CN103234496A - High-precision correction method for two-dimensional platform error of three-dimensional coordinate measuring machine - Google Patents

Abstract

The invention discloses a high-precision correction method for a two-dimensional platform error of a three-dimensional coordinate measuring machine. The high-precision correction method including utilizing a rigid grid plate with precision lower than or equal to a two-dimensional platform of the three-dimensional coordinate measuring machine as an auxiliary measuring device, separating an error of the two-dimensional platform to be measured and an error of a utilized grid plate scale from initial measured data via a least square method based self-correction algorithm according to coordinates of various marked points on the coordinate measuring machine in six-position state, and thereby realizing high-precision correction of the two-dimensional platform of the three-dimensional coordinate measuring machine. By the high-precision correction method, the two-dimensional platform errors of the three-dimensional coordinate measuring machine to be measured can be effectively obtained, the measurement precision can reach to the submicron grade. Meanwhile, the high-precision correction method requires no expensive special high-precision auxiliary devices, is high in reliability, provides the high-precision correction method for correcting the two-dimensional platform errors of the three-dimensional coordinate measuring machine, and has extremely high practical application value.

Description

A kind of high-precision correction method of three coordinate measuring machine two-dimensional stage error

Technical field

The invention belongs to the precision measurement field, relate in particular to a kind of high-precision correction method of three coordinate measuring machine two-dimensional stage error.

Background technology

The high speed development of Ultraprecision Machining is had higher requirement to the measuring accuracy of corresponding three-dimensional checkout equipment.Three coordinate measuring machine (Coordinate Measuring Machining, CMM) as traditional general purpose type high accuracy surveying instrument, irreplaceable effect is arranged in the detection of workpiece morpheme error, and just develop towards the direction of compact in size and nano-precision.The key of ultraprecise three coordinate measuring machine research is that it is carried out form and position error measurement and uncertainty evaluation, and then guarantees the measuring accuracy of its micro/nano level.

Three coordinate measuring machine is a complication system with more error source, and Chinese scholars has been carried out research widely to its error correcting method.For realizing the high-precision correction of measuring error, must accurately obtain each individual error of measuring machine.According to the requirement of coordinate measuring machine calibrating standard JJF1064-2010, general gauge block or the laser interferometer (additional survey of large-scale coordinate measuring machine is used laser interferometer to carry out the position error of indication and measured) used is as standard during the calibration dimensional measurement error of indication.Measured value and the difference between the standard value by gauge point on the measurement standard device draw the error of indication of being demarcated, and carry out match and compensation, and then realize the correction to coordinate measuring machine to be measured.But this method is used one dimension standard cubing to carry out individual error and is detected, and length consuming time, instrumentation and apparatus cost costliness, data are handled loaded down with trivial details.Especially when precision surface plate to be measured is the nanoscale that uses of ultraprecise manufacture fields such as the processing of VLSI (very large scale integrated circuit) manufacturing, high density memory device and fiber alignment or Subnano-class ultra precise workbench, traditional coordinate measuring machine calibration technique can't be used because finding more the high precision standard gauging instrument.

Summary of the invention

The technical problem to be solved in the present invention is to utilize the lower Turbogrid plates of accuracy class to isolate two-dimensional stage error and the employed Turbogrid plates staff error of three coordinate measuring machine effectively, and then realizes the high-precision correction of two-dimensional stage.

A kind of high-precision correction method of three coordinate measuring machine two-dimensional stage error is as follows:

1) select the square grid plate of n * n for use, n is natural number, these Turbogrid plates are fixed on the three-dimensional coordinates measurement machine platform, and the grid direction is alignd with x, the y axis rail direction of motion of coordinate measuring machine;

2) be that benchmark is set up coordinate system with Turbogrid plates, utilize this three coordinate measuring machine to record under the original pose state coordinate data M of all gauge point centers on the corresponding Turbogrid plates ₁

3) with Turbogrid plates with respect to original pose respectively along grid distance of each translation of the positive and negative direction of x axle, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on the Turbogrid plates respectively ₂And M ₃

