CN102062575A - Method for detecting geometric accuracy of numerically-controlled machine tool based on multi-channel laser time-sharing measurement - Google Patents

Abstract

The invention discloses a method for detecting the geometric accuracy of a numerically-controlled machine tool based on multi-channel laser time-sharing measurement. The same 3D space feed motion of the machine tool is successively measured by a laser tracker in different base point positions, and all errors of the machine tool can be separated out by the processing of measured data. The measuring process only involves the displacement measurement, so that the measurement accuracy is high. Moreover, compared with the traditional multi-station measurement principle, the system hardware cost is greatly reduced due to the adoption of the time-sharing measurement principle, and the detection efficiency is greatly improved as all the errors of the machine tool can be separated out by only one-time measurement. The method has the advantages of fastness, high accuracy and the like, and is suitable for detecting the accuracy of medium and high-grade numerically-controlled machine tools.

Description

Numerically-controlled machine geometric accuracy detection method based on laser multichannel timesharing measurement

Technical field

The present invention relates to the accurate laser measurement technology, particularly a kind of geometric accuracy detection method of the numerically-controlled machine of measuring based on the timesharing of laser multichannel.

Background technology

Along with the continuous development of manufacturing industry and precision processing technology, the requirement of numerically-controlled machine machining precision is improved day by day.Therefore, how fast and accurately detect the every error of lathe and carry out error compensation, to improving that machining accuracy of NC machine tool plays a part and important.Because geometric error is affected by environment less, good reproducibility is easy to carry out error compensation, so be the main direction of studying of machine tool error compensation.

At present, the method that is used for detecting Geometric Error for Computerized Numerical Control Milling Machine both at home and abroad has a lot, common has: material standard mensuration, laser ball bar, orthogonal grating mensuration, laser interferometry etc., but these methods exist deficiency on accuracy of detection, detection efficiency and versatility, can not satisfy lathe fast, the high-precision test requirement.

Along with robot is widely used in manufacturing industry, for the requirement of the action that adapts to robot measurement and the assembling of some large-scale workpieces, three-dimensional coordinate dynamic tracking measurement technology develops rapidly.Quick, dynamic, high-precision characteristics that laser tracking measurement system has have satisfied on a large scale, in-site measurement, no guide rail flexible measuring, have realized new demand such as dynamic tracking measurement, have become irreplaceable instrument in many fields.Though the domestic example that also has the employing laser tracker to detect lathe mostly is single step form and directly measures, when medium-to-high grade lathe was detected, measuring accuracy remained further to be improved.

Laser Tracking three-dimensional coordinate measurement system mainly is based on spherical coordinates method, trigonometry, three kinds of principles of polygon method, also it can be divided into single station, two kinds of configurations of multistation by the quantity of tracker.

When adopting single station method to measure machine tool accuracy, because the measuring accuracy of corner is limited, and the uncertain meeting of the measurement of measurement of angle itself increases with the increase of distance, differs greatly with the distance accuracy of laser interference, influenced the volume coordinate overall precision.In general, laser ranging can guarantee 1 * 10 ^-6Measuring accuracy, but consider the influence of angle error, the measurement of coordinates uncertainty of this system is ± 1 * 10 ^-5, therefore, when adopting single station method that high precision machine tool is detected, measuring accuracy is difficult to guarantee.The multistation measurement is based on polygon method positioning principle, only uses the ranging information of laser tracker in the measuring process, and without its angle measurement information, therefore has higher measuring accuracy, but need many laser trackers simultaneously impact point to be measured, cost is too high, and engineering should use the comparison difficulty.

In sum,, be necessary to propose a kind of new numerically-controlled machine accuracy checking method, to realize the quick and high Precision Detection of numerically-controlled machine at the deficiency of present numerically-controlled machine accuracy checking method.

Summary of the invention

In order to overcome quick, the high Precision Detection requirement that present detection method can not satisfy machine tool accuracy, the purpose of this invention is to provide a kind of numerically-controlled machine accuracy checking method of measuring based on the timesharing of laser multichannel, this method has fast, the precision advantages of higher, is fit to the accuracy detection of The advanced CNC.

