CN106052556B  A kind of three coordinate measuring machine spatial domain coordinates compensation method  Google Patents
A kind of three coordinate measuring machine spatial domain coordinates compensation method Download PDFInfo
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 CN106052556B CN106052556B CN201610461034.XA CN201610461034A CN106052556B CN 106052556 B CN106052556 B CN 106052556B CN 201610461034 A CN201610461034 A CN 201610461034A CN 106052556 B CN106052556 B CN 106052556B
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 G—PHYSICS
 G01—MEASURING; TESTING
 G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
 G01B11/00—Measuring arrangements characterised by the use of optical means
 G01B11/002—Measuring arrangements characterised by the use of optical means for measuring two or more coordinates
 G01B11/005—Measuring arrangements characterised by the use of optical means for measuring two or more coordinates coordinate measuring machines

 G—PHYSICS
 G01—MEASURING; TESTING
 G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
 G01B21/00—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups
 G01B21/02—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups for measuring length, width, or thickness
 G01B21/04—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups for measuring length, width, or thickness by measuring coordinates of points
 G01B21/045—Correction of measurements
Abstract
Description
Technical field
The present invention relates to a kind of raising three coordinate measuring machine (Coordinate Measuring Machine, abbreviation CMM) The analysis method of measurement accuracy is based particularly on the three coordinate measuring machine spatial domain coordinate modification side of laser traces instrument multicourt position measurement Method belongs to Technology of Precision Measurement and coordinate measuring technology field.
Background technology
Three coordinate measuring machine is as efficient precision measurement system in coordinate measuring technology, with its high certainty of measurement, speed The features such as degree is fast, flexible strong, increasingly important role is played in the fields such as the manufacturing of modernization and Aeronautics and Astronautics, It is key foundation measuring apparatus and the crucial test of quality testing and control in civilian industry production of advanced manufacturing field The 3 d space coordinate of equipment, the geometric element, curve and curved surface that can complete various parts measures, and can realize online checking And automatic measurement.With the development of the progress and Ultraprecision Machining of science and technology, to three coordinate measuring engine measurement precision Requirement it is also higher and higher.And fast and accurately CMM is demarcated, detect every error of CMM and carries out error benefit It repays, is one of the important channel for improving CMM measurement accuracy, is a kind of elder generation increasing substantially CMM measurement accuracy at lower cost Into technological means.
There are many kinds of approach and the measures for improving coordinate measuring machine accuracy, such as improves mechanical structure precision, reduces power change Shape, thermal deformation improve scale precision and using sampling policy appropriate etc..Since coordinate measuring machine is complicated, from raising The means of mechanical structure precision ensure its precision, not only of high cost, and the precision improved is extremely limited.Therefore in high precision, efficiently The coordinate measuring machine calibration technique of rate becomes the advanced technology means for improving coordinate measuring machine measurement accuracy, and Error Compensation Technology exists It is widely applied in coordinate measuring machine.What coordinate measuring machine scaling method was more commonly used at present is laser interferometer, autocollimatic The high precision instruments such as straight instrument, optical sqaure are directly separated 21 errors, and coordinate is detached indirectly using bat, ball row, ball plate etc. 21 errors of measuring machine.
It is to grow up on the basis of robot meterological that laser tracks threedimensional coordinate measurement technology the eighties in last century A kind of novel coordinate measuring technology.Since laser tracking measurement system is developed out for the first time, towards the portable of scene Formula coordinate system  laser tracker solves the problems, such as that coordinate measuring machine calibration efficiency and precision improve.It is tracked based on laser The measuring principle of instrument passes through the positioning of the global positioning system (Global Positioning System, GPS) under more base stations The calibration of CMM may be implemented in method.
