Compensation method for zero drift in preheating process of laser tracker

Abstract

The invention belongs to the field of geometric quantity measurement, and discloses a compensation method for zero drift in the preheating process of a laser tracker. The method comprises the following steps: firstly, synchronously measuring temperature and reference point coordinates so as to calibrate a zero drift curve of a laser tracker measurement coordinate system; secondly, establishing a correlation function of the surface temperature difference and the zero drift curve of the laser tracking instrument by using a polynomial fitting method; and finally reconstructing the transformation matrix and compensating the zero drift of the starting preheating process of the laser tracker every time. The compensation method can effectively compensate zero drift in each preheating process, can improve the precision and stability of measuring point coordinates, can be applied to reference coordinate zero drift compensation in large component manufacturing under the condition of rapid preheating, and serves any measurement scene where a laser tracker needs to be used.

Description

Technical Field

[0001] The invention belongs to the field of geometric quantity measurement and relates to a method for compensating zero-point drift during the preheating process of a laser tracker. Background Art

[0002] Digital measurement of large aerospace parts has become a key core technology in the field of aviation assembly. Laser trackers, with their high single-point measurement accuracy and large measurement range, are widely used for high-precision measurement of large aerospace parts. However, if the laser tracker begins measurement directly during the warm-up process, temperature fluctuations in the laser tracking head during measurement can cause zero drift in the measurement point. To meet the requirements of high-precision measurement of large parts, zero drift compensation is required. Therefore, research on zero drift compensation methods is of great significance for high-precision measurement of large parts.

[0003] Existing zero-drift compensation methods generally rely on changes in the laser tracker during preheating or introduce auxiliary measures to solve parameters related to temperature rise and perform zero-drift compensation. However, this method does not compensate based on the occurrence pattern of zero-drift, and therefore cannot effectively compensate for zero-drift during each preheating operation under different measurement conditions. Regarding laser tracker zero-drift compensation methods, Calle et al. introduced a method for compensating zero-drift based on a structural thermal expansion model during preheating in the Journal of Manufacturing Systems, Volume 41, Pages 277-286. This method compares the expansion of the lens, mechanical components, housing, and other structures before and after preheating to establish a structural expansion-temperature model to compensate for zero-drift. However, due to the uncontrollable impact of the workshop environment on zero-drift, it is impossible to effectively compensate for zero-drift under different environments, and thus has certain limitations. Gao Lanlan and others from Changchun University of Science and Technology, in their patent application "Automatic Calibration Device for Laser Opacimeters," (Chinese Patent CN2014101894228), present a method for correcting zero drift based on the ratio of transmitted and received light at varying extinction levels. This method analyzes the ratio of transmitted to received light intensity at varying extinction levels to provide real-time correction for zero drift in a laser opacimeter. However, introducing the laser into an extinction glass disk and then into a laser receiver requires a high level of site layout, making it unsuitable for large measurement sites or complex working conditions. Summary of the Invention

[0004] In response to the shortcomings of the prior art, the present invention proposes a method for compensating for zero-point drift during the preheating process of a laser tracker in order to avoid the engineering problem of zero-point drift of the measuring point coordinates caused by insufficient preheating during the preheating process. The method first synchronously collects temperature and reference point coordinate data and preprocesses them; secondly, a correlation function between the surface temperature difference of the laser tracker and the zero-point drift curve is established based on polynomial fitting; and finally, zero-point drift is compensated for each time the laser tracker is turned on and preheated. The present invention can effectively compensate for zero-point drift during each preheating process, improve the accuracy and stability of the measuring point coordinates, serve the high-precision measurement scenarios of laser trackers, and has broad application prospects.