4) step 2 is returned in the Turbogrid plates translation) in original pose, and with its respectively original relatively pose be rotated counterclockwise to 90 °, 180 ° and 270 ° of positions, the coordinate data of utilizing three coordinate measuring machine to record all gauge point centers on the corresponding Turbogrid plates respectively is M ₄, M ₅, M ₆

5) with step 2) six groups of measured coordinate data M in the step 4) ₁, M ₂, M ₃, M ₄, M ₅And M ₆Corresponding six position and attitude error of substitution are separated system of equations, that is:

Wherein I is that principal diagonal is 1 matrix, I ₁, I ₂Be the x direction of principal axis translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀Be counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yBe the nominal value of measurement point x on the Turbogrid plates and y coordinate, N _XsAnd N _YsAnd N _YtAnd N _XtBe respectively N _x, N _yThe matrix that forms owing to the positive negative direction translation of x axle; E is that all elements is 1 matrix.A _x, A _yBe two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yBe Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _iBe two ideal coordinates be the x of initial point and y coordinate offset (i=1,2 ..., 6, down with), θ _iBe the angular deflection of two ideal coordinates system, and have:

$\left[\begin{array}{c}{Q}_{\mathrm{ix}}\\ Q_{\mathrm{iy}}\end{array}\right]=M_i-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right]=\left[\begin{array}{c}{M}_{\mathrm{ix}}\\ M_{\mathrm{iy}}\end{array}\right]-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right];$

6) utilize step 2) to six measured pose data M of step 4) ₁, M ₂, M ₃, M ₄, M ₅, M ₆And the system of equations in the step 5), obtain two-dimensional stage error A _x, A _y

7) three coordinate measuring machine two-dimensional stage error is proofreaied and correct:

$T_0={[T_x,T_y]}^T-{[A_x,A_y]}^T,$

[T wherein _x, T _y] ^TBe the measured data of three coordinate measuring machine before proofreading and correct, T ₀Then be the data after proofreading and correct.

Beneficial effect of the present invention: the present invention utilizes the lower Turbogrid plates of accuracy class to carry out the measurement of a plurality of pose point coordinate on the three coordinate measuring machine two-dimensional stage to be measured, and uses the self-correcting algorithm to isolate the employed Turbogrid plates staff error of three coordinate measuring machine two-dimensional stage sum of errors effectively.Measuring method proposed by the invention need not expensive special high-accuracy and rectifies an instrument and install, has higher reliability, and measuring method is simple, does not relate to complicated actual mechanical process, is suitable for having the high-precision correction of the coordinate measuring machine two-dimensional stage error of precision surface plate.

Description of drawings

Fig. 1 is the Turbogrid plates servicing unit figure in the error correction of three coordinate measuring machine two-dimensional stage;

Fig. 2 is ideal coordinates system relation and the systematic error synoptic diagram of three coordinate measuring machine two-dimensional stage to be measured and Turbogrid plates;

Fig. 3 is that the three coordinate measuring machine global error of utilizing Turbogrid plates to record in the embodiment of the invention under original pose state distributes;

Fig. 4 is that the three coordinate measuring machine two-dimensional stage error of utilizing six pose numbers to record in the embodiment of the invention distributes.

Embodiment

A kind of high-precision correction method of three coordinate measuring machine two-dimensional stage error is as follows:

1) selects the square grid plate of n * n for use, n is natural number, the positional precision of these Turbogrid plates can be lower than the positional precision of three coordinate measuring machine two-dimensional stage to be measured, these Turbogrid plates are fixed on the three-dimensional coordinates measurement machine platform, and the grid direction is alignd with x, the y axis rail direction of motion of coordinate measuring machine, as shown in Figure 1;

2) be that benchmark is set up coordinate system with Turbogrid plates, utilize this three coordinate measuring machine to record under the original pose state coordinate data M of all gauge point centers on the corresponding Turbogrid plates ₁

3) with Turbogrid plates with respect to original pose respectively along grid distance of each translation of the positive and negative direction of x axle, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on the Turbogrid plates respectively ₂And M ₃

