CN102135412A - Workpiece combined measurement method based on distribution law of indeterminacy - Google Patents

Abstract

The invention discloses a workpiece combined measurement method based on a distribution law of indeterminacy. The method comprises the following steps of: extracting key parameters which affect measurement of the indeterminacy by analyzing the distribution law of the indeterminacy of typical near-end and far-end measuring equipment, namely a multi-joint measuring arm and a laser tracker; further comprehensively evaluating a trend of effects on the measurement of the distribution law of the indeterminacy by each key parameter based on a static single-point repeated measurement experiment; and providing the distribution law of the indeterminacy measured by two measuring instruments, so as to further obtain usage laws of the measuring equipment. Repeated measurement of key characteristic points can be realized by carrying out compatible layout on the near-end and far-end measuring equipment, thereby providing necessary basis for high-precision measurement. Finally, fusion of the measured key characteristic points is realized according to a coordinate conversion and fusion algorithm, and high-precision coordinates of the key characteristic points can be obtained according to a registration error of data fusion.

Description

A kind of workpiece combination measurement method based on the uncertainty regularity of distribution

Technical field:

The invention belongs to the high-acruracy survey application of space large scale complex part key feature point, be specifically related to the multiple measurement equipment uncertainty regularity of distribution and make up and data fusion.

Background technology:

Fast development along with space flight and aviation industry, shipping industry, electric power energy industry, auto industry etc. has emerged large quantities of large scale plant equipment and workpiece.Length overall as Air Passenger A380 has reached 73 meters, 7.14 meters of fuselage diameter, and 79.8 meters of the spanes, high 24.1 meters; The ultra large crude carrier that China builds " big brontide " captain has reached 323 meters, 60 meters of molded breadths, 29.3 meters of moldeed depth; The wind power generation blade length of Germany Vensys has reached more than 40 meter.This kind equipment all is the industrial products that are related to national economy and national defense safety, has the important strategic meaning.On the one hand, for space large scale complex equipments such as airframe, boats and ships housing, train, wind electricity blades, profile three-dimensional dimension precision is to weigh the key index of product fluid power performance and good looking appearance, and technical requirement is very high.On the other hand,,, generally adopt first split manufacturing, then the technological process of general assembly splicing because physical dimension and quality are huge for this class large scale plant equipment.In manufacturing and assembling process, how to realize efficient, accurately measurement to large scale plant equipment workpiece set size and morpheme error, be the key factor that guarantees the equipment set quality.Therefore, the space large-scale metrology has become requisite technological means in the current Large-Scale Equipment manufacturing industry.

At present, the equipment that this space-like large scale complex equipment manufacturing and assembling process are positioned with quality testing mainly comprises following two classes: (one) telemeasurement equipment, as laser tracker, electronic theodolite, total powerstation, iGPS space measurement system etc., be characterized in that measurement range is big, but the far-end precision is lower, the local space very flexible.(2) close-in measurement equipment as portable type measuring arm, three coordinate measuring machine, Digital Photogrammetric System etc., be characterized in the precision height, but measurement range is little.And the measurement range that measurement requires of space large scale complex equipment is big, the characteristic of measuring accuracy and flexibility ratio has highlighted the contradiction between overall dimensions big and local space complexity or the high measuring accuracy of local key structure.Cause under the prior art condition, the above-mentioned any measuring equipment of single employing all can't satisfy the measuring task of space large scale complex equipment fully.Especially when measuring crucial positioning reference and unique point, need multiple measurement equipment to merge the raising measuring accuracy, reduce the influence of uncertainty of measurement.Therefore, in the face of the requirement of space large scale complex part key feature point high measurement accuracy, the on-site combined type measuring method that each measuring equipment technical advantage is brought into play in research to greatest extent seems particularly urgent.

Summary of the invention:

In order to satisfy the high-precision requirement of space large scale complex part key feature point measurement, the present invention is intended to by to dissimilar measuring equipments technical advantage and uncertainty analysis of Distribution separately, a kind of highly flexible, the controlled combined type measuring method of precision are proposed, be used for the on-line measurement that space large scale complex equipments such as space flight and aviation, automobile, shipbuilding and wind-power electricity generation are made assembling process, for the measuring accuracy that improves space large scale complex part key feature point provides the corresponding techniques support.