For reaching above purpose, the present invention takes following technical scheme to be achieved:

A kind of numerically-controlled machine geometric accuracy detection method of measuring based on the timesharing of laser multichannel is characterized in that, comprises the steps:

(1) multichannel timesharing measuring process

During measurement, the control lathe is in the three dimensions feeding, and its motion path is provided with a plurality of measurement points, a laser tracker is measured the movement locus that lathe is identical successively at least three basic point positions, when machine tool motion arrives each measurement point position, the lathe stop motion, write down the range finding reading of this measurement point position laser tracker, after all measurement point measurements are finished, obtain the range finding reading of different measuring point place laser tracker; Then laser tracker is moved to other basic point position, repeat above-mentioned measuring process, until the measurement of all having finished in all basic point positions machine tool motion;

(2) measure the gained data processing step

Comprise following substep:

A, laser tracker basic point position are from demarcating

The principle of taking each basic point position coordinates to demarcate is separately established A ₀Be lathe initial measurement point, lathe is along the path movement that configures in advance, the theoretical coordinate A of each measurement point _i(x _i, y _i, z _i), i=1,2 ... n, laser tracker follow the tracks of lathe and measure the variable in distance amount of measurement point to basic point in real time, suppose aiming initial measurement point A ₀The time, the range finding reading of laser tracker is changed to 0, and then in the moving process of lathe, the range finding reading of laser tracker is exactly the relative distance variable quantity of measurement point to basic point, note initial measurement point A ₀To the first basic point P ₁Distance be designated as L ₁, measurement point A in the measuring process _iTo the first basic point P ₁The relative distance variable quantity be designated as l _1i

If the first basic point P ₁Coordinate be (x, y, z), to measurement point A _i(x _i, y _i, z _i), can set up following system of equations by 2 range formulas:

$\left\{\begin{array}{c}\sqrt{{(x-x_1)}^2+{(y-y_1)}^2+(z-z_1)}=L_1+l_{11}\\ \sqrt{{(x-x_2)}^2+{(y-y_2)}^2+{(z-z_2)}^2}=L_1+l_{12}\\ M\\ \sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}=L_1+l_{1i}\end{array}\right.---\left(1\right)$

With first equation both sides in the formula (1) square, and launch and can get:

x ₁ ²+y ₁ ²+z ₁ ²-2x ₁x-2y ₁y-2z ₁z+x ²+y ²+z ²-L ²-2Ll ₁₁-l ₁₁ ²＝0 (2)

Following formula is the first basic point P ₁(x, y z) and the quadratic nonlinearity equation of L, make C=x ²+ y ²+ z ²-L ², then can be with above-mentioned equation linearization:

x ₁ ²+y ₁ ²+z ₁ ²-2x ₁x-2y ₁y-2z ₁z+C-2Ll ₁₁-l ₁₁ ²＝0 (3)

According to the principle of least square, objective function is

$F(x,y,z,L,C)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{({x_i}^2+{y_i}^2+{z_i}^2-2x_{i}x-{2y}_{i}y-{2z}_{i}z+C-2{\mathrm{Ll}}_{1i}-{l_{1i}}^2)}^2---\left(4\right)$

By extremum principle, it is minimum desiring to make F, then must have

$\frac{\∂F}{\∂x}=0$ $\frac{\∂F}{\∂y}=0$ $\frac{\∂F}{\∂z}=0$ $\frac{\∂F}{\∂L}=0$ $\frac{\∂F}{\∂C}=0---\left(5\right)$

In the same up-to-date style (4) each second-order partial differential coefficient perseverance just, promptly

$\frac{{\∂}^{2}F}{{\∂x}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂y}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂z}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂L}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}^2>0$

$\frac{{\∂}^{2}F}{{\∂C}^2}=1>0---\left(6\right)$

Hence one can see that, and the extreme value that each equation is tried to achieve in the formula (5) is a minimal value, satisfies least square condition, and arrangement can get following normal equations group:

$\left[\begin{array}{ccccc}2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{y}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{y}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}^2& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}\\ -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}& \frac{N}{2}\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ L_1\\ C\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ -\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}(x_i^2+y_i^2+z_i^2-l_{1i}^2)\end{array}\right]---\left(7\right)$

N is that overall measurement is counted in the formula (7), when the determinant of coefficient in the formula (7) is non-vanishing, well-determined separating is arranged, and can solve x, y, z, L thus ₁Value; Repeat said process, can calibrate basic point at other P ₂, P ₃, P ₄... the volume coordinate of a plurality of positions, and L ₂, L ₃, L ₄....;

