CN104374317A - Machine tool error calibration method based on multi-point measurement technology of laser tracker - Google Patents

Machine tool error calibration method based on multi-point measurement technology of laser tracker Download PDF

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CN104374317A
CN104374317A CN201410638347.9A CN201410638347A CN104374317A CN 104374317 A CN104374317 A CN 104374317A CN 201410638347 A CN201410638347 A CN 201410638347A CN 104374317 A CN104374317 A CN 104374317A
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erect
tested point
coordinate
sigma
value
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CN104374317B (en
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陈洪芳
石照耀
闫昊
谭志
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北京工业大学
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Abstract

The invention relates to a machine tool error calibration method based on the multi-point measurement technology of a laser tracker and belongs to the technical field of precision testing. On the basis of the measurement method, firstly, points to be measured are arranged on a machine tool and numbered; during measurement, a master ball target mirror is moved to all the points to be measured respectively, the laser tracker is used for measurement outside the region of the points to be measured, the laser tracker is moved in sequence to obtain three-dimensional coordinate values of the points to be measured at different stations and an interference length measurement value between every two adjacent points to be measured, and by means of an error equation of the interference length measurement values, the initial coordinate value of each station and the initial distance value at the corresponding station are obtained according to the least square principle. By means of the initial coordinate values of all the stations, measured values of the points to be measured and the distance values between the stations and the initial point to be measured, correction values of the points to be measured can be calculated through a linear expansion equation of the error equation of the interference length measurement values. Thus, the positioning accuracy of spatial measurement points on the machine tool is improved.

Description

A kind of machine tool error scaling method based on laser tracker multimetering technology
Technical field
The present invention relates to a kind of measuring method, particularly based on the machine tool error scaling method of laser tracker multimetering technology.Belong to Precision Inspection field.
Background technology
Along with the development of modern industry, more and more higher requirement is proposed to the precision of lathe.The precision of lathe and precision stability are the important technology indexs of lathe.Because in the process of commercial measurement, manufacture, due to be worn and be out of shape, factor impact that installation etc. is different, make lathe there is error.
Improve the attention that machine tool accuracy has been subject to Many researchers.General raising machine tool accuracy has two kinds of basic skills, one is error prevention, another kind is error compensation method, wherein error compensating method common are: material standard mensuration, laser driven shock wave, orthogonal grating mensuration, laser interferometry etc., the most conventional with laser interferometer, though laser interferometer has higher measuring accuracy, build different optical paths to needing during different error measure, sense cycle is longer, can not meet high precision, fast testing requirement.
Be necessary that invention one is suitable for lathe, the method for its error of energy Fast Calibration, to improve the positioning precision of lathe space measurement point for this reason.
Summary of the invention
The machine tool error scaling method of technology, has high precision, fast real-time follow-up and the feature such as simple to operate.
For reaching above object, the present invention takes following technical scheme to be achieved:
Based on a machine tool error scaling method for laser tracker multimetering technology, comprise following measuring process:
During measurement, first the moving range of each axle of lathe is determined, then in each axle system moving range of lathe, tested point is planned, in the measurement space that the choosing of tested point needs to be distributed in whole lathe, and number in order: the 1st tested point, the 2nd tested point ... n-th tested point, presses the discharge serial number of tested point usually, number order does not have mandatory requirement, but will remember the number n of the numbering that each tested point is corresponding and tested point altogether.Then the probe of lathe is displaced with target mirror, laser tracker is placed into the edge in machine tool measuring space, if this erect-position is the initial erect-position of laser tracker, erect-position puts the mobile route that will meet and not hinder lathe, and laser tracker has straight line sighting distance to target mirror under ensureing each erect-position, guarantee that laser tracking head can follow the tested point path pre-set.
Usually tracker is placed on the periphery of machine tool measuring platform, the moving range of tested point can be met so to greatest extent and guarantee that the erect-position of laser tracker does not affect the movement of lathe.