[0005] The technical solution of the present invention:

[0006] A method for compensating zero drift during the preheating process of a laser tracker includes first synchronously collecting temperature-coordinate data and preprocessing the data during the preheating process of the laser tracker; then calibrating the correlation function between the surface temperature difference of the laser tracker head and the zero drift curve; and finally compensating for the zero drift during each startup and preheating process of the laser tracker. The steps are as follows:

[0007] The first step is the synchronous acquisition and preprocessing of temperature-coordinate data during the laser tracker warm-up process;

[0008] First, build the laser tracker measurement coordinate system: the original measurement data of the laser tracker is based on three spherical coordinate system parameters: slant distance ρ, pitch angle θ, azimuth angle Define the spatial position of the target point; the origin O is located at the mechanical reference point at the rotation center of the laser tracker. Convert the spherical coordinate system to a rectangular coordinate system: the X-axis extends along the direction of the laser beam emission, the Z-axis is in the horizontal plane and perpendicular to the X-axis, and the Y-axis is determined according to the right-hand rule and is orthogonal to the XZ plane to form a spatial rectangular coordinate system;

[0009] The mathematical transformation of the laser tracker measurement coordinate system is achieved by mapping the spherical coordinate system to the rectangular coordinate system. The specific relationship is:

[0010]

[0011] Then, spatial coordinate data and temperature data are collected synchronously: n laser trackers are placed in the measurement area as reference points, with n ≥ 3. A temperature sensor is placed on the side of the tracking head of the laser tracker, and the temperature data is continuously collected at m moments through the temperature sensor:

[0012] T=[T1,T2,…,T i ,…,T m ] (2)

[0013] Among them, T i The subscript represents the time i, i = 1, 2, ..., m;

[0014] While the temperature sensor is measuring, a laser tracker is used to continuously measure the spatial coordinate data of each reference point:

[0015]

[0016] in, It represents the spatial coordinate vector of the i-th moment measured by the laser tracker at the j-th reference point, i = 1, 2, ..., m; j = 1, 2, ..., n;

[0017] Next, solve the rotation matrix R and the translation matrix t: at time i = m, the laser tracker preheating is completed, and the coordinate vector value at time i = m is used as the global coordinate system O M , the coordinate vector values at other times are used as the local coordinate system O i , i=1,2,…,m, calculate the mean value of the coordinate vector of the global coordinate system Mean value of the coordinate vector in the local coordinate system

[0018]

[0019] Decentralization:

[0020]

[0021] Calculate the rotation matrix R and translation matrix t according to formulas (6), (7), (8), and (9):

[0022] For each decentered coordinate vector and Find the outer product And accumulate and sum to get the transition matrix H:

[0023]

[0024] Perform singular value decomposition on it:

[0025] H=U∑V T (7)

[0026] Among them, ∑ is a diagonal matrix, U and V are third-order unitary matrices, so the rotation matrix R is obtained:

[0027]

[0028] Obtain the translation matrix t:

[0029]

[0030] Finally, the three Euler angles and three translations are separated from the rotation matrix R and the translation matrix t, and the rotation matrix R is obtained by formula (8):

[0031]

[0032] Solve the Euler angle ψ along the ZYX sequence r :

[0033] ψ1=arctan2(r 21 ,r 11 ),ψ2=-arcsin(r 31 ),ψ3=arctan2(r 32 ,r 33 ) (11)

[0034] Among them, the yaw angle ψ1, the pitch angle ψ2, and the roll angle ψ3, and then the translation matrices t1, t2, and t3 corresponding to the X, Y, and Z axes are obtained from formula (9);

[0035] The second step is to calibrate the correlation function between the surface temperature difference of the laser tracking head and the zero drift curve;

[0036] Select the Euler angle ψ that has a strong correlation with the temperature rise r , r=1,2,3 and axial displacement t r ,r=1,2,3,Use monomial or polynomial fitting to establish Euler angle ψ r Temperature difference T between the laser tracking head and the surface i -T1 correlation function:

[0037] ψ r (T i -T1)=a0+a1(T i -T1)+a2(T i -T1) 2 +…+a k (T i -T1) k (12)

[0038] Establish axial displacement t r The temperature difference T between the laser tracker surface i -T1 correlation function:

[0039]

[0040] Among them, a0…a k , b0…b k are the monomial or polynomial fitting parameters;

[0041] The third step is to compensate for the zero drift during the warm-up process of each laser tracker startup;