B, measurement point volume coordinate are demarcated

Based on the actual coordinate A ' of polygon method positioning principle to each measurement point in the measuring process _i(x ' _i, y ' _i, z ' _i) demarcate, a plurality of basic point volume coordinates that bidding obtains surely are P ₁(x _P1, y _P1, z _P1), P ₂(x _P2, y _P2, z _P2), P ₃(x _P3, y _P3, z _P3), P ₄(x _P4, y _P4, z _P4) ... the initial measurement point A that demarcation obtains ₀Distance to a plurality of basic points is respectively L ₁, L ₂, L ₃, L ₄,

To the measurement point A ' in the measuring process _i(x ' _i, y ' _i, z ' _i), can set up following system of equations by 2 range formulas:

$\left\{\begin{array}{c}\sqrt{{(x_i^{\′}-x_{p1})}^2+{(y_i^{\′}-y_{p1})}^2+(z_i^{\′}-z_{p1})}=L_1+l_{1i}\\ \sqrt{{(x_i^{\′}-x_{p2})}^2+{(y_i^{\′}-y_{p2})}^2+{(z_i^{\′}-z_{p2})}^2}=L_2+l_{2i}\\ \sqrt{{(x_i^{\′}-x_{p3})}^2+{(y_i^{\′}-y_{p3})}^2+{(z_i^{\′}-z_{p3})}^2}=L_3+l_{3i}\\ \sqrt{{(x_i^{\′}-x_{p4})}^2+{(y_i^{\′}-y_{p4})}^2+{(z_i^{\′}-z_{p4})}^2}=L_4+l_{4i}\end{array}\right.$

Adopt similar basic point P ₁Demarcating steps come measurement point A ' _i(x ' _i, y ' _i, z ' _i) demarcate, the result is as follows:

$\left[\begin{array}{cccc}2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x_{\mathrm{pj}}}^2& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{y}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{z}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}\\ 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{y}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}^2& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}{z}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}\\ 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{z}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}{z}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}^2& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}\\ -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}& N/2\end{array}\right]\left[\begin{array}{c}{x}_i^{\′}\\ y_i^{\′}\\ z_i^{\′}\\ C\end{array}\right]=\left[\begin{array}{c}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ \underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pi}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ \underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ -\frac{1}{2}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\end{array}\right]---\left(9\right)$

In the formula (9), N is the basic point sum, with the actual coordinate A ' of each measurement point of obtaining _i(x ' _i, y ' _i, z ' _i) with the theoretical coordinate A of each measurement point _i(x _i, y _i, z _i) compare, obtain the kinematic error A of lathe in each measurement point _i(Δ x _i, Δ y _i, Δ z _i), i=1,2 ... n;

C, machine tool error separate

The kinematic error A of each measurement point that utilization measures _i(Δ x _i, Δ y _i, Δ z _i), adopt the error separating method of nine collimation methods, set up the kinematic error equation of each a plurality of measurement point in same position place, adopt least square method that this system of equations is found the solution, obtain every geometric error of corresponding position lathe.

In the such scheme, in the described step (1), a plurality of base station locations at laser tracker place should be or not same plane, and difference in height＞100mm.Measurement comprises that positive movement is measured and counter motion is measured to machine tool motion in each basic point position, measurement number of times＞=2 time.

The invention has the beneficial effects as follows: a kind of numerically-controlled machine geometric accuracy detection method of measuring based on the timesharing of laser multichannel is provided, owing to only relate to displacement in the measuring process, so this method has higher measuring accuracy.This principle is compared with the multistation measuring principle, the cost of system hardware greatly reduces, and just can isolate every error of lathe simultaneously by one-shot measurement, and detection efficiency is higher, satisfied quick, high-precision test requirement, the geometric accuracy that is fit to The advanced CNC detects.

Description of drawings

Below in conjunction with the drawings and the specific embodiments the present invention is described in further detail.

Fig. 1 is the schematic diagram that the numerically-controlled machine precision is measured in four tunnel timesharing.During measurement, the control lathe is in the 3d space feeding, laser tracker is measured machine tool motion at basic point P1 place earlier, after lathe is covered predefined path, laser tracker is moved on to basic point P2 place, identical motion is measured to lathe once more, by that analogy, has all finished measurement to the lathe same motion trajectory four basic point positions until laser tracker.