The present invention solves the scheme of inscribing between its technology: a kind of workpiece combination measurement method based on the uncertainty regularity of distribution, according to following steps:

(1) carries out multiple measurement device parameter analysis on Uncertainty, and set up the uncertainty regularity of distribution of measuring equipment by experiment; According to the uncertainty regularity of distribution of measuring equipment, draw the laws of use of measuring equipment;

(2) multiple measurement equipment is carried out compatible layout near key feature point;

(3) carry out the duplicate measurements of key feature point respectively with multiple measurement equipment, obtain measurement data;

(4) measurement data of two equipment gained of gained is carried out Data Fusion, refine the measurement result of coincidence measurement accuracy requirement.

Described step (1) is: carry out the analysis on Uncertainty of FARO corner, obtain the uncertainty rule of FARO corner, obtain the laws of use of FARO; Carry out the analysis on Uncertainty of Laser Tracking instrument parameter, obtain the uncertainty rule of Laser Tracking instrument parameter, obtain the laws of use of laser tracker.

Described step (2) is meant: FARO and laser tracker carry out compatible layout near key feature point.

Described step (3) is meant: FARO and laser tracker are put duplicate measurements to key feature, obtain measurement data.

Described step (4) is meant: two groups of Data Fusion that FARO and laser tracker obtain, ask for rotation matrix and translation matrix; Ask for the data configuration error, the checking measurements precision, and measurement data screened; Measure and finish.

The present invention owing to adopted different measuring equipment uncertainties to determine method and measurement data syncretizing mechanism, makes itself and existing method ratio according to the characteristic of measuring equipment uncertainty and the principle of combined type measurement data fusion, has following characteristics:

1, can be flexible and changeable at the measurement of different space large scale complex equipments, be suitable for solving the problem of different large scale key feature point high-acruracy surveys.

2, the uncertainty distribution characteristics of measuring equipment is dissolved in the dimension measurement method, is improved the measuring accuracy of system greatly, and be well suited for the combined type measuring method.

3, the measurement of far-end measuring equipment is combined with the partial high-precision of proximal measurement equipment on a large scale, make it have the function of measuring labyrinth feature equipment.

4, make full use of data anastomosing algorithm Stability Analysis of Structures, computing characteristic of simple, make the combined type measuring system be suitable for in-site measurement.

5, utilize the uncertainty regularity of distribution of measuring equipment and the range of size of measuring object,, obtain the assembled scheme of near-end and remote equipment, realize high-acruracy survey with the minimum principle of uncertainty of measurement.

Description of drawings:

Fig. 1 is a FARO gage beam structural representation of the present invention;

Fig. 2 is a laser tracker measurement coordinate system synoptic diagram of the present invention;

Fig. 3 is the compatible schematic layout pattern of combined type measuring system of the present invention;

Fig. 4 is the distribution situation synoptic diagram of crucial common point of the present invention.

Wherein: 0 is pedestal; 1 is first rotary joint; 2 is second hinge joint; 3 is the 3rd rotary joint; 4 is the 4th hinge joint; 5 is the 5th rotary joint; 6 is the 6th hinge joint; 7 is the 7th rotary joint.

Fig. 5 is multiple measurement implementation process figure.

Embodiment:

Below in conjunction with accompanying drawing the present invention is done and to describe in further detail:

Referring to Fig. 1-5, at first, uncertainty of measurement with existing near-end and far-end measuring equipment is a research object, key factor by its uncertainty of measurement of analyzing influence, based on different influence factors, study the regularity of distribution of individual equipment uncertainty of measurement respectively, thereby set up the best laws of use of two kinds of measuring equipments, according to best laws of use, for the combined method of equipment and the optimization measurement of equipment combined system are provided fundamental basis.

Secondly, need the characteristics of high-acruracy survey, propose compatible measurement scheme by remote equipment and proximal device duplicate measurements at large scale key feature point.This measurement scheme can be directed to space large scale complex part the accuracy requirement of local key feature point is measured, because two kinds of measuring equipments all can record the parameter of key feature point, can check mutually by the data fusion of relevant coordinate conversion.

