CN103234496B - A kind of High-precision correction method of three coordinate measuring machine two-dimensional stage error - Google Patents

Abstract

The invention discloses a kind of High-precision correction method of three coordinate measuring machine two-dimensional stage error.Utilize accuracy requirement less than or equal to the rigidity Turbogrid plates of three coordinate measuring machine two-dimensional stage to be measured as aided measurement device, and according to the coordinate of each gauge point on coordinate measuring machine under six position and postures recorded, use the Self-Tuning Algorithm based on least square method two-dimensional stage error to be measured and the Turbogrid plates staff error that uses to be separated from raw measurement data, the high-precision correction to three coordinate measuring machine two-dimensional stage can be realized thus.The present invention can obtain three coordinate measuring machine two-dimensional stage error to be measured effectively, and its measuring accuracy can reach sub-micrometer scale; This invention simultaneously, without the need to the special high-accuracy servicing unit of costliness, has higher reliability, for three coordinate measuring machine two-dimensional stage error provides a kind of high-precision bearing calibration, and has high actual 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 field of precision measurement, particularly relate to a kind of High-precision correction method of three coordinate measuring machine two-dimensional stage error.

Background technology

The measuring accuracy of high speed development to corresponding installation of 3d inspection of Ultraprecision Machining is had higher requirement.Three coordinate measuring machine (Coordinate Measuring Machining, CMM) as traditional general purpose type high accuracy surveying instrument, irreplaceable effect is had in the detection of workpiece Form and position error, and just towards the future development of compact in size and nano-precision.The key of ultraprecise three coordinate measuring machine research carries out form and position error measurement and uncertainty evaluation to it, and then ensure the measuring accuracy of its micro/nano level.

Three coordinate measuring machine is a complication system with more error source, and Chinese scholars conducts extensive research its error correcting method.For realizing the high-precision correction of measuring error, each individual error of measuring machine accurately must be obtained.According to the requirement of coordinate measuring machine calibrating standard JJF1064-2010, during the calibration dimensional measurement error of indication, generally use gauge block or laser interferometer (additional survey of large-scale coordinate measuring machine uses laser interferometer to carry out position error of indication measurement) as standard.Draw by the error of indication of demarcating by the difference between the measured value of gauge point on measurement standard device and standard value, and carry out matching and compensation, and then realize the correction to coordinate measuring machine to be measured.But the method uses one dimension standard cubing to carry out individual error detection, and length consuming time, instrumentation and apparatus cost are expensive, data processing is loaded down with trivial details.Especially, when precision surface plate to be measured is nanoscale or the Subnano-class ultra precise workbench of the Ultra-precision Turning field uses such as VLSI (very large scale integrated circuit) manufacture, the processing of high-density city equipment and fiber alignment, traditional coordinate measuring machine calibration technique cannot be applied because finding more high-precision standard metering instrument.

Summary of the invention

The technical problem to be solved in the present invention is the two-dimensional stage error that the Turbogrid plates utilizing accuracy class lower isolate three coordinate measuring machine effectively and the Turbogrid plates staff error used, 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, n is natural number, is fixed on three-dimensional coordinates measurement machine platform by these Turbogrid plates, and aligns in the x of grid direction and coordinate measuring machine, y-axis guide rail movement direction;

2) be that benchmark sets up coordinate system with Turbogrid plates, the coordinate data M of all gauge point centers on corresponding Turbogrid plates under utilizing this three coordinate measuring machine to record original position and posture ₁;

3) by Turbogrid plates relative to original pose respectively along each translation in the positive and negative direction of x-axis grid distance, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on Turbogrid plates respectively ₂and M ₃;

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

5) by step 2) to step 4) in measured six groups of coordinate data M ₁, M ₂, M ₃, M ₄, M ₅and M ₆substitute into corresponding six position and attitude error and be separated system of equations, that is:

Wherein I to be principal diagonal be 1 matrix, I ₁, I ₂for the x-axis direction translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀for counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yfor the nominal value of measurement point x and y coordinate on Turbogrid plates, N _xsand N _ysand N _ytand N _xtbe respectively N _x, N _ythe matrix formed due to the positive negative direction translation of x-axis; E to be all elements be 1 matrix.A _x, A _yfor two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yfor Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _ibe two ideal coordinates system initial points x and y coordinate offset (i=1,2 ..., 6, lower with), θ _ibe the angular deflection of two ideal coordinates systems, 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 step 4) measured by six pose data M ₁, M ₂, M ₃, M ₄, M ₅, M ₆and step 5) in system of equations, obtain two-dimensional stage error A _x, A _y.