Fig. 2 is the mathematical model that the numerically-controlled machine precision is measured in four tunnel timesharing, wherein P1, P2, P3, P4 are four positions of basic point, the machine tool motion zone provides by square, wherein A0 is the initial measurement point, a plurality of measurement points that distributing on every limit of square simultaneously, the number of measurement point can be provided with according to precision and the actual conditions measured.

Embodiment

As shown in Figure 1 and Figure 2: a kind of numerically-controlled machine geometric accuracy detection method of measuring based on the timesharing of laser multichannel, it is characterized in that, comprise the steps:

(1) multichannel timesharing measuring process

During measurement, the control lathe is in the three dimensions feeding, and 4 measurement points are set on every limit of its square moving region, a laser tracker is measured the movement locus that lathe is identical successively at least three basic point positions, when machine tool motion arrives each measurement point position, the lathe stop motion, write down the range finding reading of this measurement point position laser tracker, after all measurement point measurements are finished, obtain the range finding reading of the laser tracker at different measuring point place; Then laser tracker is moved to other basic point position, repeat above-mentioned measuring process, until the measurement of all having finished in all basic point positions machine tool motion; A plurality of basic points position at laser tracker place should be or not same plane, and difference in height＞100mm.Measurement comprises that positive movement is measured and counter motion is measured to machine tool motion in each basic point position, measurement number of times＞=2 time.Repeatedly measurement can improve the uncertain evaluation precision of measurement and can reduce the measuring error that the timesharing measurement causes simultaneously.

(2) measure the gained data processing step

Comprise following substep:

When adopting the multichannel time-sharing method to measure, how accurately isolating the every error of lathe by the mass data that measures is key problem in the algorithm, should calibrate laser tracker diverse location position of basic point on it when measuring earlier, and then the space measurement point coordinate demarcated, carry out error separating at last.Be measured as example with four station timesharing below, said process is set forth.

1) the basic point locus is from demarcating

The principle of taking each basic point position coordinates to demarcate is separately established A ₀Be lathe initial measurement point, lathe is along the path movement that configures in advance, the theoretical coordinate A of each measurement point _i(x _i, y _i, z _i), i=1,2 ... n, laser tracker is followed the tracks of lathe and is measured the variable in distance amount of measurement point to basic point in real time, because the laser tracker range finding is based on the laser interference principle, and measurement point is provided with irrelevant to the relative variation of basic point distance and the range finding zero-bit of laser tracker, therefore, suppose aiming initial measurement point A ₀The time, the range finding reading of laser tracker is changed to 0, and then in the moving process of lathe, the range finding reading of laser tracker is exactly the relative distance variable quantity of measurement point to basic point, note initial measurement point A ₀To the first basic point P ₁Distance be designated as L ₁, measurement point A in the measuring process _iTo the first basic point P ₁The relative distance variable quantity be designated as l _1i

If basic point P ₁Coordinate be (x, y, z), to measurement point A _i(x _i, y _i, z _i), can set up following system of equations by 2 range formulas:

$\left\{\begin{array}{c}\sqrt{{(x-x_1)}^2+{(y-y_1)}^2+(z-z_1)}=L_1+l_{11}\\ \sqrt{{(x-x_2)}^2+{(y-y_2)}^2+{(z-z_2)}^2}=L_1+l_{12}\\ M\\ \sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}=L_1+l_{1i}\end{array}\right.---\left(10\right)$

At this moment the actual institute of the basic point timing signal measure dot number of getting will be the overdetermined equation group from the calibration equation group often more than 4, and available least square method is found the solution.For fear of selecting of iterative initial value, adopt the method for resolving that above-mentioned least square problem is found the solution.

With first equation both sides in the formula (10) square, and launch and can get:

x ₁ ²+y ₁ ²+z ₁ ²-2x ₁x-2y ₁y-2z ₁z+x ²+y ²+z ²-L ²-2Ll ₁₁-l ₁₁ ²＝0 (11)

Following formula is the first basic point P ₁(x, y z) and the quadratic nonlinearity equation of L, make C=x ²+ y ²+ z ²-L ², then can be with above-mentioned equation linearization:

x ₁ ²+y ₁ ²+z ₁ ²-2x ₁x-2y ₁y-2z ₁z+C-2Ll ₁₁-l ₁₁ ²＝0 (12)

According to the principle of least square, objective function is

$F(x,y,z,L,C)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{({x_i}^2+{y_i}^2+{z_i}^2-2x_{i}x-{2y}_{i}y-{2z}_{i}z+C-2{\mathrm{Ll}}_{1i}-{l_{1i}}^2)}^2---\left(13\right)$