At last, realized the data fusion of combination metering system by studying corresponding registration Algorithm and fusion rule.Algorithm mainly realizes with the far-end measuring system as global coordinate system, and the measurement coordinate by the proximal measurement system has been realized the registration link of combination metering system to the conversion of global measuring coordinate system; Uncertainty minimum with combination metering system is a purpose, based on the fusion method under the least mean-square error condition, refines satisfactory measurement result.

Specific implementation process is as follows:

One, determines the uncertainty regularity of distribution and the laws of use (is example with proximal measurement equipment FARO P12-7 seven joint measurment arms and far-end measuring equipment LeicaAT901-LR laser tracker) of multiple measurement equipment

1, the proximal measurement equipment FARO seven joint measurment arm corner uncertainty regularities of distribution

FARO seven joint measurment arms comprise pedestal 0 as shown in Figure 1; First rotary joint 1, the 3rd rotary joint 3, the 5th rotary joint 5, the 7th rotary joint 7 around horizontal rotational shaft are cradle head; Second hinge joint 2, the 4th hinge joint 4, the 6th hinge joint 6 around vertical axes is rotated are hinge joint.By theoretical analysis as can be known: the principal element that influences the FARO gage beam is the corner between sounding rod.Therefore, at its 7 joint rotation angle θ ₁～θ ₂Carry out a series of duplicate measurementss, by studying its duplicate measurements precision, and then the research corner influences rule to the precision of FARO gage beam.Because in the middle of the actual measurement process, 7 joint rotation angles are couple state, cooperatively interact and could work.In order to study the independent effect of each joint rotation angle,, change a certain joint rotation angle separately and study successively by keeping other joint rotation angles constant to FARO gage beam repeatable accuracy.

At first stipulate the use zero-bit state of joint arm, promptly rotary articulated arm is to θ ₁=0, θ ₂=π/4, θ ₃=0, θ ₄=π/4, θ ₅=0, θ ₆=π/4, θ ₇, be designated as the initial position of measurement at=0 o'clock.Under the initial position prerequisite, experiment is at 7 joints, and the corresponding 7 big groups that are divided into are tested, and the size according to the joint rotational angle range in every big group experiment is divided into 5 positions, respectively these 5 fixed positions are carried out 50 times continuous random sampling, wherein the slewing area in each joint is: 0≤θ ₁≤ 2 π (Ψ ₁), 0≤θ ₂≤ pi/2 (Ψ ₂), 0≤θ ₃≤ 2 π (Ψ ₃), 0≤θ ₄≤ π (Ψ ₄), 0≤θ ₅≤ 2 π (Ψ ₅), 0≤θ ₆≤ π (Ψ ₆), 0≤θ ₇≤ 2 π (Ψ ₇).With rotary joint 7 is example, and experimental state is that other joint angles is constant, and θ ₇Evenly get five positions in 0～2 π angular range, as shown in table 1, each position is respectively adopted a little 50.In like manner, to other joint rotation angles θ ₁～θ ₆Respectively do the experiment of five groups, finally obtain 7 big group 35 group's experimental datas.

Table 1 joint seven experimental viewpoint change

For the above-mentioned data of respectively organizing,, introduced the notion of standard deviation in order to reflect the dispersion degree of repeated measurement data.Particularly, three coordinate datas of each each group of joint have been carried out standard deviation A respectively _x, A _y, A _zCalculating.On this basis, with X, Y, the standard deviation A of three coordinates of Z _x, A _y, A _zThe quadratic sum root be defined as error modulus A _i, that is:

$A_i=\sqrt{{A_x}^2+{A_y}^2+{A_z}^2}(i=1,...,5)---\left(1\right);$

The error modulus combines the dispersion degree of three coordinates, and reflection is the spatial spreading degree of duplicate measurements point in fact, i.e. duplicate measurements precision.The error modulus is big more, and the uncertainty influence is big more, and repeatable accuracy is poor more.For the different corners in each joint, by calculating the error modulus of its corresponding 5 small set of data, the variation that can reflect corner influences rule to the uncertainty in this joint; Standard deviation A on three coordinate directions of different five groups of data of corner _x, A _y, A _zComparison on corresponding coordinate can reflect that corner changes to this joint X Y, the uncertainty regularity of distribution of Z component.

