CN110345867A - A method of the space CMM Point Coordinates error is corrected based on inverse distance weighting - Google Patents
A method of the space CMM Point Coordinates error is corrected based on inverse distance weighting Download PDFInfo
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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 techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
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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
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/045—Correction of measurements
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Abstract
The invention discloses a kind of methods based on the inverse distance weighting amendment space CMM Point Coordinates error, belong to Precision Inspection field.Three coordinate measuring machine (Coordinate Measuring Machine is obtained first with laser traces instrument multi-court position measuring technique based on the measurement method, abbreviation CMM) D coordinates value of measured point in airspace, correction value is obtained by TRAC CAL software data processing.Using anti-distance weighting (Inverse Distance Weighting, IDW), algorithm acquires the correction value of every bit in airspace after acquisition correction value, to further increase the measurement accuracy of CMM.
Description
Technical field
The present invention relates to a kind of raising three coordinate measuring machine (Coordinate Measuring Machine, abbreviation CMM)
The interpolation computing method of measurement accuracy is based particularly on the three coordinate measuring machine airspace coordinate of laser traces multi-court position measuring technique
The amendment of error belongs to Technology of Precision Measurement field.
Background technique
Coordinate measuring machine (Coordinate Measuring Machine, CMM) is as high efficiency in coordinate measuring technology
Precision measurement system, it is high with its measurement accuracy, speed is fast, flexible strong the features such as, in the manufacturing and aviation of modernization, boat
It etc. plays increasingly important role in fields, is the key foundation measuring device and civilian row of advanced manufacturing field
The crucial test equipment of quality testing and control in industry production can complete the geometric elements of various parts, curve and curved surface
3 d space coordinate measurement, and it is able to achieve on-line checking and automatic measurement.Progress and Ultra-precision Turning with science and technology
The development of technology, the requirement to three coordinate measuring engine measurement precision are also higher and higher.And fast and accurately CMM is demarcated,
Detect every error of CMM and carry out error compensation, be one of the important channel for improving CMM measurement accuracy, be it is a kind of with compared with
Low cost increases substantially the advanced technology means of CMM measurement accuracy.
Laser traces instrument is the special equipment for calibrating CMM, by complete under more base stations as portable coordinate measurement system
Quick, high-precision detection may be implemented in the localization method of ball positioning system (Global Positioning System, GPS)
CMM kinematic error.The special measurement software TRAC-CAL of laser traces instrument can provide the error of the tested point of planning, but right
Error in any point in CMM measurement space can not provide.The arrow for the tested point planned in obtaining CMM measurement space
When compensating after amount error using error of the spatial interpolation algorithm to any point in measurement space, the measurement essence of CMM can be made
Degree is further promoted.The airspace interpolation precision of general interpolation algorithm and the regular degree of interpolation algorithm, interpolation area are closely related,
It especially when sample density is lower, is also not quite similar for the precision of the various interpolation of different spaces form, therefore studies interpolation and calculate
Method is of great significance to the fitting precision difference of different spaces model.
It is necessary to design a kind of method based on the inverse distance weighting amendment space CMM Point Coordinates error, energy thus
The enough airspace high-accuracy compensation CMM error of coordinate, to improve CMM space measurement point coordinate measurement precision.
Summary of the invention
The present invention proposes a kind of method based on the inverse distance weighting amendment space CMM Point Coordinates error, it is therefore an objective to
One kind is provided based on laser traces multi-court position measuring technique and utilizes anti-distance weighting algorithm (Inverse Distance
Weighting, abbreviation IDW) error compensating method that three coordinate measuring machine space Point Coordinates are modified, enable
The measurement accuracy of three coordinate measuring machine is improved in actual measurement.To achieve the above objectives, the present invention adopts the following technical scheme that:
The technical solution adopted by the present invention is a kind of based on the inverse distance weighting amendment space CMM Point Coordinates error
Method: this method includes the following steps:
Step 1: the measurement space in three coordinate measuring machine airspace is divided；Open laser traces instrument operating software TRAC CAL
It is operated.Since the pitch range of laser traces instrument is -20 °~+85 °, exceeds or laser can be caused to chase after close to the range
The mechanical oscillation of track instrument influence measurement accuracy, therefore should cook up the three coordinate measuring machine that can smoothly measure in each erect-position
Airspace range, and plan in the space measuring route of laser traces instrument, enable the entire measurement space of measuring route covering.
