CN113310445B - A Calibration Method for Multi-Instrument Combination Measuring System - Google Patents

Abstract

The invention relates to a method for calibrating a multi-instrument combination measurement system. A multi-tooth indexing table is used as a standard to calibrate the rotation error of the coordinate system of the multi-instrument combination measurement system; a linear guide rail with a laser interferometer is used as a standard to calibrate the multi-instrument The translation error of the coordinate system of the combined measurement system; the length scale is used as the standard to calibrate the space distance length error of the common measuring point and the non-common measuring point of the multi-instrument combined measuring system. The invention makes up for the problem that the calibration method of the existing single measuring instrument cannot be directly applied to the calibration of the multi-instrument combined measurement system, ensures the uniform, accurate and reliable values of the multi-instrument combined measurement system, and facilitates the research and development of the multi-instrument combined measurement system upgrades and field applications.

Description

A calibration method for a multi-instrument combined measurement system

Technical Field

The invention relates to a calibration method for a multi-instrument combination measurement system, which is a calibration method for the accuracy of external parameters and coordinate measurement of the multi-instrument combination measurement system, and belongs to the field of measurement and testing.

Background Art

In the face of large space, high precision, multi-information, low cost, efficient and reliable measurement requirements in large equipment manufacturing such as aerospace and shipbuilding, a multi-instrument combination measurement system composed of multiple or multiple measuring instruments has become an important measurement method and has been widely used. As shown in Figure 1, in a multi-instrument combination measurement system, each measuring instrument measures in its own instrument coordinate system, and multiple measuring instruments calculate their external parameters (coordinate system rotation and translation conversion parameters) through a set of common measurement points to convert each instrument coordinate system to the system coordinate system; the common measurement point is measured by two or more measuring instruments, and its coordinates are obtained by fusion calculation of the measurement data of these instruments; the non-common measurement point is measured by only one measuring instrument, and its coordinates are obtained by converting the measurement data of the instrument to the system coordinate system through the external parameters of the instrument. In summary, the multi-instrument combination measurement system inevitably involves the coordinate system of each measuring instrument, the data fusion of public measurement points, and the data conversion of non-public measurement points. In order to ensure the uniformity, accuracy and reliability of the measurement values of the multi-instrument combination measurement system, the test of its external parameters and coordinate measurement cannot directly apply the calibration method of a single measuring instrument (such as "JJF 1242 Laser Tracking Three-Dimensional Coordinate Measurement System Calibration Specification", "JJF 1408 Articulated Arm Coordinate Measuring Machine Calibration Specification", etc.). At present, the overall calibration problem of the multi-instrument combination measurement system in the existing technology has not been solved.

Summary of the invention

The present invention provides a calibration method for a multi-instrument combination measurement system to make up for the problem that the existing calibration method for a single measuring instrument cannot be directly applied to the calibration of a multi-instrument combination measurement system. By respectively testing the external parameters, common measurement point coordinates and non-common measurement point coordinates of the multi-instrument combination measurement system, it is ensured that the measurement values of the multi-instrument combination measurement system are unified, accurate and reliable.

The present invention adopts the following technical solutions:

A calibration method for a multi-instrument combination measurement system adopts a multi-tooth dividing table as a standard to calibrate the coordinate system rotation error of the multi-instrument combination measurement system; adopts a linear guide rail with a laser interferometer as a standard to calibrate the coordinate system translation error of the multi-instrument combination measurement system; adopts a length ruler as a standard to calibrate the spatial distance length error of the common measurement point and the non-common measurement point of the multi-instrument combination measurement system.