The follower of traditional laser tracking system is the shaft precise rotation device that can intersect around two vertical axis of space, The rotation direction of tracking lens or interferometer beam is controlled respectively using two fixed joints, if two rotation when shaft rotates The intersection point of shaft axis is unstable, will cause measurement error, or even laser interferometer can be caused to break light, and whole system is caused to measure It interrupts.Rigging error, structural instability and the thermal deformation etc. of tracking mirror also bring along error simultaneously.It can be seen that comparing In linear measure longimetry, angle measurement can more influence the uncertainty of measurement of laser tracking system.Three are being carried out using laser tracker In the calibration of coordinate measuring machine, although only having used laser tracker precise interference surveys the long measurement method in conjunction with multicourt position, swash The threedimensional ball measurement of coordinates of optical tracker system is not used, but due to the limitation of conventional commercial laser tracker mechanical structure, So that conventional laser tracking system precision is difficult to improve.
German National quantitative study institute (PTB) and United Kingdom National physics laboratory (NPL) joint research and development are dedicated for school The laser traces instrument of quasi numericallycontrolled machine tool and coordinate measuring machine, is capable of providing the range measurement of full accuracy.Interferometer is mounted in universal Around only as the movement of the fixation sphere of the reference mirror of interferometer in regulating device.Due to this principle, the radial direction of rotating machinery shaft Measurement accuracy can't be significantly affected with lateral deviation.The precision of laser tracking is not influenced by mechanical structure, is depended primarily on With reference to the quality of spherical surface and the variation of spatial position.Measurement accuracy can be increased substantially and shorten entire detection cycle.
It is necessary to design a kind of three coordinate measuring machine spatial domain coordinate modification measured based on laser traces instrument multicourt position thus Method, can highprecision calibrating three coordinate measuring machine, to improve the measurement accuracy of three coordinate measuring machine space measurement point.
Invention content
It is an object of the invention to propose a kind of three coordinate measuring machine spatial domain coordinates compensation method, it is therefore an objective to provide a kind of base It is measured in laser traces instrument multicourt position and using Tri linear interpolation (Trilinear interpolation) to space any point The error compensating method being modified enables the measurement accuracy that three coordinate measuring machine is improved in actually measuring.It compares existing Some analysis methods, this method have the characteristics that high certainty of measurement, measurement cost are relatively low and easy to operate.
To achieve the above objectives, the present invention adopts the following technical scheme that：
A kind of three coordinate measuring machine spatial domain coordinates compensation method measured based on laser traces instrument multicourt position, this method include Following step：
Step 1：Build laser traces instrument multicourt position measurement model.Under CMM coordinate systems, if CMM measures tested point in space For A_{i}(x_{i},y_{i},z_{i}), wherein i=1,2,3 ..., n；The centre of sphere of laser traces instrument internal standard ball is O；The station of laser traces instrument Position coordinate is P_{j}(X_{j},Y_{j},Z_{j}), wherein j=1,2,3 ..., m；P_{j}To A_{1}The distance of point is d_{j}；Laser traces instrument in measurement process Measurement data be l_{ij}, such as Fig. 1.Following relationship is established by 2 range formulas of three dimensions：
Equation number is m × n, and unknown number number is 4m+3n.For make equation group can solution should meet：
m×n≥4m+3n (2)
Then m and n meets m >=4, n >=16.
Step 2：It divides and measures space, the vertex of such as Fig. 2, small cubes space are tested point, determine tested point A_{i} CMM measures the coordinate value (x in spatial dimension_{i},y_{i},z_{i}), the mobile route of object of planning target mirror is as shown in Fig. 3.Laser traces The erectposition of instrument is P_{1}, control CMM movement target mirrors and be moved to tested point A according to the path planned_{i}, and measure at this time swash The measurement data l of light tracker_{i1}.Laser traces instrument is moved successively to each erectposition P_{j}, wherein j=1,2,3 ..., m, and by rule It draws path running target mirror and completes all tested point measurement data l_{ij}Measurement.