Step 2: building laser traces multi-court position measurement model；Under three coordinate measuring machine coordinate system, if three-dimensional coordinates measurement
It is C that machine, which measures tested point in space,i(xi,yi,zi), wherein i=1,2,3 ..., n；The erect-position coordinate of laser traces instrument is Pj(Xj,
Yj,Zj), wherein j=1,2,3 ..., m；PjTo CiThe distance of point is dj；The measurement data of laser traces instrument is in measurement process
lij, following relationship is established by three-dimensional space two o'clock range formula:
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；I.e. when carrying out multi-court position measurement, at least four erect-positions are empty to three coordinate machine bed
Between measure and measure points no less than 16；It determines erect-position number, plans each erect-position in three coordinate measuring machine coordinate system
Under position and tested point path, save after the completion of the step and be arranged and generate measurement document.
Step 3: importing three coordinate measuring machine for the measuring route of generation, controls three coordinate measuring machine according to preset path
Movement successively moves laser traces instrument and completes measurement under each erect-position.It can be obtained after having measured by software TRAC CAL
Plan the error correction values of tested point.
Step 4: carrying out interpolation calculation using IDW algorithm for the correction value of acquisition, so that it is any to obtain entire measurement space
The coordinate modification value of point.
For IDW algorithm, it has been corrected around the size of the correction value Δ on space any point S (x, y, z) and the point
Measurement point CiThe Δ of (x, y, z)iWith substantial connection, it can regard the result by these measurement point error contributions as.It considers
Difference of each sampled point to interpolation point distance, percentage contribution etc., and the bigger percentage contribution of distance is smaller.
Assuming that S is any point measured in three coordinate measuring engine measurement spatial dimension, coordinate is (xS,yS,zS)；Really
Determine S point small cubes space affiliated in grid division space；8 vertex for setting up cube are Ci, then to be inserted o'clock to eight
The distance on vertex is divided into:
Then according to point S to be inserted to each sampled point CiDistance and in sampled point CiOn correction value, can calculate S point in x,
Y, the coordinate modification value Δ x in z-axisS,ΔyS,ΔzSCalculation formula is as follows
In formula n be known coordinate of the branch around tested point number, u be adjustable range weight inverse index, one
As be 2.
Step 5: interpolation precision evaluation；In order to evaluate the interpolation of interpolation method, mean error (mean is selected
Error, ME), root-mean-square error (root mean squareerror, RMSE), to evaluate interpolation precision
In conclusion being interfered with the high-precision of laser traces instrument and being surveyed based on laser traces instrument multi-court position measuring technique
Long value is constraint condition, and the modification method of error compensation value is finally obtained using high-precision interpolation algorithm, can effectively be mentioned
The precision of high three coordinate measuring machine measuring point measurement.
Detailed description of the invention
Fig. 1 is the movement routine of target mirror；
Fig. 2 is CMM laser traces instrument multistation level measuring system；
Fig. 3 is that measurement space lattice divides and IDW algorithm schematic diagram；
Fig. 4 a is the space coordinate correction value of IDW algorithm x-axis direction；
Fig. 4 b is the space coordinate correction value in IDW algorithm y-axis direction；
Fig. 4 c is the space coordinate correction value in IDW algorithm z-axis direction.
Fig. 5 is that measurement space lattice divides and Tri linear interpolation schematic diagram；
Fig. 6 a is the space coordinate correction value of Tri linear interpolation x-axis direction；
Fig. 6 b is the space coordinate correction value in Tri linear interpolation y-axis direction；
Fig. 6 c is the space coordinate correction value in Tri linear interpolation z-axis direction；
Specific embodiment
Present invention will be described in further detail below with reference to the accompanying drawings, to enable those skilled in the art referring to specification text
Word can be implemented accordingly.
Relative interference is carried out in experiment using CMM laser traces instrument multistation level measuring system as shown in Figure 2 and surveys long value
Measurement, therefore analyzed by following step:
Step 1: the measurement model of building three coordinate measuring machine airspace error opens laser traces instrument operating software TRAC
CAL sets the spatial dimension that laser traces instrument can be measured smoothly in each erect-position in the airspace of measuring machine, considers measurement essence
The time required to degree and experiment, determine that the erect-position number of laser traces instrument is 4, four erect-positions in the same plane, are not put respectively
At four angles of three coordinate machine bed, the position coordinates of laser traces instrument are set.