7) three coordinate measuring machine two-dimensional stage error is corrected:

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

Wherein [T _x, T _y] ^tfor the data before correction measured by three coordinate measuring machine, T ₀be then the data after correction.

Beneficial effect of the present invention: the Turbogrid plates that the present invention utilizes accuracy class lower to carry out the measurement of multiple pose point coordinate in three coordinate measuring machine two-dimensional stage to be measured, and use the Turbogrid plates staff error that Self-Tuning Algorithm is effectively isolated three coordinate measuring machine two-dimensional stage error and used.Measuring method proposed by the invention rectifies an instrument and device without the need to the special high-accuracy of costliness, there is higher reliability, and measuring method is simple, does not relate to complicated actual mechanical process, be suitable for the high-precision correction of the coordinate measuring machine two-dimensional stage error with precision surface plate.

Accompanying drawing explanation

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 schematic diagram of three coordinate measuring machine two-dimensional stage to be measured and Turbogrid plates;

Fig. 3 is the three coordinate measuring machine global error distribution utilizing Turbogrid plates to record under original position and posture in the embodiment of the present invention;

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

Embodiment

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

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

2) be that benchmark sets up coordinate system with Turbogrid plates, the coordinate data M of all gauge point centers on corresponding Turbogrid plates under utilizing this three coordinate measuring machine to record original position and posture ₁;

3) by Turbogrid plates relative to original pose respectively along each translation in the positive and negative direction of x-axis grid distance, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on Turbogrid plates respectively ₂and M ₃;

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

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

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

Wherein M _x, M _yfor the transverse and longitudinal coordinate of measured value, N _x, N _yfor the nominal value of measurement point x and y coordinate on Turbogrid plates, A _x, A _yfor two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yfor Turbogrid plates x and the y coordinate staff error of measurement point, V, W are x and the y coordinate offset of two ideal coordinates system initial points, and θ is the angular deflection of two ideal coordinates systems, and white point is actual measurement gauge point, and stain is desirable measurement markers point.Get in above formula:

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

According to the data that original pose records, following system of equations can be obtained:

$\left[\begin{array}{c}{Q}_{1x}\\ Q_{1y}\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right]=\left[\begin{array}{ccccccc}I& 0& I& 0& 1& 0& -{\left[N_y\right]}^T\\ 0& I& 0& I& 0& 1& {\left[N_x\right]}^T\\ 1& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0\\ \left[N_y\right]& -\left[N_x\right]& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& \left[N_y\right]& -\left[N_x\right]& 0& 0& 0\\ \left[N_x\right]& \left[N_y\right]& 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{A}_x\\ A_y\\ G_x\\ G_y\\ V_1\\ W_1\\ {\mathrm{\θ}}_1\end{array}\right],$

In formula, Q _1xand Q _1yfor original pose data measured, [] ^tfor this transpose of a matrix.It can thus be appreciated that if measure n × n point on original pose, the number of unknown number is 4n ²+ 3, and equation number is 2n ²+ 7, now equation number is less than the number of unknown number, and therefore system of equations has infinite solution.When pose number is 3, the number of unknown number is 4n ²+ 9, and equation number is 6n ²-2n+7, now system of equations application least square method has solution.When pose number continues to increase, equation number is much larger than the number of unknown number, therefore the precision of the solution of equations using least square method to calculate is higher.Therefore, in practical application, pose number can not be less than 3, and the increase of pose number can improve computational accuracy effectively.The present invention selects pose number to be 6 carry out error correction.By step 2) to step 4) in measured six groups of coordinate data M ₁, M ₂, M ₃, M ₄, M ₅and M ₆substitute into corresponding six position and attitude error and be separated system of equations, that is:

Wherein I to be principal diagonal be 1 matrix, I ₁, I ₂for the x-axis direction translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀for counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yfor the nominal value of measurement point x and y coordinate on Turbogrid plates, N _xsand N _ysand N _ytand N _xtbe respectively N _x, N _ythe matrix formed due to the positive negative direction translation of x-axis; E to be all elements be 1 matrix.A _x, A _yfor two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yfor Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _ibe two ideal coordinates system initial points x and y coordinate offset (i=1,2 ..., 6, lower with), θ _ibe the angular deflection of two ideal coordinates systems, 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 step 4) measured by six pose data M ₁, M ₂, M ₃, M ₄, M ₅, M ₆with step 5) system of equations, two-dimensional stage error A can be obtained _x, A _y.

7) three coordinate measuring machine two-dimensional stage error is corrected:

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

Wherein [T _x, T _y] ^tfor the data before correction measured by three coordinate measuring machine, T ₀be then the data after correction.