Control lathe and move to each point to be measured, and measure interference length-measuring value now and record the coordinate figure of tested point under lathe coordinate system, the coordinate figure of following all coordinate systems is all the coordinate figure under lathe coordinate system, move laser tracker successively to all the other erect-positions, suppose that erect-position number is m, the coordinate of each erect-position is (X k, Y k, Z k), wherein k=1,2 ..., m.Lathe arranges n tested point, and the coordinate of tested point is (x i, y i, z i), wherein i=1,2 ..., n.Erect-position number demand fulfillment equation m × n >=3n+4m.。Move laser tracker successively to each erect-position, and by the complete all tested points of tested point proceeding measurement until complete the measurement of all erect-positions.
If laser tracker to the distance of the initial tested point of lathe is, in measuring process, laser tracker obtains relative interference measurement increment between tested point is l i, under machine coordinates, choosing the tested point being numbered 1 is initial measurement point, and the initial measurement point tested point all for this reason under each erect-position, when target mirror is from initial measurement point T 0(x, y, z), moves to any tested point T i(x, y, z), laser tracker interference length-measuring increment is l, then spatially two-point defined line equation can set up following relational expression:
( x i - X j ) 2 + ( y i - Y j ) 2 + ( z i - Z j ) 2 = d j + l i - - - ( 1 )
In above formula, to be that lathe is to be measured respectively count and laser tracker standing capacity i and j.Suppose that laser tracker measures tested point under m erect-position, under lathe coordinate system, the coordinate of each erect-position is (X j, Y j, Z j), wherein j=1,2 ..., m.Lathe has n tested point, the coordinate of tested point is (x i, y i, z i), wherein i=1,2 ..., n.
During actual measurement, l itrue value high-precision interference can be utilized relatively to find range replacement, then the error equation of i-th tested point under a jth erect-position is:
v ij = ( ( x i - X j ) 2 + ( y i - Y j ) 2 + ( z i - Z j ) 2 - d i ) - l i - - - ( 2 )
If tested point (x i, y i, z i) gather for T, erect-position coordinate (X j, Y j, Z j) gather for P, laser interference length-measuring l iset is L, to the distance d of initial tested point under each erect-position jset is D; Least square method process equation (2) is utilized to make error sum of squares E (T, P, D) minimum:
E ( T , P , D ) = Σ i = 1 Σ j = 1 v ij 2 ( L , P , T , D ) ( i = 1,2,3 , . . . n , j = 1,2,3 , . . . m ) - - - ( 3 )
Because equation (2) is a Nonlinear System of Equations, directly use equation (2) to solve abnormal cumbersome, adopt following manner to solve:
Suppose there be n lathe tested point, had m laser tracker standing capacity; Under lathe coordinate system, unknown parameter is 3n tested point coordinate T i(x i, y i, z i) and 3m laser tracking erect-position coordinate P j(X j, Y j, Z j) and m each erect-position under to the distance d of initial tested point j.