4) step 2 is returned in the Turbogrid plates translation) in original pose, and with its respectively original relatively pose be rotated counterclockwise to 90 °, 180 ° and 270 ° of positions, the coordinate data of utilizing three coordinate measuring machine to record all gauge point centers on the corresponding Turbogrid plates respectively is M ₄, M ₅, M ₆

5) make up two ideal coordinates system according to error source, as shown in Figure 2, the error of each gauge point can be expressed as follows:

$\left[\begin{array}{c}{M}_x\\ M_y\end{array}\right]-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right]=\left[\begin{array}{c}{A}_x\\ A_y\end{array}\right]+\left[\begin{array}{c}{G}_x\\ G_y\end{array}\right]+\left[\begin{array}{c}-N_y\·\mathrm{\θ}\\ N_x\·\mathrm{\θ}\end{array}\right]+\left[\begin{array}{c}V\\ W\end{array}\right],$

M wherein _x, M _yBe the horizontal ordinate of measured value, N _x, N _yBe the nominal value of measurement point x on the Turbogrid plates and y coordinate, A _x, A _yBe two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yBe Turbogrid plates x and the y coordinate staff error of measurement point, V, W are that two ideal coordinates are x and the y coordinate offset of initial point, and θ is the angular deflection of two ideal coordinates system, and white point is the actual measurement gauge point, and stain is desirable measurement markers point.In following formula, get:

$\left[\begin{array}{c}{M}_x\\ M_y\end{array}\right]-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right]=\left[\begin{array}{c}{Q}_x\\ Q_y\end{array}\right],$

Data according to original pose records can obtain following system of equations:

$\left[\begin{array}{c}{Q}_{1x}\\ Q_{1y}\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right]=\left[\begin{array}{ccccccc}I& 0& \mathrm{<figure-callout\; id="0"\; label="I"\; filenames="130328185223.png,130328185224.png"\; state="\{\{state\}\}">I</figure-callout>}& 0& 1& 0& -{\left[N_y\right]}^T\\ 0& I& 0& \mathrm{<figure-callout\; id="0"\; label="I"\; filenames="130328185223.png,130328185224.png"\; state="\{\{state\}\}">I</figure-callout>}& 0& 1& {\left[N_x\right]}^T\\ 1& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0\\ \left[N_y\right]& -\left[N_x\right]& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& \left[N_y\right]& -\left[N_x\right]& 0& 0& 0\\ \left[N_x\right]& \left[N_y\right]& 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{A}_x\\ A_y\\ G_x\\ G_y\\ V_1\\ W_1\\ {\mathrm{\&theta;}}_1\end{array}\right],$

In the formula, Q _1xAnd Q _1yFor original pose records data, [] ^TBe this transpose of a matrix.Hence one can see that, if measure n * n point on the original pose, the number of unknown number is 4n ²+ 3, and equation number is 2n ²+ 7, this moment equation number less than the number of unknown number, so system of equations has infinite solution.When the pose number was 3, the number of unknown number was 4n ²+ 9, and equation number is 6n ²-2n+7, system of equations application this moment least square method has solution.When the pose number continued to increase, equation number was much larger than the number of unknown number, so the precision of the solution of equations that the use least square method calculates is more high.Therefore, in the practical application, the pose number can not be less than 3, and the increase of pose number can improve computational accuracy effectively.It is 6 to carry out error correction that the present invention selects the pose number.With step 2) six groups of measured coordinate data M in the step 4) ₁, M ₂, M ₃, M ₄, M ₅And M ₆Corresponding six position and attitude error of substitution are separated system of equations, that is:

Wherein I is that principal diagonal is 1 matrix, I ₁, I ₂Be the x direction of principal axis translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀Be counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yBe the nominal value of measurement point x on the Turbogrid plates and y coordinate, N _XsAnd N _YsAnd N _YtAnd N _XtBe respectively N _x, N _yThe matrix that forms owing to the positive negative direction translation of x axle; E is that all elements is 1 matrix.A _x, A _yBe two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yBe Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _iBe two ideal coordinates be the x of initial point and y coordinate offset (i=1,2 ..., 6, down with), θ _iBe the angular deflection of two ideal coordinates system, and have:

$\left[\begin{array}{c}{Q}_{\mathrm{ix}}\\ Q_{\mathrm{iy}}\end{array}\right]=M_i-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right]=\left[\begin{array}{c}{M}_{\mathrm{ix}}\\ M_{\mathrm{iy}}\end{array}\right]-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right];$

6) utilize step 2) to six measured pose data M of step 4) ₁, M ₂, M ₃, M ₄, M ₅, M ₆With the system of equations of step 5), can obtain two-dimensional stage error A _x, A _y

7) three coordinate measuring machine two-dimensional stage error is proofreaied and correct:

$T_0={[T_x,T_y]}^T-{[A_x,A_y]}^T,$

[T wherein _x, T _y] ^TBe the measured data of three coordinate measuring machine before proofreading and correct, T ₀Then be the data after proofreading and correct.

Embodiment

The precise 2-D platform that adopts among the embodiment is the workbench of the coordinate measuring machine Global Classical of Hai Kesikang, and the rigidity Turbogrid plates are the supporting Turbogrid plates of Hai Kesikang, and the mark point tolerance is ± 1mm on the Turbogrid plates, and the experimental situation temperature is 20 ℃.The trimming process of three coordinate measuring machine two-dimensional stage error is:

1) Turbogrid plates are fixed on the three-dimensional coordinates measurement machine platform, and the grid direction aligns with x, the y axis rail direction of motion of coordinate measuring machine, as shown in Figure 1.

2) be that benchmark is set up coordinate system with Turbogrid plates 1.4 * 4 grid points in 120mm on the Turbogrid plates * 120mm regional extent are measured by six pose numbers, and per two grid spacings are L ₁=40mm obtains the global error of the direct measured value of original pose as shown in Figure 3.In order to realize that to two-dimensional stage error high-precision correction the high-precision correction method that needs further to adopt the present invention to propose is handled.Utilize this three coordinate measuring machine to record the coordinate data M of Turbogrid plates corresponding all gauge point centers under original pose state ₁

3) with Turbogrid plates with respect to original pose respectively along grid distance of each translation of the positive and negative direction of x axle, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on the Turbogrid plates respectively ₂And M ₃

4) step 2 is returned in the Turbogrid plates translation) in original pose, and with its respectively original relatively pose be rotated counterclockwise to 90 °, 180 ° and 270 ° of positions, the coordinate data of utilizing three coordinate measuring machine to record all gauge point centers on the corresponding Turbogrid plates respectively is M ₄, M ₅, M ₆

5) with step 2) six groups of measured coordinate data M in the step 4) ₁, M ₂, M ₃, M ₄, M ₅And M ₆Corresponding six position and attitude error of substitution are separated system of equations, that is:

Wherein I is that principal diagonal is 1 matrix, I ₁, I ₂Be the x direction of principal axis translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀Be counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yBe the nominal value of measurement point x on the Turbogrid plates and y coordinate, N _XsAnd N _YsAnd N _YtAnd N _XtBe respectively N _x, N _yThe matrix that forms owing to the positive negative direction translation of x axle; E is that all elements is 1 matrix.A _x, A _yBe two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yBe Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _iBe two ideal coordinates be the x of initial point and y coordinate offset (i=1,2 ..., 6, down with), θ _iBe the angular deflection of two ideal coordinates system, and have:

$\left[\begin{array}{c}{Q}_{\mathrm{ix}}\\ Q_{\mathrm{iy}}\end{array}\right]=M_i-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right]=\left[\begin{array}{c}{M}_{\mathrm{ix}}\\ M_{\mathrm{iy}}\end{array}\right]-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right].$

6) obtain three coordinate measuring machine two-dimensional stage error A at the measured value of each location point as shown in Figure 4 through handling, wherein the 1-16 point is x axis error value, and the 17-32 point is y axis error value.By to the analysis of each measuring point error among Fig. 4 as can be known, three coordinate measuring machine two-dimensional stage error is limited to ± 0.002mm, and the Turbogrid plates staff error is limited to ± 0.8mm, conforms to nominal value.