By experiment, can obtain the uncertainty regularity of distribution that following each joint rotation angle changes:

1) the first rotary joint corner is at 0≤θ ₁When changing in≤2 π scopes, the apparatus measures uncertainty has the trend that reduces with the increase of angle substantially; At X, Y, on the Z direction, integral body, uncertainty of measurement is along with the increase of angle has the trend that reduces, but trend is not obvious on the Y direction.

2) the second hinge joint corner is at 0≤θ ₂When changing in≤pi/2 the scope, on X, Y, Z direction, at 0≤θ ₂Uncertainty of measurement is along with the increase of angle has the trend of increase, at 2 π/5＜θ in≤2 π/5 scopes ₂The trend that reduces is arranged again in the≤pi/2 scope.

3) the 3rd rotary joint corner is at 0≤θ ₃In≤2 π scopes during change, the apparatus measures uncertainty has the trend of increase with the increase of angle, but trend is not obvious; On Y, Z direction, at 0≤θ ₃Uncertainty of measurement has the trend that reduces along with the increase of angle has the trend of increase in pi/2＜θ≤3 π/4 scopes in the≤pi/2 scope, and the trend of increase is arranged again subsequently, and the Y direction is that the trend that increases is not obvious; And the variation of uncertainty is just opposite with the above two on directions X.

4) the 4th hinge joint corner is at 0≤θ ₄When changing in≤π the scope, the apparatus measures uncertainty has the trend of increase with the increase of angle; On X, Z direction, have earlier and reduce (0≤θ ₄≤ π/4) trend of back increase; Uncertainty of measurement is along with the increase of angle has the trend that reduces on the Y direction.

5) the 5th rotary joint corner is at 0≤θ ₅When changing in≤2 π scopes, the apparatus measures uncertainty has the trend of increase with the increase of angle; 0≤θ on Y, Z direction ₅Uncertainty of measurement is along with the increase of angle has the trend of increase, at π≤θ in the≤π scope ₅In≤2 π scopes, uncertainty of measurement has the trend that reduces on the Y direction, then has to increase earlier the trend that afterwards reduces on X, Z direction.

6) the 6th hinge joint corner is at 0≤θ ₆When changing in≤π the scope, the apparatus measures uncertainty has the trend of increase with the increase of angle; Uncertainty of measurement then has first increase (0≤θ along with the increase of angle has the trend of increase on directions X on Y, Z direction ₄≤ pi/2) trend that reduces after.

7) the 7th rotary joint corner is at 0≤θ ₇When changing in≤2 π scopes, measuring accuracy changes not quite basically, and this has also just in time verified the purpose of design in this joint, and it is to be that equipment improves the gage beam dirigibility, and additional optional the 7th configuration should be minimum to the uncertainty of measurement influence.But can find out joint angles changes increase to the influence of uncertainty of measurement trend on the whole; Uncertainty of measurement then has the trend of increase along with the increase of angle has the trend that reduces on directions X on Y, Z direction.

Concrete measurement statistics is as shown in table 2.

Standard deviation (mm) on each measuring position of table 2 X, Y, the Z direction

In sum, along with the variation of single joint in self slewing area, except that first rotary joint had the trend that reduces slightly, there was the trend that always increases in each joint to the influence of uncertainty; The trend significant degree of hinge joint is greater than cradle head; The rule that influences that rotate three coordinates in identical joint differs, and susceptibility is also different, and influence is little than X, Z direction on the Y direction.The influence degree of the terminal uncertainty of measurement that different joint rotations brings is different, substantially the influence that shows as rotary joint (comprising joint 1,3,5,7) is less than hinge joint (comprising joint 2,4,6), and changes the trend that the influence to measurement result increases the closer to the joint rotation angle of pedestal end.