Step 3：By formula (1) equal sign both sides simultaneously square and transplant obtain equation：
It enablesThen formula (3) is converted into：
Object function is defined as according to least square method：
Make F (X_{j},Y_{j},Z_{j}, k) and minimum, (5) formula should meet following condition：
Meet simultaneously：
Write formula (6) as matrix form：
Erectposition coordinate P can be obtained in solution formula (8)_{i}(X_{j},Y_{j},Z_{j}) and d_{j}。
Step 4：Write formula (1) as error equation：
The error sum of squares obtained using Least Square in Processing formula (9) is：
Formula (10) is a nonlinear equation, and following calculating process is used for convenience of solving：
It enables
Taylor series expansion is carried out to formula (11) using Taylor series expansion, obtains following equation：
Formula (12) is substituted into formula (9), abbreviation has after arranging：
Wherein：Equation (13) is after optimizing Solving model.In formula (12), (13), it is designated as _{0}It is the approximation of the numerical value, x_{i}_{0}、y_{i}_{0}、z_{i}_{0}It is provided by CMM, X_{j}_{0}、Y_{j} _{0}、Z_{j}_{0}、d_{j}It is obtained by solution equation group formula (8).
Enable v_{ij}=0, formula (13) is write as to the form of matrix：
Ax=B (14)
Wherein：
Wherein dx_{i}、dy_{i}、dz_{i}And dX_{j}、dY_{j}、dZ_{j}For the correction value and erectposition P of tested point corresponding coordinate_{j}Corresponding coordinate Correction value.Tested point A can be obtained in solving equations (14)_{i}Correction value (dx_{i},dy_{i},dz_{i})。
Step 5：According to formula (12), tested point A is influenced_{i}Correction value (dx_{i},dy_{i},dz_{i}) variable of precision has x_{i}_{0}、 y_{i}_{0}、 z_{i}_{0}And X_{j}_{0}、Y_{j}_{0}、Z_{j}_{0}、d_{j}, wherein x_{i}_{0}、y_{i}_{0}、z_{i}_{0}It is determined as constant, therefore X after completing step 1_{j}_{0}、Y_{j}_{0}、 Z_{j}_{0}、d_{j}The precision of solution directly affects (dx_{i},dy_{i},dz_{i}) solving precision.X is improved using recursion alternative manner_{j}_{0}、Y_{j}_{0}、Z_{j} _{0}、d_{j}The precision of solution.
The step of alternative manner, is as follows：
1. by point coordinates (x to be measured_{i}_{0},y_{i}_{0},z_{i}_{0}) with obtained correction value (dx_{i},dy_{i},dz_{i}) be added, obtain (x_{i} _{0}',y_{i}_{0}',z_{i}_{0}')；
2. by (x_{i}_{0}',y_{i}_{0}',z_{i}_{0}') and step 2 in obtained l_{ij}Substitution formula (8), solution obtain P_{j}'(X_{j}',Y_{j}', Z_{j}') and d_{j}'；
3. by (x_{i}_{0}',y_{i}_{0}',z_{i}_{0}')、P_{j}'(X_{j}',Y_{j}',Z_{j}') and d_{j}' formula (14) is substituted into, solution obtains in iteration Between correction value (dx_{i}',dy_{i}',dz'_{i}).When iterations are equal to 1, by (dx_{i}',dy_{i}',dz'_{i}) obtained with step 4 (dx_{i},dy_{i},dz_{i}) be compared；It, will be in the intermediate correction value and last iteration of current iteration when iterations are more than 1 Between correction value be compared, see whether the order of magnitude of numerical value is reducing, if there is reduction trend then need to subsequently continue iteration, Iteration is terminated if without reducing；
4. by (x_{i}_{0},y_{i}_{0},z_{i}_{0})、P_{j}'(X_{j}',Y_{j}',Z_{j}') and d_{j}' formula (14) is substituted into, it solves equation group and obtains highprecision Correction value；
5. 1. repeating step arrive process 4., wherein in 1. and (x_{i}_{0},y_{i}_{0},z_{i}_{0}) carry out add operation correction value it is total Newest solution obtains, until iteration ends.
Step 6：Assuming that Q is any point that CMM is measured in measurement spatial dimension, coordinate is (x_{Q},y_{Q},z_{Q}).It determines Q points small cubes space affiliated in grid division space.If cubical 8 vertex are A, B, C, D, E, F, G, H, wherein For plane ADHE perpendicular to the xaxis of CMM, the distance of Q points to plane ADHE is L_{x}；Plane ABFE is perpendicular to the yaxis of CMM, and Q points are to flat The distance of face ABFE is L_{y}；For plane ABCD perpendicular to the zaxis of CMM, the distance of Q points to plane ABCD is L_{z}。
The measuring point correction value of A, B, C, D, E, F, G, H are obtained by step 5.Correction value using 8 vertex passes through formula (17) method of Tri linear interpolation finds out the error correction values of the measuring point.