Preferably, the coordinate system rotation error calibration of the multi-instrument combined measurement system includes the following steps:

Step 1: A multi-instrument combined measurement system consisting of N measuring instruments, one of which is fixed on a multi-tooth indexing table, and the remaining N-1 measuring instruments are fixed next to the multi-tooth indexing table. The overall layout of the N measuring instruments is consistent with that in field applications;

Step 2: Return the scale lines of the multi-tooth indexing table to zero, calibrate the external parameters of the N measuring instruments in the system, and record the coordinate system rotation matrix of the measuring instruments on the multi-tooth indexing table as R0;

Step 3: The multi-tooth indexing table rotates by an angle θ, and the indication θ _r1 of the multi-tooth indexing table is recorded;

Step 4: calibrate the external parameters of N measuring instruments in the system, repeat three times, and record the coordinate system rotation matrix of the measuring instrument on the multi-tooth indexing table as R ₁₁ , R ₁₂ , and R ₁₃ ;

Step 5. Calculate the changes ΔR ₁₁ , ΔR ₁₂ , ΔR ₁₃ between the coordinate system rotation matrices R ₁₁ , R _{12 , R 13 and} R ₀ respectively, as shown in formula (1); calculate the corresponding rotation angles θ _m11 , θ _m12 , θ _m13 using the Rodriguez formula, as shown in formula (2); and calculate the differences Δθ ₁₁ , Δθ ₁₂ , Δθ ₁₃ with θ _r1 , as shown in formula (3); take the maximum value and record it as the coordinate system rotation error Δθ ₁ at that angle, as shown in formula (4);

Where r _1js represents the sth element in the matrix ΔR _1j , j = 1, 2, 3;

θ _m1j = arcsin(u ² +v ² +w ² ) (2);

j＝1，2，3。in,

j=1, 2, 3.

Δθ _1j =|θ _m1j -θ _r1 | (3);

Wherein, j = 1, 2, 3;

Δθ ₁ =max{Δθ ₁₁ ,Δθ ₁₂ ,Δθ ₁₃ } (4);

Step 6: Rotate the multi-tooth indexing table to the indicated values θ _r2 , θ _r3 , …, θ _rM in sequence according to the step θ, repeat steps 4 and 5, measure the coordinate system rotation errors Δθ ₂ , Δθ ₃ , …, Δθ _M at each location, and take the maximum value as the coordinate system rotation error Δθ of this calibration, as shown in formula (5);

Δθ=max{Δθ ₁ , Δθ ₂ ,..., Δθ _M } (5).

Preferably, the coordinate system translation error calibration of the multi-instrument combined measurement system includes the following steps:

Step 1: A multi-instrument combined measurement system consisting of N measuring instruments, one of which is fixed on a mobile workbench of a linear guide rail, and the remaining N-1 measuring instruments are fixed beside the linear guide rail. The overall layout of the N measuring instruments is consistent with that in field applications.

Step 2: Reset the laser interferometer, calibrate the external parameters of N measuring instruments in the system, and record the coordinate translation vector of the measuring instrument on the mobile workbench as T ₀ ;

Step 3, the moving table moves along the linear guide rail by a displacement d, and the indication d _r1 of the laser interferometer is recorded at this time;

Step 4: calibrate the external parameters of N measuring instruments in the system, repeat three times, and record the coordinate translation vectors of the measuring instruments on the mobile workbench as T ₁₁ , T ₁₂ , and T ₁₃ ;

Step 5: Calculate the changes ΔT ₁₁ , ΔT ₁₂ , ΔT ₁₃ between the coordinate system translation vectors T ₁₁ , T ₁₂ , T ₁₃ and T ₀ respectively, as shown in formula (6), calculate the corresponding translations d _m11 , d _m12 , d _m13 in combination with the calculation formula of the vector modulus, as shown in formula (7), and calculate the differences Δd ₁₁ , Δd ₁₂ , Δd ₁₃ with d _r1 , as shown in formula (8), take the maximum value and record it as the coordinate system translation error Δd ₁ at this position, as shown in formula (9);

Wherein, t _x1j , t _y1j , t _z1j represent three elements in the vector ΔT _1j , j = 1, 2, 3;

Wherein, j = 1, 2, 3;