2, FARO gage beam laws of use

According to the FARO uncertainty regularity of distribution, for reducing Measurement Uncertainty, the laws of use that can draw FARO is:

1) equipment should be arranged in from the nearer position of Measuring Object as far as possible;

2) rotate at hinge joint and rotary joint and realize by rotary joint can reach impact point equally the time as far as possible;

3) select to operate from base coordinate system rotary joint far away;

4) keep angle not excessive for hinge joint as far as possible, and for rotary joint should make its be in the experiment initial position around;

5) for Measuring Object, be that reference dimension is measured with the Y direction, perhaps significant dimensions is placed on the Y orientation measurement.

3, the laser measurement instrument parameter uncertainty regularity of distribution

Laser tracking measurement system is the measuring principle of polar coordinates (spherical coordinates), and the initial point of coordinate system is the follower head center, is X-axis with the horizontal dial zero direction, the direction that makes progress with the normal of scale is the Z axle, determine Y-axis with the right-handed coordinate system rule, set up measurement coordinate system, as shown in Figure 2.When tracker during in spatial movement, instrument is angle value α, the β on record interfeerometry ranging value L and horizontal dial and the vertical circle automatically, according to above-mentioned three observed readings, can obtain a little space three-dimensional rectangular coordinate x, y, z according to the polar coordinate measurement principle.Therefore, the measurement mathematical distribution rule of laser tracker is as the formula (2):

$\left\{\begin{array}{c}x=L\sin \mathrm{\β}\cos \mathrm{\α}\\ y=L\sin \mathrm{\β}\sin \mathrm{\α}\\ z=L\cos \mathrm{\β}\end{array}\right.---\left(2\right);$

The measurement space that uses with Leica AT901-LR laser tracker is benchmark, at above-mentioned three influence factors, this measurement space is carried out grid dividing, on the grid intersection point measurement point is set, and it is 100 specimen sample that measurement point is carried out sample number.Measure the utmost point and directly be decided to be 2000mm, 3000mm, 4000mm, 5000mm and five positions of 6300mm; The α that takes measurement of an angle is decided to be 45 °, 60 °, 70 °, 80 °, 90 °, 100 °, 110 °, 120 °, 135 ° etc.; The β that takes measurement of an angle is decided to be 85 °, 90 ° and 95 °.From the multi-group data of measuring, seek independent effect rule and the cross influence rule of three influence factors to uncertainty.Below be the uncertainty impact analysis and the regularity of distribution thereof when α, β, L are changed:

1) when the α that takes measurement of an angle changes between 45 °, 60 °, 70 °, 80 °, 90 °, 100 °, 110 °, 120 °, 135 °, 27 measured measurement points on utmost point footpath 2000mm, 3000mm and 6300mm carry out standard deviation A to three coordinate datas of each measurement point _x, A _y, A _zCalculating, and error of calculation modulus A.Difference according to utmost point footpath is divided into three groups, the Changing Pattern of relative error modulus A, and standard deviation A _x, A _y, A _zChanging Pattern.It is as follows to reach a conclusion: when α changed by 0 °～90 °, A was and reduces trend; When becoming by 90 °～180 °, A presents slow increase tendency again, and amplitude of variation is less than 0 °～90 °.Wherein the uncertainty on the Y direction is big and fluctuation is also apparent in view; The variation of uncertainty is very little on X, Z direction, can ignore substantially.Along with the increase of L, the influence that the same equal angles of α changes uncertainty of measurement increases.

2) remain unchanged when the α that takes measurement of an angle is 90 °, when β changed between 85 °, 90 °, 95 ° and 112 °, 27 measured measurement points on utmost point footpath 2000mm, 3000mm and 4000mm carried out standard deviation A to three coordinate datas of each measurement point _x, A _y, A _zCalculating, and error of calculation modulus A.Difference according to utmost point footpath is divided into three groups, the Changing Pattern of relative error modulus A, and standard deviation A _x, A _y, A _zChanging Pattern.Can get β when 85 °～112 ° change, A has and reduces the general trend that afterwards increases earlier; Influence to Y is less, and the influence of X, Z is suitable.β has the trend of amplification to the influence of A in the L direction.

3) constant at utmost point footpath L, when α changes, when β changes, record 20 groups of data between 85 °, 90 °, 95 ° and 102 ° between 45 °, 60 °, 90 °, 120 °, 135 °.Three coordinate datas to every group of measurement data are carried out standard deviation A _x, A _y, A _zCalculating, and error of calculation modulus A, thus draw α to the influence of uncertainty of measurement in the regularity of distribution on the β direction and β the regularity of distribution of influence on the α direction to uncertainty.