Embodiment

The precise 2-D platform adopted in embodiment is the workbench of the coordinate measuring machine Global Classical of Hai Kesikang, and rigidity Turbogrid plates are the supporting Turbogrid plates of Hai Kesikang, and Turbogrid plates marking point tolerance is ± 1mm, and experimental situation temperature is 20 DEG C.The trimming process of three coordinate measuring machine two-dimensional stage error is:

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

2) with Turbogrid plates 1 for benchmark sets up coordinate system.Measure by six pose numbers the grid point of 4 × 4 in 120mm × 120mm regional extent on Turbogrid plates, every 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 two-dimensional stage error high-precision correction, the High-precision correction method adopting the present invention to propose further is needed to process.This three coordinate measuring machine is utilized to record the coordinate data M of Turbogrid plates corresponding all gauge point centers under original position and posture ₁.

3) by Turbogrid plates relative to original pose respectively along each translation in the positive and negative direction of x-axis grid distance, utilize three coordinate measuring machine to record the coordinate data M of all gauge point centers on Turbogrid plates respectively ₂and M ₃.

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

5) by step 2) to step 4) in measured six groups of coordinate data M ₁, M ₂, M ₃, M ₄, M ₅and M ₆substitute into corresponding six position and attitude error and be separated system of equations, that is:

Wherein I to be principal diagonal be 1 matrix, I ₁, I ₂for the x-axis direction translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀for counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yfor the nominal value of measurement point x and y coordinate on Turbogrid plates, N _xsand N _ysand N _ytand N _xtbe respectively N _x, N _ythe matrix formed due to the positive negative direction translation of x-axis; E to be all elements be 1 matrix.A _x, A _yfor two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yfor Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _ibe two ideal coordinates system initial points x and y coordinate offset (i=1,2 ..., 6, lower with), θ _ibe the angular deflection of two ideal coordinates systems, 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) through process obtain three coordinate measuring machine two-dimensional stage error A each location point measured value as shown in Figure 4, wherein 1-16 point is x-axis error amount, and 17-32 point is y-axis error amount.By known to the analysis of each measuring point error in Fig. 4, three coordinate measuring machine two-dimensional stage error is limited to ± 0.002mm, and 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 being approximately normal distribution, and expanded uncertainty is U=ku.Two-dimensional stage error only considers 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 μm and 1.4248 μm, 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 μm (x-axis), 0.03 μm (y-axis).

7) three coordinate measuring machine two-dimensional stage error is corrected:

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

Wherein $\left[\begin{array}{c}{T}_x\\ T_y\end{array}\right]$ For the data before correction measured by three coordinate measuring machine, T ₀be then the data after correction.

Claims (1)

1. a High-precision correction method for 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, n is natural number, is fixed on three-dimensional coordinates measurement machine platform by these Turbogrid plates, and aligns in the x of grid direction and coordinate measuring machine, y-axis guide rail movement direction;

2) be that benchmark sets up coordinate system with Turbogrid plates, the coordinate data M of all gauge point centers on corresponding Turbogrid plates under utilizing this three coordinate measuring machine to record original position and posture ₁;

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

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

5) by step 2) to step 4) in measured six groups of coordinate data M ₁, M ₂, M ₃, M ₄, M ₅and M ₆substitute into corresponding six position and attitude error and be separated system of equations, that is:

Wherein I to be principal diagonal be 1 matrix, I ₁, I ₂for the x-axis direction translation matrix of I, R ₉₀, R ₁₈₀, R ₂₇₀for counterclockwise 90 °, 180 ° and 270 ° of rotation matrixs of I, N _x, N _yfor the nominal value of measurement point x and y coordinate on Turbogrid plates, N _xsand N _ysand N _ytand N _xtbe respectively N _x, N _ythe matrix formed due to the positive negative direction translation of x-axis; E to be all elements be 1 matrix; A _x, A _yfor two-dimensional stage x and the y error of coordinate of measurement point, G _x, G _yfor Turbogrid plates x and the y coordinate staff error of measurement point, V _i, W _ibe x and the y coordinate offset of two ideal coordinates system initial points, i=1,2 ..., 6, θ _ibe the angular deflection of two ideal coordinates systems, Q _ix, Q _iybe respectively the error in x and the y direction of measurement point on Turbogrid plates in i-th pose, and have:

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

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

7) three coordinate measuring machine two-dimensional stage error is corrected:

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

Wherein [T _x, T _y] ^tfor the data before correction measured by three coordinate measuring machine, T ₀be then the data after correction.