Δd _1j =|d _m1j -d _r1 | (8);

Wherein, j = 1, 2, 3;

Δd ₁ =max{Δd ₁₁ ,Δd ₁₂ ,Δd ₁₃ } (9);

Step 6: Move the movable worktable to the indicated values d _r2 , d _r3 , …, d _rM along the linear guide rail in sequence according to the step d, repeat steps 4 and 5, measure the coordinate system translation errors Δd ₂ , Δd ₃ , …, Δd _M at each location, and take the maximum value as the coordinate system translation error Δd of this calibration, as shown in formula (10);

Δd=max{Δd ₁ , Δd ₂ ,..., Δd _M } (10).

Preferably, the calibration of the spatial length indication error of the common measurement point of the multi-instrument combined measurement system comprises the following steps:

Step 1: The multi-instrument combination measurement system composed of N measuring instruments is placed according to the overall layout consistent with the field application. M length scales are arranged within the measurement range of the multi-instrument combination measurement system. A target seat is installed at each end of each length scale, which can be adapted to the targets of different measuring instruments in the multi-instrument combination measurement system and keep the measurement point unchanged with the change of target type. The directions of the length scales include horizontal, vertical, inclined and other different directions;

Step 2: Ensure that the measuring points at both ends of the M length scales can be measured by two or more measuring instruments in the multi-instrument combination measurement system, take the measuring points at both ends of the length scale as common measuring points, coordinate with other common measuring points, calibrate the external parameters of the multi-instrument combination measurement system, and calculate the coordinates of the common measuring points through data fusion; repeat three times, and record the coordinates of the common measuring points at both ends of the i-th length scale in the j-th pass as ( _xi1j , _yi1j , _zi1j ) and ( _xi2j , _yi2j , _zi2j ), i = 1, 2, ..., M, j = 1, 2, 3;

Step 3: Calculate the length l _m1j of the first length scale using the coordinates ( _xi1j , _yi1j , z _i1j ) and ( _xi2j , _yi2j , z _i2j ), as shown in formula (11), and calculate the difference Δl _1j between the length scale and the reference value l _r1j of the length scale, as shown in formula (12); take the maximum value of Δl ₁₁ , Δl ₁₂ , and Δl ₁₃ as the spatial length indication error Δl ₁ at the first length scale, as shown in formula (13);

Wherein, j = 1, 2, 3;

Δl _1j =|l _m1j -l _r1 | (12);

Wherein, j = 1, 2, 3;

Δl ₁ =max{Δl ₁₁ ,Δl ₁₂ ,Δl ₁₃ } (13);

Step 4, repeat step 3, and calculate the spatial length indication error Δl _i at the remaining M-1 length scales in turn, i=2, 3, ..., M; take the maximum value of the spatial length indication error at the M length scales as the spatial length indication error Δl of the common measurement point of this calibration, as shown in formula (14);

Δl=max{Δl ₁ , Δl ₂ ,..., Δl _M } (14).

Furthermore, the calibration of the spatial length indication error of the non-common measurement points of the multi-instrument combined measurement system includes the following steps:

Step 1: a multi-instrument combination measurement system consisting of N measuring instruments is placed according to an overall layout consistent with that in field applications, and external parameters of the multi-instrument combination measurement system are calibrated;

Step 2: Arrange M length scales within the measurement range of the multi-instrument combination measurement system. A target seat is installed at each end of each length scale, which can be adapted to the targets of different measuring instruments in the multi-instrument combination measurement system and keep the measurement point unchanged with the change of target type. The directions of the length scales include horizontal, vertical and inclined directions.