[0042] Re-place a temperature sensor on the side of the laser tracking head. Its installation position is consistent with the temperature sensor installation position used in the process of calibrating the laser tracker to measure the zero drift curve of the coordinate system. Restart the laser tracker to preheat and measure c, c ≥ 1 point. Select the Euler angle parameter ψ fitted by formula (12) and (13) r and axial displacement t r Compensation is performed; the temperature is T t , initial temperature T 0 , according to the temperature difference T t -T 0 , predict the Euler angle deflection ψ r (T t -T 0 ), axial displacement t r (T t -T 0 ), reconstruct the rotation matrix R c :

[0043]

[0044] Translation matrix t c :

[0045]

[0046] Among them, R Z 、R Y 、R X is the rotation matrix around the Z, Y, and X axes after reconstruction;

[0047] Finally, the coordinate x of the reference point measured by the laser tracker is substituted into formula (16) to obtain the coordinate after compensation:

[0048] X c =R c x+t c (16)

[0049] By measuring the temperature-drift parameters of n, n≥3 points at a time, a function is established to compensate for the zero drift of each startup preheating, thereby realizing the compensation of the zero drift during the preheating process of a laser tracker.

[0050] The beneficial effect of the present invention is that the method fully takes into account that the zero-point drift of the laser tracker is caused by the drift of the laser tracking head coordinate system, and can effectively compensate for the zero-point drift of the measuring point during each preheating process; in addition, except for the temperature sensor, the present invention does not introduce any other additional equipment, and has low requirements for the layout of the measurement site, low cost, and is convenient for rapid on-site implementation; the present invention can be applied to measurement scenarios that require the use of a laser tracker, saves measurement time, ensures the overall measurement accuracy and stability of the geometric features of large aviation parts, and has broad engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a flow chart of the method for compensating for zero drift during the warm-up process of the laser tracker;

[0052] Figure 2 This is a schematic diagram of laser tracker measurement, where O is the laser tracker head coordinate system, P 1 -Public point 1 of the target ball, P 2 -Public point 2 of the target ball, P 3 -Public point 3 of the target ball, P 4 - Public point No. 4 of the target ball;

[0053] Figure 3 It is the temperature curve measured by temperature sensor 1;

[0054] Figure 4 From the local coordinate system O1 to the global coordinate system O M Schematic diagram of matrix transformation, where (a) shows the correspondence between the X, Y, and Z axes in the two coordinate systems, and (b) shows the spatial distribution of the common points of the four target spheres in the two coordinate systems; -Coordinates of the reference point in the local coordinate system O1, -Global coordinate system O M Coordinates of the lower reference point;

[0055] Figure 5 are the three Euler angles ψ r , 1≤r≤3 and three axial displacements t r , 1≤r≤3 schematic diagram;

[0056] Figure 6 are the three Euler angles ψ r , 1≤r≤3 zero drift diagram;

[0057] Figure 7 are the three axial displacements t r , 1≤r≤3 zero drift diagram;

[0058] Figure 8 is the monomial regression analysis graph of ψ1;

[0059] Figure 9 This is the monomial regression analysis diagram of t3;

[0060] Figure 10 This is a measurement diagram after the laser tracker is restarted, where O is the laser tracker head coordinate system, P 5 - Common point of the target ball; DETAILED DESCRIPTION

[0061] The specific implementation of the present invention is described in detail below in conjunction with the technical solutions and drawings.

[0062] This embodiment uses a laser tracker of model AT960 produced by Leica, which has a measurement range of 60m and a measurement uncertainty of ±15μm+6μm / m; and selects four 1.5-inch target balls as common points to be measured.

[0063] Attachment Figure 1 The following is a flow chart of the method. The method first synchronously measures the temperature and the reference point coordinates to calibrate the zero drift curve of the laser tracker measurement coordinate system. Secondly, the monomial fitting method is used to establish the correlation function between the surface temperature difference of the laser tracker and the zero drift curve. Finally, the transformation matrix is reconstructed to compensate for the zero drift during each startup and warm-up process of the laser tracker. The specific steps of the method are as follows:

[0064] The first step is to calibrate the zero drift curve of the laser tracker measurement coordinate system

[0065] As attached Figure 2 As shown, first place four laser tracker target balls in the measurement area, each serving as a reference point P 1 、P 2 、P 3 、P 4 , place a temperature sensor 1 on the surface of the laser tracker, O is the coordinate system of the laser tracker head, and continuously collect temperature data for 200 moments through temperature sensor 1:

[0066] T=[22.58,22.81,…,i,…,29.81], i=1,2,…,200

[0067] While temperature sensor 1 is measuring, a laser tracker is used to continuously measure the spatial coordinates of each reference point:

[0068]

[0069] The temperature difference curve measured by temperature sensor 1 is shown in the attached figure. Figure 3 shown.