So unknown number is 3n+4m altogether, and each erect-position can provide n interference length-measuring value, m × n equation altogether, for making equation have solution, and demand fulfillment m × n >=3n+4m, peer-to-peer (2) is carried out linear expansion and can be obtained:
v ij = L ij o - d j 0 - l i + ( x i 0 - X j 0 ) L ij 0 ( Δx i - ΔX j ) + ( y i 0 - Y j 0 ) L ij o ( Δ y i - ΔY j ) + ( z i 0 - Z j 0 ) L ij o ( Δz i - ΔZ j ) - Δ d j - - - ( 4 )
Wherein:
Equation (4) is optimization and resolves model, needs given iterative initial value, wherein Δ x when the variable being designated as zero is and resolves in formula i, Δ y i, Δ z i,, be respectively the coordinate correction value of reference frame tested point and the corrected value of laser tracker erect-position coordinate particle, for each erect-position particle is to the corrected value of the distance of initial tested point.In actual measurement initial value needs the D coordinates value optimizing tested point under can directly reading reference frame.And the coordinate initial value of each erect-position particle of laser tracker, and each erect-position particle needs to ask for the following method to the distance initial value of initial tested point:
If the approximate value of laser tracker erect-position coordinate is as iterative initial value, so the tested point coordinate needing to ask for corrected value might as well be set temporarily as true value, then tested point coordinate T in equation (1) i(x, y, z) and interference length-measuring increment be known variables, utilize the tested point coordinate figure under each erect-position and interference length-measuring increment, the initial tested point distance value that under the coordinate figure of Calibration of Laser tracker particle under each erect-position and corresponding erect-position, particle arrives respectively, as j=1, then equation (1) becomes:
( x i - X 1 ) 2 + ( y i - Y 1 ) 2 + ( z i - Z 1 ) 2 = d 1 + l i - - - ( 5 )
Write equation (5) as error equation:
v i = ( x i - X 1 ) 2 + ( y i - Y 1 ) 2 + ( z i - Z 1 ) 2 - ( d 1 + l i ) - - - ( 6 )
Wherein,, be the coordinate figure of laser tracker first erect-position under lathe coordinate system, (x i, y i, z i) tested point coordinate figure for measuring under corresponding erect-position, be the error amount that under the 1st erect-position, each tested point is corresponding.
If carry out least square to above formula to solve and can obtain:
∂ v i 2 ∂ X 1 = Σ i = 1 n x i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i 2 X 1 - 2 Σ i = 1 n y i x i Y 1 - 2 Σ i = 1 n z i x i Z 1 - 2 Σ i = 1 n l i x i d 1 + Σ i = 1 n x i k = 0 - - - ( 7 )
∂ v i 2 ∂ Y 1 = Σ i = 1 n x i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i y i X 1 - 2 Σ i = 1 n y i 2 Y 1 - 2 Σ i = 1 n z i y i Z 1 - 2 Σ i = 1 n l i y i d 1 + Σ i = 1 n y i k = 0 - - - ( 8 )
∂ v i 2 ∂ Z 1 = Σ i = 1 n x i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i z i X 1 - 2 Σ i = 1 n y i z i Y 1 - 2 Σ i = 1 n z i 2 Z 1 - 2 Σ i = 1 n l i z i d 1 + Σ i = 1 n z i k = 0 - - - ( 9 )
∂ v i 2 ∂ d 1 = Σ i = 1 n l i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i l i X 1 - 2 Σ i = 1 n y i l i Y 1 - 2 Σ i = 1 n z i l i Z 1 - 2 Σ i = 1 n l i 2 d 1 + Σ i = 1 n l i k = 0 - - - ( 10 )
∂ v i 2 ∂ k 1 = Σ i = 1 n ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i X 1 - 2 Σ i = 1 n y i Y 1 - 2 Σ i = 1 n z i Z 1 - 2 Σ i = 1 n l i d 1 + Σ i = 1 n k = 0 - - - ( 11 )
The initial distance value d under the coordinate figure of the 1st erect-position under lathe coordinate system and corresponding erect-position can be tried to achieve in simultaneous equation (7) and (11), with should.Time, can in the hope of the initial distance value d of all the other erect-positions under the coordinate figure and corresponding erect-position of lathe coordinate system.Utilize the initial value of each erect-position point and tested point measured value and corresponding erect-position to the distance value of initial tested point, namely can pass through the corrected value that equation (4) solves each tested point.
Corrected value is added the three-dimensional value of former measurement point is the high-precision three-dimensional coordinate figure after final optimization pass.
To sum up, the inventive method, based on laser tracker multipoint positioning measuring technique, utilizes laser tracker high precision to survey long value as constraint, effectively can improve the precision of lathe space measurement point D coordinates value.
Accompanying drawing explanation
Fig. 1 is that laser follows the tracks of multimetering model schematic.
Fig. 2 is the schematic diagram of the machine tool error scaling method based on laser tracker multimetering technology.