Step 2: planning survey path is arranged laser traces instrument path to be measured under each erect-position, is rationally arranged
Afterwards, laser traces instrument Survey Software TRAC CAL generates the document of measurement, and measuring route is imported three coordinate measuring machine, prepares to survey
Amount.The tested point in three coordinate measuring machine space is 42, is 14 in the tested point of sustained height, path planning is as shown in Figure 1.
Step 3: laser traces instrument is placed in default erect-position P1, as shown in Fig. 2, opening the measurement of TRAC CAL software
Interface enables three coordinate measuring machine be moved according to preset path, such as Fig. 1.It carries out turning station after being measured, successively moves laser
Tracker is to erect-position P2, erect-position P3, erect-position P4, the measurement of all tested points is completed by planning path running target mirror.
After measuring successfully, Discrepancy Report is checked, obtain measurement point X, Y, the error correction values of Z axis.The corresponding X of each measurement point
The error correction values of axis are as shown in table 1:
The correction value of the X-axis of 1 tested point of table
Step 4: it is handled using coordinate offset of the IDW algorithm to each planning point of acquisition, to obtain entire three
The coordinate offset of arbitrary point in coordinate measuring machine airspace.The S point coordinate measured in three coordinate measuring engine measurement space is
(xS,yS,zS), eight nearest point C of S point distanceiAnd its corresponding correction value Δi, calculate CiTo the distance d of tested pointi, band
Enter formula (4), the correction value of any point S in space can be found out.The coordinate of the distribution of the coordinate modification value of x-axis such as Fig. 4 a, y-axis
Distribution such as Fig. 4 c of the distribution of the correction value such as coordinate modification value of Fig. 4 b, z-axis.
Step 5: interpolation precision evaluation；Correction value, which is brought into formula (5) and formula (6), can acquire inserting for IDW algorithm
Value precision, the X-axis of coordinate measuring machine, Y-axis, the mean error and root-mean-square error of Z axis are as shown in table 2:
2 IDW algorithm interpolation precision of table
| X-axis | Y-axis | Z axis | |
| Mean error/mm | 9.754E-05 | 3.859E-05 | 2.429E-05 |
| Root-mean-square error/mm | 9.876E-03 | 6.212E-03 | 4.987E-03 |
In order to further evaluate the arithmetic accuracy proposed by the present invention based on the IDW amendment space CMM Point Coordinates error,
IDW algorithm and Tri linear interpolation algorithm are compared.
For Tri linear interpolation algorithm, it is assumed that S is any point that CMM is measured in measurement spatial dimension, coordinate S
(xS,yS,zS)；Small cubes space belonging to determining S point in grid division space；Set up cube 8 vertex be A, B, C,
D, E, F, G, H, wherein for plane ADEF perpendicular to the x-axis of CMM, the distance of S point to plane ADEF is Lx；Plane CDEH perpendicular to
The y-axis of CMM, the distance of S point to plane CDEH are Ly；Perpendicular to the z-axis of CMM, the distance of S point to plane EFGH is plane EFGH
Lz；The measuring point correction value of A, B, C, D, E, F, G, H are obtained by step 4；Pass through (7) three line of formula using the correction value on 8 vertex
The method of property interpolation finds out x respectively, y, the error correction values of z-axis；
WhereinΔA、ΔB、ΔC、ΔD、ΔE、ΔF、ΔG、ΔH、ΔSRespectively A,
B, the coordinate modification value of C, D, E, F, G, H, S；
The coordinate that the S point measured in measuring machine measurement spatial dimension is surveyed in three coordinates is (xS,yS,zS), determine S point in net
Lattice measure in space belonging to small cubes space, eight vertex of the cube are respectively A, B, C, D, E, F, G, H, such as Fig. 5,
And determining corresponding coordinate, the space coordinate correction value of this 8 points is provided by step 4, respectively ΔA、ΔB、ΔC、ΔD、ΔE、
ΔF、ΔG、ΔH、ΔQ, calculate corresponding k1、k2、k3, substitute into formula (7), the space coordinate correction value of S point can be found out, in this way
The space coordinate amendment to pre-set space is just completed, the space coordinate amendment distribution such as space coordinate of Fig. 6 a, y-axis of x-axis is repaired
The space coordinate of positive value distribution such as Fig. 6 b, z-axis correct Distribution value such as Fig. 6 c.