[0070] Then solve the rotation matrix R and translation matrix t: select the preheating completion time i=200 as the global coordinate system, and the remaining time as the local coordinate system, and calculate the decentralized coordinate ΔP according to formula (3) and formula (4): 200j , ΔP ij , perform singular value decomposition according to formula (6) and formula (7) to obtain the rotation matrix R and translation matrix t from the local coordinate system to the global coordinate system. Figure 4 From one of the local coordinate systems O1 to the global coordinate system O M Matrix transformation diagram, is the coordinate of the reference point in the local coordinate system O1, is the global coordinate system O M Coordinates of the lower reference point.

[0071] The second step is to establish the correlation function between the surface temperature difference of the laser tracker and the zero drift curve

[0072] As attached Figure 4 As shown, the laser tracking head coordinate system is rotated 90 degrees clockwise around the Z axis to obtain three Euler angles ψ r , 1≤r≤3 and three axial displacements t r , 1≤r≤3 zero drift diagram, as shown in the attached Figure 5 , Attachment Figure 6 As shown in the figure, the Euler angle ψ1 and axial displacement parameter t3 with strong correlation with temperature rise are selected, and the Euler angle, axial displacement parameter and the surface temperature difference T of the laser tracker are respectively fitted using formulas (12) and (13). i -T0 correlation function, attached Figure 7 and attached Figure 8 Polynomial regression analysis graphs of ψ1 and t3, respectively.

[0073] The third step is to compensate for the zero drift during the warm-up process of each laser tracker startup.

[0074] As attached Figure 9 As shown, a temperature sensor 2 is re-placed on the side of the laser tracking head. Its installation position is consistent with the temperature sensor installation position used in the process of calibrating the laser tracker to measure the zero drift curve of the coordinate system. Restart the laser tracker to preheat and measure a reference point P 5 , the coordinates are:

[0075]

[0076] According to formula (12) and formula (13), the Euler angle deflection and axial displacement are predicted:

[0077]

[0078] Finally, the rotation matrix R is reconstructed according to formula (14) c , the translation matrix is t3(T t -T 0 ), the coordinate P 5 Substituting into formula (16) we get the coordinates after compensation:

[0079]

[0080] Zero drift compensation is achieved during the preheating process of the laser tracker.

[0081] Calculate and compare the reference point P before and after compensation 5The variance of coordinate drift is: 1.574-04>>1.612e-05, the range is: 4.756e-02>>1.447e-02, and the interquartile range is: 1.63.e-2>>6.924e-3. Therefore, this method greatly improves the accuracy and stability of the measured point coordinates.

[0082] The present invention is different from traditional zero drift compensation methods. This method fully considers that the zero drift of the laser tracker is caused by the drift of the laser tracking head coordinate system. It can effectively compensate for the zero drift of the measuring point during each preheating process and can be quickly applied to measurement site practice to ensure the overall measurement accuracy and stability of the geometric features of large aviation parts. It has broad engineering application prospects.