β is to the regularity of distribution of influence on the α direction of uncertainty---it is the boundary that amplitude of variation is 90 ° with the α value, reduce earlier afterwards to increase, to Y to influence rule comparatively obvious, be the Z direction secondly, minimum is X;

α is to the regularity of distribution of influence on the β direction of uncertainty of measurement---and it is that the boundary reduces earlier afterwards to increase that amplitude of variation is 90 ° with the β value.Wherein the influence degree to Y is the most obvious, is Z secondly, and that minimum is X.

4) when α and β are 0 °, when change utmost point footpath L changes, record 5 groups of data in 2000mm, 3000mm, 4000mm, 5000mm and 6000mm scope.Three coordinate datas to every group of measurement data are carried out standard deviation A _x, A _y, A _zCalculating, and error of calculation modulus A changes and influences rule to what uncertainty was brought thereby draw utmost point footpath L.

Keep then α be 0 ° constant, change β is respectively 85 °, 90 ° and 95 °, when being 2000mm, 3000mm and 6300mm, L records three groups of data, basis of calculation difference and error modulus, thus draw the rule that L changes in the β direction the influence of uncertainty of measurement.

In like manner keep β be 0 ° constant, change α is respectively 45 °, 90 ° and 120 °, when being 2000mm, 3000mm and 6300mm, L records three groups of data, basis of calculation difference and error modulus, thus draw the rule that L changes in the α direction the influence of uncertainty of measurement.

L is to the rule that influences of uncertainty of measurement---and secondly along with the increase of L, the uncertainty of measurement of three coordinate datas has the trend of increase, and the X of increase tendency maximum, is Z, moreover be Y;

The rule that L changes in the α direction the influence of uncertainty of measurement---when changing for 0 °～90 °, influence degree has the trend that reduces, 90 ° of trend that increase is arranged again when changing for 180 °.This trend of coordinate figure Y is comparatively obvious; Secondly being Z, is X at last;

Rule---the trend that influence degree has increase to reduce again that L changes in the β direction the influence of uncertainty of measurement, X is to the amplitude minimum that increases, and Y and Z are suitable.

Table 3 has provided error situation of change under several situations.

Error situation of change (mm) under several situations of table 3

4, Leica laser tracker laws of use

By to the analysis on Uncertainty of laser tracker and the regularity of distribution as can be known: the uncertainty of laser tracker is less than FARO joint measurment arm: promptly the radially uncertainty of laser tracker is little, and laterally uncertainty is big.Therefore, the laws of use that can draw laser measuring apparatus is:

1) equipment layout makes object be vertical shape to be measured relatively as far as possible;

2) two factor-alphas that angle measurement accuracy is low relatively and β are comparatively obvious to the influence of coordinate direction Y and Z, so the layout of equipment should suitably will be measured on the high-precision measuring object deflection directions X;

3), can measure with reference to the Laser Tracking instrument parameter uncertainty regularity of distribution if special coordinate requirement is arranged.

Two, the multiple measurement instrument is carried out compatible layout near near the tested large scale key feature point

Laser measuring apparatus belongs to far-end measuring equipment, and measurement range is wide; Gage beam belongs to proximal measurement equipment, and measurement range is narrower.In order to realize that large scale key feature point is carried out high-acruracy survey, two surveying instruments are carried out compatible formula layout.As shown in Figure 3.1 is the measurement space (shown in the grid filling) of joint arm measuring instrument, and 2 is the measurement space (shown in the right oblique line filling) of laser measuring apparatus.