By extremum principle, it is minimum desiring to make F, then must have

$\frac{\∂F}{\∂x}=0$ $\frac{\∂F}{\∂y}=0$ $\frac{\∂F}{\∂z}=0$ $\frac{\∂F}{\∂L}=0$ $\frac{\∂F}{\∂C}=0---\left(14\right)$

In the same up-to-date style (13) each second-order partial differential coefficient perseverance just, promptly

$\frac{{\∂}^{2}F}{{\∂x}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂y}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂z}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂L}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}^2>0$

$\frac{{\∂}^{2}F}{\∂C^2}=1>0---\left(15\right)$

Hence one can see that, and the extreme value that each equation is tried to achieve in the formula (14) is a minimal value, satisfies least square condition, and arrangement can get following normal equations group

$\left[\begin{array}{ccccc}2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{y}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{y}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}^2& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}\\ -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}& \frac{N}{2}\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ L_1\\ C\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ -\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}(x_i^2+y_i^2+z_i^2-l_{1i}^2)\end{array}\right]---\left(16\right)$

N is that overall measurement is counted in the formula (16), when the determinant of coefficient in the formula (16) is non-vanishing, well-determined separating is arranged, and can solve x, y, z, L thus ₁Value; Repeat said process, can calibrate basic point at other P ₂, P ₃, P ₄The volume coordinate of position, and L ₂, L ₃, L ₄

2) the measurement point volume coordinate is demarcated

After intact to four basic point location positions of laser tracker, just can be based on polygon method positioning principle to the actual coordinate A ' of each measurement point in the measuring process _i(x ' _i, y ' _i, z ' _i) (i=1,2 ... n) demarcate.Four basic point volume coordinates that bidding obtains surely are P ₁(x _P1, y _P1, z _P1), P ₂(x _P2, y _P2, z _P2), P ₃(x _P3, y _P3, z _P3), P ₄(x _P4, y _P4, z _P4), demarcate the initial measurement point A that obtains ₀Distance to four basic points is respectively L ₁, L ₂, L ₃, L ₄

To the measurement point A ' in the measuring process _i(x ' _i, y ' _i, z ' _i), can set up following system of equations by 2 range formulas:

$\left\{\begin{array}{c}\sqrt{{(x_i^{\′}-x_{p1})}^2+{(y_i^{\′}-y_{p1})}^2+(z_i^{\′}-z_{p1})}=L_1+l_{1i}\\ \sqrt{{(x_i^{\′}-x_{p2})}^2+{(y_i^{\′}-y_{p2})}^2+{(z_i^{\′}-z_{p2})}^2}=L_2+l_{2i}\\ \sqrt{{(x_i^{\′}-x_{p3})}^2+{(y_i^{\′}-y_{p3})}^2+{(z_i^{\′}-z_{p3})}^2}=L_3+l_{3i}\\ \sqrt{{(x_i^{\′}-x_{p4})}^2+{(y_i^{\′}-y_{p4})}^2+{(z_i^{\′}-z_{p4})}^2}=L_4+l_{4i}\end{array}\right.$

Adopt similar basic point P ₁Demarcating steps come measurement point A ' _i(x ' _i, y ' _i, z ' _i) demarcate, the result is as follows:

$\left[\begin{array}{cccc}2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x_{\mathrm{pj}}}^2& 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{y}_{\mathrm{pj}}& 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{z}_{\mathrm{pj}}& -\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}\\ 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{y}_{\mathrm{pj}}& 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}^2& 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}{z}_{\mathrm{pj}}& -\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}\\ 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{z}_{\mathrm{pj}}& 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}{z}_{\mathrm{pj}}& 2\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}^2& -\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}\\ -\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}& -\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}& -\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}& 2\end{array}\right]\left[\begin{array}{c}{x}_i^{\′}\\ y_i^{\′}\\ z_i^{\′}\\ C\end{array}\right]=\left[\begin{array}{c}\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ \underset{j=1}{\overset{4}{\mathrm{\Σ}}}{y}_{\mathrm{pi}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ \underset{j=1}{\overset{4}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ -\frac{1}{2}\underset{j=1}{\overset{4}{\mathrm{\Σ}}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\end{array}\right]$

Actual coordinate A ' with each measurement point of obtaining _i(x ' _i, y ' _i, z ' _i) with the theoretical coordinate A of each measurement point _i(x _i, y _i, z _i) compare, obtain the kinematic error A of lathe in each measurement point _i(Δ x _i, Δ y _i, Δ z _i), i=1,2 ... n;

3) machine tool error separates

The kinematic error of each measurement point that utilization measures, adopt the error separating method of nine collimation methods, set up the kinematic error equation of each same position place four measuring point, adopt least square method that this system of equations is found the solution, obtain every geometric error of corresponding position.

