}{s_2}(n-r_2)-f\left(r_2\right)=G_2(r_2+1,t_2+1)$

(5) calculate the difference of zero error and the ratio of transducer spacing or shearing displacement: $\frac{e_1}{s_1}-\frac{e_2}{s_2}=\frac{B_1-B_2}{k_1{s}_1+k_2{s}_2-r}$

Wherein: $B_1={\tilde{f}}_1\left(k_1{s}_1\right)-{\tilde{f}}_2\left(k_1{s}_1\right),$ $B_2={\tilde{f}}_2\left(k_2{s}_2\right)-{\tilde{f}}_1\left(k_2{s}_2\right)$

(6) eliminate the influence of zero error, and try to achieve a certain transducer spacing appraisal curve each point tram relation when surveying;

(7) try to achieve the appraisal curve of measured parameter: $\tilde{f}\left(n\right)={\tilde{f}}_2\left(n\right)+f(r_m-1)+(e_1/s_1-e_2/s_2)\·(n-r_m+1)$ Or $\tilde{f}\left(n\right)={\tilde{f}}_2\left(n\right)+f\left(r_m\right)+(e_1/s_1-e_2/s_2)\·(n-r_m)$

(8) remove the linear deflection amount of appraisal curve, try to achieve final appraisal curve.

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