Claims

1. A method for compensating zero drift during the warm-up process of a laser tracker, characterized in that: Here are the steps: The first step is the synchronous acquisition and preprocessing of temperature-coordinate data during the laser tracker warm-up process; First, the laser tracker measurement coordinate system is constructed. The laser tracker's raw measurement data is based on three spherical coordinate system parameters: slant range ρ, pitch angle θ, and azimuth angle φ, which define the spatial position of the target point. The origin O is located at the mechanical reference point at the laser tracker's rotation center. The spherical coordinate system is converted to a rectangular coordinate system: the X-axis extends along the direction of the laser beam emission, the Z-axis lies in the horizontal plane and is perpendicular to the X-axis, and the Y-axis is determined according to the right-hand rule and is orthogonal to the XZ plane to form a spatial rectangular coordinate system. The mathematical transformation of the laser tracker measurement coordinate system is achieved by mapping the spherical coordinate system to the rectangular coordinate system. The specific relationship is: Then, spatial coordinate data and temperature data are collected synchronously: n laser trackers are placed in the measurement area as reference points, with n ≥ 3. A temperature sensor is placed on the side of the tracking head of the laser tracker, and the temperature data is continuously collected at m moments through the temperature sensor: T=[T1,T2,…,T i ,…,T m ] (2) Among them, T i The subscript represents the time i, i = 1, 2, ..., m; While the temperature sensor is measuring, a laser tracker is used to continuously measure the spatial coordinate data of each reference point: in, It represents the spatial coordinate vector of the i-th moment measured by the laser tracker at the j-th reference point, i = 1, 2, ..., m; j = 1, 2, ..., n; Next, solve the rotation matrix R and the translation matrix t: at time i = m, the laser tracker preheating is completed, and the coordinate vector value at time i = m is used as the global coordinate system O M , the coordinate vector values at other times are used as the local coordinate system O i , i=1,2,…,m, calculate the mean value of the coordinate vector of the global coordinate system Mean value of the coordinate vector in the local coordinate system Decentralization: Calculate the rotation matrix R and translation matrix t according to formulas (6), (7), (8), and (9): For each decentered coordinate vector and ΔP i j Find the outer product And accumulate and sum to get the transition matrix H: Perform singular value decomposition on it: H=U∑V T (7) Among them, ∑ is a diagonal matrix, U and V are third-order unitary matrices, so the rotation matrix R is obtained: Obtain the translation matrix t: Finally, the three Euler angles and three translations are separated from the rotation matrix R and the translation matrix t, and the rotation matrix R is obtained by formula (8): Solve the Euler angle ψ along the ZYX sequence r : ψ1=arctan2(r 21 ,r 11 ),ψ2=-arcsin(r 31 ),ψ3=arctan2(r 32 ,r 33 ) (11) Among them, the yaw angle ψ1, the pitch angle ψ2, and the roll angle ψ3, and then the translation matrices t1, t2, and t3 corresponding to the X, Y, and Z axes are obtained from formula (9); The second step is to calibrate the correlation function between the surface temperature difference of the laser tracking head and the zero drift curve; Select the Euler angle ψ that has a strong correlation with the temperature rise r , r=1,2,3 and axial displacement t r ,r=1,2,3,Use monomial or polynomial fitting to establish Euler angle ψ r Temperature difference T between the laser tracking head and the surface i -T1 correlation function: ψ r (T i -T1)=a0+a1(T i -T1)+a2(T i -T1) 2 +…+a k (T i -T1) k (12) Establish axial displacement t r The temperature difference T between the laser tracker surface i -T1 correlation function: Among them, a0…a k , b0…b k are the monomial or polynomial fitting parameters; The third step is to compensate for the zero drift during the warm-up process of each laser tracker startup; Re-place a temperature sensor on the side of the laser tracking head. Its installation position is consistent with the temperature sensor installation position used in the process of calibrating the laser tracker to measure the zero drift curve of the coordinate system. Restart the laser tracker to preheat and measure c, c ≥ 1 point. Select the Euler angle parameter ψ fitted by formula (12) and (13) r and axial displacement t r Compensation is performed; the temperature is T t , initial temperature T 0 , according to the temperature difference T t -T 0 , predict the Euler angle deflection ψ r (T t -T 0 ), axial displacement t r (T t -T 0 ), reconstruct the rotation matrix R c : R c =R Z R Y R X Translation matrix t c : Among them, R Z 、R Y 、R X is the rotation matrix around the Z, Y, and X axes after reconstruction; Finally, the coordinate x of the reference point measured by the laser tracker is substituted into formula (16) to obtain the coordinate after compensation: X c =R c x+t c (16) By measuring the temperature-drift parameters of n, n≥3 points at a time, a function is established to compensate for the zero drift of each startup preheating, thereby realizing the compensation of the zero drift during the preheating process of a laser tracker.

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