Below provide and use the example that the multichannel measurement method detects a precision of numerical control milling machine.

During measurement, the control milling machine is in the 3d space feeding, and the moving region is set at 500mm * 600mm * 400mm, and opal is installed near the cutter, in the measuring process, and the motion of laser tracker real-time follow-up opal, thus the milling machine movement locus is measured.Milling machine is along X, Y, when the Z direction is moved, and every motion 100mm is provided with a measurement point, and when milling machine moved to each measurement point, milling machine stopped 6 seconds, write down the range finding reading of current location laser tracker.When each basic point position measurement, twice measurement carried out in motion to milling machine, when measuring at every turn, comprises milling machine positive movement and counter motion are measured each once.When milling machine when initial point position moves to the final position, forward is measured and is finished 73 measurement points when just surveying.Milling machine counter motion then, when milling machine when the final position moves to initial point position, oppositely measure and finish 72 measurement points during anti-the survey.When finishing the forward measurement and oppositely measuring, measurement for the first time finishes, totally 145 measurement points.Repeat said process then, the measurement second time is carried out in motion to milling machine.When finishing above-mentioned measure for twice, the measurement of first basic point position finishes, and then laser tracker is moved to other basic point position, repeats above-mentioned measuring process, until the measurement of all having finished in all basic point positions the milling machine motion.

Theoretical coordinate A according to each measurement point _i(x _i, y _i, z _i) (i=1,2 ... n) and the range finding reading Δ l of four basic point position laser trackers _1i, Δ l _2i, Δ l _3i, Δ l _4i(i=1,2 ... n), the basic point locus that utilizes the front just can calibrate the actual coordinate A ' of each measurement point in the milling machine motion process from calibration algorithm and measurement point volume coordinate calibration algorithm _i(x ' _i, y ' _i, z ' _i) (i=1,2 ... n), can isolate every error of milling machine simultaneously

Table 1 has provided when adopting four tunnel timesharing to measure, the part measurement point coordinate that demarcation obtains, table 2 has provided the every geometric error of milling machine that X-axis diverse location place picks out, and wherein data unit is mm in the table (1), and the implication and the unit of each physical quantity are as follows in the table (2): δ _x(x) be positioning error, the mm of unit; δ _y(x), δ _z(x) be straightness error, the mm of unit; ε _x(x) be roll error, unit is rad; ε _y(x) be pitch error, unit is rad; ε _z(x) be Run-out error, unit is rad.

Table 1 four tunnel timesharing measure portion measurement point calibration results

Measurement point	x	y	z
				A 1	-100.01346	0.00825	-0.00779
A 2	-200.02169	0.00943	-0.01155
				A 3	-300.02641	0.00861	-0.00401
A 4	-500.01859	-99.99307	-0.00662

Every geometric error that table 2X axle diverse location place picks out

Error	δ x(x)	δ y(x)	δ z(x)	ε x(x)	ε y(x)	ε z(x)
							x＝100	0.02725	-0.01053	-0.01438	-0.000019	0.000018	-0.000105
x＝200	0.02574	-0.00627	-0.02244	-0.000015	0.000032	-0.000098
							x＝300	0.02352	-0.00741	-0.01788	-0.0000049	0.000019	-0.000089
x＝400	0.01739	-0.01233	-0.02096	0.0000020	0.000015	-0.000096
							x＝500	0.01095	-0.01416	-0.02205	0.000011	0.000028	-0.000109

In this measuring process, the milling machine motion measurement once (comprised positive movement and counter motion) 25 minutes approximately, each base station location will be measured twice tool motion, approximately about 50 minutes, finish the measurement of milling machine motion 200 minutes approximately four basic point positions, and by calculating the every error that just can isolate milling machine, detection efficiency improves greatly then, and accuracy of detection is higher, has satisfied quick, the high Precision Detection requirement of The advanced CNC.