Interpolation precision is calculated.Mean error can be found out by bringing the correction value of acquisition into formula (5) and formula (6)
With root-mean-square error.The results are shown in Table 3 for accuracy comparison:
3 accuracy comparison result of table
It can be seen that carrying out amendment precision of the error of coordinate amendment in airspace than Tri linear interpolation side to CMM using IDW algorithm
It greatly improves.
Claims (1)
1. a kind of method based on the inverse distance weighting amendment space CMM Point Coordinates error: this method includes the following steps:
Step 1: the measurement space in three coordinate measuring machine airspace is divided；Laser traces instrument operating software TRAC CAL is opened to carry out
Operation；Since the pitch range of laser traces instrument is -20 °~+85 °, exceeds or laser traces instrument can be caused close to the range
Mechanical oscillation, influence measurement accuracy, therefore the airspace for the three coordinate measuring machine that can smoothly measure in each erect-position should be cooked up
Range, and plan in the space measuring route of laser traces instrument, enable the entire measurement space of measuring route covering；
Step 2: building laser traces multi-court position measurement model；Under three coordinate measuring machine coordinate system, if three coordinate measuring machine is surveyed
Tested point is C in quantity spacei(xi,yi,zi), wherein i=1,2,3 ..., n；The erect-position coordinate of laser traces instrument is Pj(Xj,Yj,
Zj), wherein j=1,2,3 ..., m；PjTo CiThe distance of point is dj；The measurement data of laser traces instrument is l in measurement processij, press
Three-dimensional space two o'clock range formula establishes following relationship:
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；I.e. when carrying out multi-court position measurement at least four erect-positions to three coordinate machine bed space into
Row measurement and measurement are counted no less than 16；It determines erect-position number, plans each erect-position under three coordinate measuring machine coordinate system
Position and the path of tested point, which saves after the completion is arranged and generates measurement document；
Step 3: importing three coordinate measuring machine for the measuring route of generation, and control three coordinate measuring machine is moved according to preset path,
It successively moves laser traces instrument and completes measurement under each erect-position；Can be obtained by software TRAC CAL after having measured plan to
The error correction values of measuring point；
Step 4: carrying out interpolation calculation using IDW algorithm for the correction value of acquisition, to obtain entire measurement space arbitrary point
Coordinate modification value；
For IDW algorithm, modified survey around the size of the correction value Δ on space any point S (x, y, z) and the point
Measure point CiThe Δ of (x, y, z)iWith substantial connection, it can regard the result by these measurement point error contributions as；In view of respectively adopting
Difference of the sampling point to interpolation point distance, percentage contribution etc., and the bigger percentage contribution of distance is smaller；
Assuming that S is any point measured in three coordinate measuring engine measurement spatial dimension, coordinate is (xS,yS,zS)；Determine S point
Small cubes space belonging in grid division space；8 vertex for setting up cube are Ci, then to be inserted o'clock to eight vertex
Distance is divided into:
Then according to point S to be inserted to each sampled point CiDistance and in sampled point CiOn correction value, calculate S point in x, y, z-axis
On coordinate modification value Δ xS,ΔyS,ΔzSCalculation formula is as follows
N is the number of known coordinate of the branch around tested point in formula, and u is the index of adjustable range weight inverse, and u takes 2；
Step 5: interpolation precision evaluation；In order to evaluate the interpolation of interpolation method, mean error ME and root-mean-square error are selected
RMSE evaluates interpolation precision
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| CN115638754A (en) * | 2022-10-03 | 2023-01-24 | 北京工业大学 | Three-coordinate measuring machine precision distribution method based on inter-zone analytic method |
| CN116610905A (en) * | 2023-07-20 | 2023-08-18 | 中国空气动力研究与发展中心计算空气动力研究所 | Inverse distance weight data interpolation method based on anisotropic scale correction |
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