Fig. 3 is each coordinate correction value curve map utilizing laser multimetering Optimized model to ask for
Embodiment
Below in conjunction with accompanying drawing, the invention will be further described:
1) as shown in Figure 2, arrange some tested points by lathe, planned the mobile route of tested point and numbered.Then the probe on main shaft is changed into the standard ball target mirror of laser tracker, measure tested point by tested point numbering moving target target mirror.Move laser tracker successively under different erect-positions, again by identical number order duplicate measurements tested point.
2) suppose have 96 tested points, i.e. n=96.5 erect-positions, i.e. m=5 are moved altogether during measurement.Under lathe coordinate system, the coordinate figure of tested point is Ti (x i, y i, z i), measure the interference length-measuring value l between adjacent tested point i, then utilize the tested point coordinate figure T under each erect-position i(x i, y i, z i) and interference length-measuring value l iby the simultaneous solution of equation (7) (11) can try to achieve laser tracker erect-position coordinate approximate value and and corresponding erect-position under laser tracker to the approximate value of initial tested point distance, in like manner can try to achieve the erect-position coordinate approximate value value of laser tracker under all the other erect-positions, and then as the initial guess of equation (4) iterative.Each erect-position approximate value of laser tracker and tested point measured value and erect-position are substituted into equation (4) to the approximate value of initial tested point distance, the corrected value of each tested point can be solved.Directly measure the tested point initial value obtained under utilizing the tested point corrected value asked for add reference frame, be revised high precision tested point coordinate figure.
3) with 2) in method obtain successively 5 erect-positions initial value and and corresponding erect-position to the distance value of initial tested point, add the coordinates measurements of tested point, namely solve the corrected value of each tested point by equation (4).Corrected value is added the three-dimensional value of point to be measured is the high-precision three-dimensional coordinate figure after final optimization pass.
Embodiment 2:
In order to verify that laser follows the tracks of validity and the correctness that model is resolved in multimetering optimization, test as follows, laser tracker measures 36 the space tested points provided by three coordinate measuring machine under 5 erect-positions, and its coordinate figure is as shown in table 1.
36 measurement points (unit: mm) that table 1 three coordinate measuring machine provides
Altogether measure lathe three planes, each plane surveying 12 tested points, the Z axis coordinate of three planes is respectively-550.738mm,-400.738mm,-250.738mm, be initial measurement plane with the plane of Z=-550.738mm, number at remaining 12 measurement points of this planar movement clockwise, the first floor starting point spatial value of numbering 1 is (600.498mm, 550.831mm,-550.738mm), the second layer starting point coordinate value of numbering 13 is (600.498mm, 550.831mm,-400.738mm), the third layer starting point coordinate value of numbering 25 is (600.498mm, 550.831mm,-250.738mm).To each coordinate correction value drafting curve map as shown in Figure 3 that laser multimetering Optimized model is asked for.As can be seen from the figure, the three-axis measurement error of lathe is between 0.01mm to-0.008mm.

Claims (1)

1., based on a machine tool error scaling method for laser tracker multimetering technology, comprise following measuring process:
During measurement, first the moving range of each axle of lathe is determined, then in each axle system moving range of lathe, tested point is planned, in the measurement space that the choosing of tested point needs to be distributed in whole lathe, and number in order: the 1st tested point, the 2nd tested point ... n-th tested point, presses the discharge serial number of tested point usually, number order does not have mandatory requirement, but will remember the number n of the numbering that each tested point is corresponding and tested point altogether; Then the probe of lathe is displaced with target mirror, laser tracker is placed into the edge in machine tool measuring space, if this erect-position is the initial erect-position of laser tracker, erect-position puts the mobile route that will meet and not hinder lathe, and laser tracker has straight line sighting distance to target mirror under ensureing each erect-position, guarantee that laser tracking head can follow the tested point path pre-set;