Claims (3)

1. a numerically-controlled machine geometric accuracy detection method of measuring based on the timesharing of laser multichannel is characterized in that, comprises the steps:

(1) multichannel timesharing measuring process

During measurement, the control lathe is in the three dimensions feeding, and its motion path is provided with a plurality of measurement points, a laser tracker is measured the movement locus that lathe is identical successively at least three basic point positions, when machine tool motion arrives each measurement point position, the lathe stop motion, write down the range finding reading of this measurement point position laser tracker, after all measurement point measurements are finished, obtain the range finding reading of the laser tracker at different measuring point place; Then laser tracker is moved to other basic point position, repeat above-mentioned measuring process, until the measurement of all having finished in all basic point positions machine tool motion;

(2) measure the gained data processing step

Comprise following substep:

A, laser tracker basic point position are from demarcating

The principle of taking each basic point position coordinates to demarcate is separately established A ₀Be lathe initial measurement point, lathe is along the path movement that configures in advance, the theoretical coordinate A of each measurement point _i(x _i, y _i, z _i), i=1,2 ... n, laser tracker follow the tracks of lathe and measure the variable in distance amount of measurement point to basic point in real time, suppose aiming initial measurement point A ₀The time, the range finding reading of laser tracker is changed to 0, and then in the moving process of lathe, the range finding reading of laser tracker is exactly the relative distance variable quantity of measurement point to basic point, note initial measurement point A ₀To the first basic point P ₁Distance be designated as L ₁, measurement point A in the measuring process _iTo the first basic point P ₁The relative distance variable quantity be designated as l _1i

If the first basic point P ₁Coordinate be (x, y, z), to measurement point A _i(x _i, y _i, z _i), can set up following system of equations by 2 range formulas:

$\left\{\begin{array}{c}\sqrt{{(x-x_1)}^2+{(y-y_1)}^2+(z-z_1)}=L_1+l_{11}\\ \sqrt{{(x-x_2)}^2+{(y-y_2)}^2+{(z-z_2)}^2}=L_1+l_{12}\\ M\\ \sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2}=L_1+l_{1i}\end{array}\right.---\left(1\right)$

With first equation both sides in the formula (1) square, and launch and can get:

x ₁ ²+y ₁ ²+z ₁ ²-2x ₁x-2y ₁y-2z ₁z+x ²+y ²+z ²-L ²-2Ll ₁₁-l ₁₁ ²＝0 (2)

Following formula is the first basic point P ₁(x, y z) and the quadratic nonlinearity equation of L, make C=x ²+ y ²+ z ²-L ², then can be with above-mentioned equation linearization:

x ₁ ²+y ₁ ²+z ₁ ²-2x ₁x-2y ₁y-2z ₁z+C-2Ll ₁₁-l ₁₁ ²＝0 (3)

According to the principle of least square, objective function is

$F(x,y,z,L,C)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{({x_i}^2+{y_i}^2+{z_i}^2-2x_{i}x-{2y}_{i}y-{2z}_{i}z+C-2{\mathrm{Ll}}_{1i}-{l_{1i}}^2)}^2---\left(4\right)$

By extremum principle, it is minimum desiring to make F, then must have

$\frac{\∂F}{\∂x}=0$ $\frac{\∂F}{\∂y}=0$ $\frac{\∂F}{\∂z}=0$ $\frac{\∂F}{\∂L}=0$ $\frac{\∂F}{\∂C}=0---\left(5\right)$

Simultaneously in (4) formula each second-order partial differential coefficient perseverance just, promptly

$\frac{{\∂}^{2}F}{{\∂x}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂y}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂z}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i^2>0$ $\frac{{\∂}^{2}F}{{\∂L}^2}=8\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}^2>0$

$\frac{{\∂}^{2}F}{{\∂C}^2}=1>0---\left(6\right)$

Hence one can see that, and the extreme value that each equation is tried to achieve in the formula (5) is a minimal value, satisfies least square condition, and arrangement can get following normal equations group:

$\left[\begin{array}{ccccc}2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{y}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{y}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{z}_i& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i^2& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i\\ 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i{l}_{1i}& 2\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}^2& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}\\ -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i& -\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}& \frac{N}{2}\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ L_1\\ C\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{z}_i(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{l}_{1i}(x_i^2+y_i^2+z_i^2-l_{1i}^2)\\ -\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}(x_i^2+y_i^2+z_i^2-l_{1i}^2)\end{array}\right]---\left(7\right)$