Three, the key feature point is carried out duplicate measurements, and carry out fusion treatment measuring resulting data

The key feature point coordinate data that two cover measuring equipments are obtained makes up the measurement data point set respectively, and the common point point set that measuring equipment A is recorded is defined as: { p _i| p _i∈ R ³, i=1,2 ..., N}, the common point point set that measuring equipment B records is defined as: { q _i| q _i∈ R ³, i=1,2 ..., N}.Two groups of measured key feature point set coordinates are carried out center of gravity calculating, the coordinate homogenizing of the common point of two coordinate systems is calculated to being the center of gravity coordinate of initial point with the center of gravity, be designated as respectively

With

The coordinate of the center of gravity of two coordinate systems is respectively P _R=(x _R, y _R, z _R) and Q _R=(x ' _R, y ' _R, z ' _R)Be shown below:

$\left\{\begin{array}{c}{x}_R=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i}{n},y_R=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i}{n},z_R=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i}{n}\\ x_R^{\′}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i^{\′}}{n},y_R^{\′}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i^{\′}}{n},Z_R^{\′}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{z}_i^{\′}}{n}\\ {\stackrel{\‾}{x}}_i=x_i-x_R,{\stackrel{\‾}{y}}_i=y_i-y_R,{\stackrel{\‾}{z}}_i=z_i-z_R\\ {\stackrel{\‾}{x}}_i^{\′}=x_i^{\′}-x_R^{\′},{\stackrel{\‾}{y}}_i^{\′}=y_i^{\′}-y_R^{\′},{\stackrel{\‾}{z}}_i^{\′}=z_i^{\′}-z_R^{\′}\end{array}\right.---\left(3\right);$

That is: $\stackrel{\‾}{P}=P-P_R,$ $\stackrel{\‾}{Q}=Q-Q_R.$

The result obtains following relation:

P _R＝RQ _R (4)；

In order to improve the precision of data registration, promptly to reduce the response point spacing minimum of two groups of data after registration, i.e. the alignment of two point sets coupling is converted to and makes following objective function minimum, is shown below:

f(R，T)＝min∑[Rp+T-q] ² (5)；

Through after the center of gravityization of coordinate system, the objective function deformable is:

$\mathrm{\Σ}{\left|\right|\stackrel{\‾}{P}-R\stackrel{\‾}{Q}\left|\right|}^2=\mathrm{\Σ}({\stackrel{\‾}{P}}^T\stackrel{\‾}{P}+{\stackrel{\‾}{Q}}^T\stackrel{\‾}{Q}-2{\stackrel{\‾}{P}}^{T}R\stackrel{\‾}{Q})---\left(6\right);$

Can obviously draw by formula, ask objective function to minimize and also just equal to ask

Maximization.Order

Then objective function can be converted into the diagonal of a matrix element summation operator maximization of asking matrix RJ again.J carried out svd J=U ∧ V ^TSo, can draw optimum rotation matrix R=VU ^T, can get:

T＝P _R-R·Q _R (7)；

By said process, can obtain rotation matrix and translation matrix in the data registration.

In addition, the data registration error of two measuring equipment gained is calculated:

E＝P-(R·Q+T) (8)；

According to the measuring accuracy requirement of setting, extract the measurement data that meets the demands, reject the measurement data that does not satisfy accuracy requirement, finish combined data and measure.

Practical measuring examples

The practicality of the measuring method of inventing in order to verify, the standard ball of laying some on the marble testing table is as crucial common point, the uncertainty regularity of distribution based on resulting multiple measurement equipment in the implementation process, Leica AT901-LR laser tracker and the FARO gage beam that is adopted carried out the compatibility layout, laws of use with reference to two kinds of surveying instruments, respectively common point is carried out the point data collection, then two kinds of surveying instrument gained measurement data are carried out data fusion, translation vector and the rotation matrix required to the two coordinate conversion calculate, and ask for the data registration error, the measurement result of accuracy requirement is satisfied in extraction, reject the data that do not meet the demands, checking combined type measuring equipment is to the rationality of large-size workpiece key feature point high-precision measuring method.

According to the high characteristics of laser tracker telemeasurement precision, in the example with laser tracker as system's global coordinate system, data space merges main the conversion to the laser tracker measurement coordinate system by the measurement coordinate system of FARO gage beam to be realized.