Usually tracker is placed on the periphery of machine tool measuring platform, the moving range of tested point can be met so to greatest extent and guarantee that the erect-position of laser tracker does not affect the movement of lathe;
Control lathe and move to each point to be measured, and measure interference length-measuring value now and record the coordinate figure of tested point under lathe coordinate system, the coordinate figure of following all coordinate systems is all the coordinate figure under lathe coordinate system, move laser tracker successively to all the other erect-positions, suppose that erect-position number is m, the coordinate of each erect-position is (X k, Y k, Z k), wherein k=1,2 ..., m; Lathe arranges n tested point, and the coordinate of tested point is (x i, y i, z i), wherein i=1,2 ..., n; Erect-position number demand fulfillment equation m × n>=3n+4m; ; Move laser tracker successively to each erect-position, and by the complete all tested points of tested point proceeding measurement until complete the measurement of all erect-positions;
If laser tracker is d to the distance of the initial tested point of lathe j, in measuring process, laser tracker obtains relative interference measurement increment between tested point is l i, under machine coordinates, choosing the tested point being numbered 1 is initial measurement point, and the initial measurement point tested point all for this reason under each erect-position, when target mirror is from initial measurement point T 0(x, y, z), moves to any tested point T i(x, y, z), laser tracker interference length-measuring increment is l, then spatially two-point defined line equation can set up following relational expression:
( x i - X j ) 2 + ( y i - Y j ) 2 + ( z i - Z j ) 2 = d j + l i - - - ( 1 )
In above formula, to be that lathe is to be measured respectively count and laser tracker standing capacity i and j; Suppose that laser tracker measures tested point under m erect-position, under lathe coordinate system, the coordinate of each erect-position is (X j, Y j, Z j), wherein j=1,2 ..., m; Lathe has n tested point, the coordinate of tested point is (x i, y i, z i), wherein i=1,2 ..., n;
During actual measurement, l itrue value high-precision interference can be utilized relatively to find range replacement, then the error equation of i-th tested point under a jth erect-position is:
v ij = ( ( x i - X j ) 2 + ( y i - Y j ) 2 + ( z i - Z j ) 2 - d i ) - l i - - - ( 2 )
If tested point (x i, y i, z i) gather for T, erect-position coordinate (X j, Y j, Z j) gather for P, laser interference length-measuring l iset is L, to the distance d of initial tested point under each erect-position jset is D; Least square method process equation (2) is utilized to make error sum of squares E (T, P, D) minimum:
E ( T , P , D ) = Σ i = 1 Σ j = 1 v ij 2 ( L , P , T , D ) ( i = 1,2,3 , . . . n , j = 1,2,3 , . . . m ) - - - ( 3 )
Because equation (2) is a Nonlinear System of Equations, directly use equation (2) to solve abnormal cumbersome, adopt following manner to solve:
Suppose there be n lathe tested point, had m laser tracker standing capacity; Under lathe coordinate system, unknown parameter is 3n tested point coordinate Ti (x i, y i, z i) and 3m laser tracking erect-position coordinate P j(X j, Y j, Z j) and m each erect-position under to the distance d of initial tested point j; So unknown number is 3n+4m altogether, and each erect-position can provide n interference length-measuring value, m × n equation altogether, for making equation have solution, and demand fulfillment m × n>=3n+4m, peer-to-peer (2) is carried out linear expansion and can be obtained:
v ij = L ij o - d j 0 - l i + ( x i 0 - X j 0 ) L ij 0 ( Δx i - ΔX j ) + ( y i 0 - Y j 0 ) L ij o ( Δy i - ΔY j ) + ( z i 0 - Z j 0 ) L ij o ( Δz i - ΔZ j ) - Δd j - - - ( 4 )