WhereinΔ_{A}、Δ_{B}、Δ_{C}、Δ_{D}、Δ_{E}、Δ_{F}、Δ_{G}、Δ_{H}、Δ_{Q}, be respectively A, the coordinate modification value of B, C, D, E, F, G, H, Q.
The Δ acquired using formula (17)_{Q}The spatial correction values of as Q points sit the correction value plus the measuring point that CMM is provided Mark (x_{Q},y_{Q},z_{Q}), as finally optimize obtained highprecision coordinate value.
In conclusion based on laser traces instrument multicourt position measuring technique, is interfered with the highprecision of laser traces instrument and surveyed Long value is constraints, and processing is iterated to correction value, finally by the modification method of Tri linear interpolation, can effectively be carried The precision that high CMM measuring points measure.
Description of the drawings
Fig. 1 is laser traces instrument interference lengthmeasuring schematic diagram；
Fig. 2 is to measure space to divide schematic diagram；
Fig. 3 is the mobile route of target mirror；
Fig. 4 is CMM laser traces instrument multistation level measuring systems；
Fig. 5 a are the curve graphs of xaxis direction correction value；
Fig. 5 b are the curve graphs of yaxis adjustment in direction value；
Fig. 5 c are the curve graphs of zaxis adjustment in direction value；
Fig. 6 is to measure space lattice to divide and Tri linear interpolation schematic diagram；
Fig. 7 a are the space coordinate correction values of xaxis direction；
Fig. 7 b are the space coordinate correction values in yaxis direction；
Fig. 7 c are the space coordinate correction values in zaxis direction.
Specific implementation mode
Present invention will be described in further detail below with reference to the accompanying drawings, to enable those skilled in the art with reference to specification text Word can be implemented according to this.
Long value is surveyed to carry out relative interference using CMM laser traces instrument multistation level measuring system as shown in Figure 4 in experiment Measurement, therefore analyzed by following step：
Step 1：Build laser traces instrument multicourt position measurement model.The time required to considering measurement accuracy and experiment, determines and swash The number of light tracker erectposition is 5,5 erectpositions not in approximately the same plane.Number of the space tested point under CMM coordinate systems For 4 × 4 × 4=64, the measuring point number under sustained height is 4 × 4=16.
Step 2：It divides and measures space, determine the coordinate of 64 tested points, corresponding coordinate such as table 1,
The coordinate of 1 tested point of table
Laser traces instrument is positioned over default erectposition P_{1}, as shown in figure 4, by the preset path running target mirror of Fig. 3, it is recorded The data l measured up to laser traces instrument when tested point_{i1}, the measurement until completing all 64 measuring points.It then carries out turning station, successively Laser traces instrument is moved to erectposition P_{2}, erectposition P_{3}, erectposition P_{4}, erectposition P_{5}, all tested points are completed by planning path running target mirror It measures and records measurement data l_{ij}, 5 × 64=320 numerical value is measured altogether.
Step 3：By 64 measuring point coordinates and the 320 measurement data l measured_{ij}Substitution formula (8) simultaneously solves equation group, i.e., The erectposition coordinate P of laser traces instrument can be solved_{j}(X_{j},Y_{j},Y_{j})、P_{j}To A_{1}The distance of point.
Step 4：By the coordinate of 64 measuring points, 320 measurement data l_{ij}, laser traces instrument erectposition coordinate P_{j}(X_{j},Y_{j}, Y_{j}) and P_{j}To A_{1}The distance d of point_{j}Substitution formula (14) solves the space coordinate correction value that equation group can be obtained 64 measuring points.