When being spaced apart L ₁During=40mm, the probability distribution of measuring error is owing to be approximately normal distribution, and expanded uncertainty is U=ku.The two-dimensional stage error is only considered the uncertainty that the error of indication causes, then u=σ.Get k=2, obtain two-dimensional stage x, y deflection error uncertainty is respectively 1.2892 μ m and 1.4248 μ m, this value and MCV-500 Doppler type laser interferometer obtain three coordinate measuring machine two-dimensional stage measured value deviation to be measured and are respectively 0.07 μ m(x axle), 0.03 μ m(y axle).

7) three coordinate measuring machine two-dimensional stage error is proofreaied and correct:

$T_0=\left[\begin{array}{c}{T}_x\\ T_y\end{array}\right]-\left[\begin{array}{c}{A}_x\\ A_y\end{array}\right],$

Wherein $\left[\begin{array}{c}{T}_x\\ T_y\end{array}\right]$ Be the measured data of three coordinate measuring machine before proofreading and correct, T ₀Then be the data after proofreading and correct.

Claims (1)

1. the high-precision correction method of a three coordinate measuring machine two-dimensional stage error is characterized in that its step is as follows:

1) select the square grid plate of n * n for use, n is natural number, these Turbogrid plates are fixed on the three-dimensional coordinates measurement machine platform, and the grid direction is alignd with x, the y axis rail direction of motion of coordinate measuring machine;

2) be that benchmark is set up coordinate system with Turbogrid plates, utilize this three coordinate measuring machine to record under the original pose state coordinate data M of all gauge point centers on the corresponding Turbogrid plates ₁

3) with the original relatively pose of Turbogrid plates respectively along grid distance of each translation of the positive and negative direction of x axle, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on the Turbogrid plates respectively ₂And M ₃

4) step 2 is returned in the Turbogrid plates translation) in original pose, and with its respectively original relatively pose be rotated counterclockwise to 90 °, 180 ° and 270 ° of positions, the coordinate data of utilizing three coordinate measuring machine to record all gauge point centers on the corresponding Turbogrid plates respectively is M ₄, M ₅, M ₆

5) with step 2) six groups of measured coordinate data M in the step 4) ₁, M ₂, M ₃, M ₄, M ₅And M ₆Corresponding six position and attitude error of substitution are separated system of equations, that is:

Wherein I is that principal diagonal is 1 matrix, I ₁, I ₂Be the x direction of principal axis translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀Be counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yBe the nominal value of measurement point x on the Turbogrid plates and y coordinate, N _XsAnd N _YsAnd N _YtAnd N _XtBe respectively N _x, N _yThe matrix that forms owing to the positive negative direction translation of x axle; E is that all elements is 1 matrix.A _x, A _yBe two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yBe Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _iBe two ideal coordinates be the x of initial point and y coordinate offset (i=1,2 ..., 6, down with), θ _iBe the angular deflection of two ideal coordinates system, and have:

$\left[\begin{array}{c}{Q}_{\mathrm{ix}}\\ Q_{\mathrm{iy}}\end{array}\right]=M_i-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right]=\left[\begin{array}{c}{M}_{\mathrm{ix}}\\ M_{\mathrm{iy}}\end{array}\right]-\left[\begin{array}{c}{N}_x\\ N_y\end{array}\right];$

6) utilize step 2) to six measured pose data M of step 4) ₁, M ₂, M ₃, M ₄, M ₅, M ₆And the system of equations of step 5), obtain two-dimensional stage error A _x, A _y

7) three coordinate measuring machine two-dimensional stage error is proofreaied and correct:

$T_0={[T_x,T_y]}^T-{[A_x,A_y]}^T,$

[T wherein _x, T _y] ^TBe the measured data of three coordinate measuring machine before proofreading and correct, T ₀Then be the data after proofreading and correct.

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