N is that overall measurement is counted in the formula (7), when the determinant of coefficient in the formula (7) is non-vanishing, well-determined separating is arranged, and can solve x, y, z, L thus ₁Value; Repeat said process, can calibrate basic point at other P ₂, P ₃, P ₄... the volume coordinate of a plurality of positions, and L ₂, L ₃, L ₄....;

B, measurement point volume coordinate are demarcated

Based on the actual coordinate A ' of polygon method positioning principle to each measurement point in the measuring process _i(x ' _i, y ' _i, z ' _i) demarcate, a plurality of basic point volume coordinates that bidding obtains surely are P ₁(x _P1, y _P1, z _P1), P ₂(x _P2, y _P2, z _P2), P ₃(x _P3, y _P3, z _P3), P ₄(x _P4, y _P4, z _P4) ... the initial measurement point A that demarcation obtains ₀Dividing in addition to the distance of a plurality of basic points is L ₁, L ₂, L ₃, L ₄,

To the measurement point A ' in the measuring process _i(x ' _i, y ' _i, z ' _i), can set up following system of equations by 2 range formulas:

$\left\{\begin{array}{c}\sqrt{{(x_i^{\′}-x_{p1})}^2+{(y_i^{\′}-y_{p1})}^2+(z_i^{\′}-z_{p1})}=L_1+l_{1i}\\ \sqrt{{(x_i^{\′}-x_{p2})}^2+{(y_i^{\′}-y_{p2})}^2+{(z_i^{\′}-z_{p2})}^2}=L_2+l_{2i}\\ M\\ \sqrt{{(x_i^{\′}-x_{\mathrm{pj}})}^2+{(y_i^{\′}-y_{\mathrm{pj}})}^2+{(z_i^{\′}-z_{\mathrm{pj}})}^2}=L_j+l_{\mathrm{ji}}\end{array}\right.---\left(8\right)$

Adopt similar basic point P ₁Demarcating steps come measurement point A ' _i(x ' _i, y ' _i, z ' _i) demarcate, the result is as follows:

$\left[\begin{array}{cccc}2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x_{\mathrm{pj}}}^2& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{y}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{z}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}\\ 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{y}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}^2& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}{z}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}\\ 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}{z}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}{z}_{\mathrm{pj}}& 2\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}^2& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}\\ -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pj}}& -\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}& N/2\end{array}\right]\left[\begin{array}{c}{x}_i^{\′}\\ y_i^{\′}\\ z_i^{\′}\\ C\end{array}\right]=\left[\begin{array}{c}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{x}_{\mathrm{pj}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ \underset{j=1}{\overset{N}{\mathrm{\Σ}}}{y}_{\mathrm{pi}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ \underset{j=1}{\overset{N}{\mathrm{\Σ}}}{z}_{\mathrm{pj}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\\ -\frac{1}{2}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(x_{\mathrm{pj}}^2+y_{\mathrm{pj}}^2+z_{\mathrm{pj}}^2-L_j^2-2L_j{l}_{\mathrm{ji}}-l_{\mathrm{ji}}^2)\end{array}\right]---\left(9\right)$

In the formula (9), N is the basic point sum, with the actual coordinate A ' of each measurement point of obtaining _i(x ' _i, y ' _i, z ' _i) with the theoretical coordinate A of each measurement point _i(x _i, y _i, z _i) compare, obtain the kinematic error A of lathe in each measurement point _i(Δ x _i, Δ y _i, Δ z _i), i=1,2 ... n;

C, machine tool error separate

The kinematic error A of each measurement point that utilization measures _i(Δ x _i, Δ y _i, Δ z _i), adopt the error separating method of nine collimation methods, set up the kinematic error equation of each a plurality of measurement point in same position place, adopt least square method that this system of equations is found the solution, obtain every geometric error of corresponding position lathe.

2. the numerically-controlled machine geometric accuracy detection method of measuring based on the timesharing of laser multichannel as claimed in claim 1 is characterized in that, in the described step (1), a plurality of base station locations at laser tracker place should be or not same plane, and difference in height＞100mm.

3. the numerically-controlled machine geometric accuracy detection method of measuring based on the timesharing of laser multichannel as claimed in claim 1, it is characterized in that, in the described step (1), measurement comprises that positive movement is measured and counter motion is measured to machine tool motion in each basic point position, measurement number of times＞=2 time.

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