Wherein: L ij 0 = ( ( x i 0 - X j 0 ) 2 + ( y i 0 - Y j 0 ) 2 + ( z i 0 - Z j 0 ) 2 ) 1 / 2
Equation (4) is optimization and resolves model, needs given iterative initial value, wherein Δ x when the variable being designated as zero is and resolves in formula i, Δ y i, Δ z i, Δ X j, Δ Y j, Δ Z jbe respectively the coordinate correction value of reference frame tested point and the corrected value of laser tracker erect-position coordinate particle, Δ d jfor each erect-position particle is to the corrected value of the distance of initial tested point; In actual measurement initial value needs the D coordinates value optimizing tested point under can directly reading reference frame; And the coordinate initial value of each erect-position particle of laser tracker with the distance initial value of each erect-position particle to initial tested point need to ask for the following method:
If the approximate value of laser tracker erect-position coordinate is as iterative initial value, so the tested point coordinate needing to ask for corrected value might as well be set temporarily as true value, then tested point coordinate T in equation (1) i(x, y, z) and interference length-measuring increment l ifor known variables, utilize the tested point coordinate figure under each erect-position and interference length-measuring increment, respectively the coordinate figure P of Calibration of Laser tracker particle under each erect-position jthe initial tested point distance value d that under (x, y, z) and corresponding erect-position, particle arrives j, as j=1, then equation (1) becomes:
( x i - X 1 ) 2 + ( y i - Y 1 ) 2 + ( z i - Z 1 ) 2 = d 1 + l i - - - ( 5 )
Write equation (5) as error equation:
v i = ( x i - X 1 ) 2 + ( y i - Y 1 ) 2 + ( z i - Z 1 ) 2 - ( d 1 + l i ) - - - ( 6 )
Wherein, X 1, Y 1, Z 1for the coordinate figure of laser tracker first erect-position under lathe coordinate system, (x i, y i, z i) tested point coordinate figure i=1 for measuring under corresponding erect-position, 2 ..., n, v iit is the error amount that under the 1st erect-position, each tested point is corresponding;
If k = X 1 2 + Y 1 2 + Z 1 2 - d 1 2 , Carry out least square to above formula to solve and can obtain:
∂ v i 2 ∂ X 1 = Σ i = 1 n x i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i 2 X 1 - 2 Σ i = 1 n y i x i Y 1 - 2 Σ i = 1 n z i x i Z 1 - 2 Σ i = 1 n l i x i d 1 + Σ i = 1 n x i k = 0 - - - ( 7 )
∂ v i 2 ∂ Y 1 = Σ i = 1 n x i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i y i X 1 - 2 Σ i = 1 n y i 2 Y 1 - 2 Σ i = 1 n z i y i Z 1 - 2 Σ i = 1 n l i y i d 1 + Σ i = 1 n y i k = 0 - - - ( 8 )
∂ v i 2 ∂ Z 1 = Σ i = 1 n x i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i z i X 1 - 2 Σ i = 1 n y i z i Y 1 - 2 Σ i = 1 n z i 2 Z 1 - 2 Σ i = 1 n l i z i d 1 + Σ i = 1 n z i k = 0 - - - ( 9 )
∂ v i 2 ∂ d 1 = Σ i = 1 n l i ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i l i X 1 - 2 Σ i = 1 n y i l i Y 1 - 2 Σ i = 1 n z i l i Z 1 - 2 Σ i = 1 n l i 2 d 1 + Σ i = 1 n l i k = 0 - - - ( 10 )
∂ v i 2 ∂ k 1 = Σ i = 1 n ( x i 2 + y i 2 + z i 2 - l i 2 ) - 2 Σ i = 1 n x i X 1 - 2 Σ i = 1 n y i Y 1 - 2 Σ i = 1 n z i Z 1 - 2 Σ i = 1 n l i d 1 + Σ i = 1 n k = 0 - - - ( 11 )
The initial distance value d under the coordinate figure of the 1st erect-position under lathe coordinate system and corresponding erect-position can be tried to achieve in simultaneous equation (7) and (11), with should j=2,3 ... during m, can in the hope of the initial distance value d of all the other erect-positions under the coordinate figure and corresponding erect-position of lathe coordinate system; Utilize the initial value of each erect-position point and tested point measured value and corresponding erect-position to the distance value of initial tested point, namely can pass through the corrected value that equation (4) solves each tested point;
Corrected value is added the three-dimensional value of former measurement point is the high-precision three-dimensional coordinate figure after final optimization pass.
CN201410638347.9A 2014-11-06 2014-11-06 Machine tool error scaling method based on laser tracker multimetering technology CN104374317B (en)

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