For determining of crucial common point quantity,, generally select 6 common points or the common point more than 6 comparatively suitable in order to improve the coordinate conversion precision.Adopt 7 common points to carry out the data fusion registration of laser tracker coordinate system and FARO gage beam coordinate system in the example.Under laboratory environment,, adopt laser tracker and FARO free arm to measure S successively respectively according to order shown in Figure 4 ₁～S ₇Seven points.During measurement, respectively based on the resulting measuring equipment uncertainty regularity of distribution and laws of use in the implementation process, so that obtain the high-acruracy survey result, each instrument repeats respectively to adopt ten times when gathering same point.And adopt the method remove maximal value and minimum value and to average to draw the coordinate figure that will merge, shown in table 4 and table 5.

Table 4FARO gage beam is measured the common point coordinate figure

Table 5 laser tracker is measured the common point coordinate figure

Above-mentioned measurement result is carried out Data Fusion, can obtain rotation matrix and translation matrix is as follows:

$R=\left[\begin{array}{ccc}0.8404& -0.0094& 0.5419\\ 0.5420& 0.0067& -0.8404\\ 0.0043& 0.9999& 0.0107\end{array}\right]$

$T=\left[\begin{array}{c}-1007.5314\\ 3217.4467\\ -493.5044\end{array}\right]$

Pass through above-mentioned data registration and calculate, the data that 7 measured points of FARO gage beam pass through behind the data fusion registrations are as shown in table 6:

Result behind the table 6FARO gage beam measurement coordinate figure registration

The coordinate figure of the unconverted shown in above-mentioned registration results and the table 3 is compared calculating according to formula (8), and the error E that can get this data registration Algorithm is:

$E=\left[\begin{array}{ccc}-0.012& 0& -0.009\\ 0.019& 0.001& 0.008\\ 0.023& -0.037& 0.004\\ -0.001& -0.008& -0.005\\ -0.023& 0.017& -0.002\\ -0.006& 0.024& 0.003\\ 0.001& 0.003& 0.001\end{array}\right]$

By the result as can be known: the single coordinate maximum error of registration results is 0.037mm, meets the high-acruracy survey requirement of large scale key feature point.In addition, if registration error is bigger, measurement result that can error is bigger is rejected, and reduces the influence of uncertainty of measurement.

Above content is to further describing that the present invention did in conjunction with concrete preferred implementation; can not assert that the specific embodiment of the present invention only limits to this; for the general technical staff of the technical field of the invention; without departing from the inventive concept of the premise; can also make some simple deduction or replace, all should be considered as belonging to the present invention and determine scope of patent protection by claims of being submitted to.

Claims (5)

1. workpiece combination measurement method based on the uncertainty regularity of distribution is characterized in that: according to following steps:

(1) carries out multiple measurement device parameter analysis on Uncertainty, and set up the uncertainty regularity of distribution of measuring equipment by experiment; According to the uncertainty regularity of distribution of measuring equipment, draw the laws of use of measuring equipment;

(2) multiple measurement equipment is carried out compatible layout near key feature point;

(3) carry out the duplicate measurements of key feature point respectively with multiple measurement equipment, obtain measurement data;

(4) measurement data of two equipment gained is carried out Data Fusion, refine the measurement result of coincidence measurement accuracy requirement.

2. a kind of according to claim 1 workpiece combination measurement method based on the uncertainty regularity of distribution, it is characterized in that, described step (1) is: carry out the analysis on Uncertainty of FARO corner, obtain the uncertainty rule of FARO corner, obtain the laws of use of FARO; Carry out the analysis on Uncertainty of Laser Tracking instrument parameter, obtain the uncertainty rule of Laser Tracking instrument parameter, obtain the laws of use of laser tracker.

3. a kind of according to claim 1 workpiece combination measurement method based on the uncertainty regularity of distribution is characterized in that, described step (2) is meant: FARO and laser tracker carry out compatible layout near key feature point.

4. a kind of according to claim 1 workpiece combination measurement method based on the uncertainty regularity of distribution is characterized in that described step (3) is meant: FARO and laser tracker are put duplicate measurements to key feature, obtains measurement data.

5. a kind of according to claim 1 workpiece combination measurement method based on the uncertainty regularity of distribution is characterized in that, described step (4) is meant: two groups of Data Fusion that FARO and laser tracker obtain, ask for rotation matrix and translation matrix; Ask for the data configuration error, the checking measurements precision, and measurement data screened; Measure and finish.

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