Step 5：The precision of measuring point coordinate correction value is improved using iterative algorithm.It is as follows：
1. by 64 point coordinates (x to be measured_{i}_{0},y_{i}_{0},z_{i}_{0}) with obtained correction value (dx_{i},dy_{i},dz_{i}) be added, obtain 64 A coordinate (x_{i}_{0}',y_{i}_{0}',z_{i}_{0}')；
2. by 64 coordinate (x_{i}_{0}',y_{i}_{0}',z_{i}_{0}') and step 2 in obtained 320 l_{ij}Substitution formula (8), solves To P_{j}'(X_{j}',Y_{j}',Z_{j}') and d_{j}'；
3. by (x_{i}_{0}',y_{i}_{0}',z_{i}_{0}')、P_{j}'(X_{j}',Y_{j}',Z_{j}') and d_{j}' formula (14) is substituted into, solution obtains in iteration Between correction value (dx_{i}',dy_{i}',dz'_{i}).When iterations are equal to 1, by (dx_{i}',dy_{i}',dz_{i}') obtained with step 4 (dx_{i},dy_{i},dz_{i}) be compared；It, will be in the intermediate correction value and last iteration of current iteration when iterations are more than 1 Between correction value be compared, see whether the order of magnitude of numerical value is reducing, if there is reduction trend then need to subsequently continue iteration, Iteration is terminated if without reducing；
4. by (x_{i}_{0},y_{i}_{0},z_{i}_{0})、P_{j}'(X_{j}',Y_{j}',Z_{j}') and d_{j}' substitute into formula (14), solve equation group obtain precision compared with High correction value；
5. 1. repeating step arrive process 4., wherein in 1. and (x_{i}_{0},y_{i}_{0},z_{i}_{0}) carry out add operation correction value it is total Newest solution obtains, until iteration ends.
To determine that iterative algorithm is effective in the present invention, an emulation experiment has also been carried out herein to be verified. Emulation uses 18 measuring points, 4 erectpositions, the error of introducing and the result such as table 2 acquired.
3 error, noniteration correction value, 1 correction value of iteration, iteration correction value (units of table 2x axis directions introducing： mm)
3 not iteration correction value, 1 correction value of iteration, iteration correction values are made comparisons with the error of introducing respectively, also may be used To be clear that, the error of the correction value acquired the introducing more more close than the correction value for being not added with iteration after iteration is added, Therefore iterative algorithm is effective, and the algorithm of iteration is added can obtain more accurately correction value than method before.
The data that previous experiments obtain are calculated by algorithm, the xaxis direction amendment of 64 finally acquired measuring point Value such as Fig. 5 a, yaxis adjustment in direction value such as Fig. 5 b, zaxis adjustment in direction value such as Fig. 5 c.It can be seen from the figure that CMM is without compensation Xaxis measurement error is between 0.0026mm to 0.0035mm；Yaxis measurement error is between 0.0025mm to 0.0019mm；Zaxis Measurement error is between 0.0056mm to 0.0060mm.
Step 6：CMM is (x in the coordinate for measuring the Q points measured in spatial dimension_{Q},y_{Q},z_{Q}), determine that Q points are surveyed in grid Small cubes space belonging in quantity space, cubical eight vertex are respectively A, B, C, D, E, F, G, H, such as Fig. 6, and Determine corresponding coordinate, the space coordinate correction value of this 8 points is calculated by step 5, respectively Δ_{A}、Δ_{B}、Δ_{C}、Δ_{D}、 Δ_{E}、Δ_{F}、Δ_{G}、Δ_{H}、Δ_{Q}, calculate corresponding k_{1}、k_{2}、k_{3}, substitute into formula (17), you can and the space coordinate correction value of P points is found out, This completes the space coordinate amendments to preset space, such as Fig. 7 a, Fig. 7 b, Fig. 7 c.
By Fig. 7 a, Fig. 7 b, Fig. 7 c, it is clear that the xaxis of CMM, yaxis precision are preferable, and the precision of z axis is opposite It is poor；(270~340mm) × (700~800mm) × ( 500~450mm), (200~240mm) × (800~850mm) × ( 540~400mm) is that this grid measures the optimal measurement space divided.
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