Step 3, the multi-instrument combined measurement system measures M length scales, ensuring that the measurement points of each length scale are measured by only one measuring instrument, and the measurement points at both ends of the same length scale are not measured by the same measuring instrument, that is, the measurement points on the M length scales are all non-public measurement points; complete data conversion according to the external parameters of the multi-instrument combined measurement system to obtain the coordinates of the non-public measurement points; repeat three times; the coordinates of the public measurement points at both ends of the i-th length scale in the j-th pass are recorded as ( _xi1j , _yi1j , _zi1j ) and ( _xi2j , _yi2j , _zi2j ), i=1, 2, ..., M, j=1, 2, 3;

Step 4: Calculate the length l _m1j of the first length scale using the coordinates ( _xi1j , _yi1j , z _i1j ) and ( _xi2j , _yi2j , z _i2j ), as shown in formula (11), and calculate the difference Δl _1j between the length scale and the reference value l _r1j of the length scale, as shown in formula (12); take the maximum value of Δl ₁₁ , Δl ₁₂ , and Δl ₁₃ as the spatial length indication error Δl ₁ at the first length scale, as shown in formula (13);

Step 5: Repeat step 4 to calculate the spatial length indication error Δl _i at the remaining M-1 length scales, i = 2, 3, ..., M. The maximum value of the spatial length indication error at the M length scales is taken as the spatial length indication error Δl of the non-public measurement point of this calibration, as shown in formula (14).

The beneficial effects of the present invention are as follows: a systematic and traceable multi-instrument combination measurement system calibration method is provided for different test requirements of external parameters, public measurement points and non-public measurement points, which makes up for the problem that the existing calibration method of a single measuring instrument cannot be directly applied to the calibration of a multi-instrument combination measurement system, ensures that the measurement values of the multi-instrument combination measurement system are unified, accurate and reliable, and facilitates the research and development, upgrading and on-site application of the multi-instrument combination measurement system.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of a multi-instrument combined measurement system.

FIG2 is a schematic diagram of the calibration of the coordinate system rotation error of the multi-instrument combination measurement system.

FIG3 is a schematic diagram of the coordinate translation error calibration of the multi-instrument combined measurement system.

FIG4 is a schematic diagram of the calibration of the spatial length indication error of the common measurement point of the multi-instrument combination measurement system.

FIG5 is a schematic diagram of the calibration of the spatial length indication error of non-common measurement points in a multi-instrument combination measurement system.

DETAILED DESCRIPTION

The preferred implementation modes of the present invention are described in detail below with reference to the embodiments and the accompanying drawings.

Embodiment 1:

Taking a multi-instrument combined measurement system consisting of two measuring instruments as an example, the coordinate system rotation error calibration of the multi-instrument combined measurement system is shown in Figure 2, including the following steps:

Step 1: Fix the first measuring instrument on the multi-tooth indexing table, and fix the second measuring instrument next to the multi-tooth indexing table. The overall layout of the two measuring instruments is consistent with their on-site application.

Step 2: Return the scale line of the multi-tooth indexing table to zero, calibrate the external parameters of the two measuring instruments in the system according to the operation manual of the multi-instrument combination measurement system, and record the coordinate system rotation matrix of the measuring instrument on the multi-tooth indexing table as R ₀ .

Step 3: The multi-tooth indexing table rotates to an angle θ, and the indication θ _r1 of the multi-tooth indexing table is recorded.

Step 4: Calibrate the external parameters of the two measuring instruments in the system according to the operating manual of the multi-instrument combined measuring system, repeat three times, and record the coordinate system rotation matrix of the measuring instrument on the multi-tooth indexing table as R ₁₁ , R ₁₂ , and R ₁₃ .

Step 5: Calculate the changes ΔR ₁₁ , ΔR ₁₂ , ΔR ₁₃ between the coordinate system rotation matrices R ₁₁ , R 12 , R ₁₃ and R ₀ respectively, as shown in formula (15), and calculate the corresponding rotation angles θ _{m11 ,} θ _m12 , θ m13 by combining the Rodriguez formula.

θ _m12 , θ _m13 , as shown in formula (16), and calculate the differences Δθ ₁₁ , Δθ ₁₂ , Δθ ₁₃ with θ _r1 , as shown in formula (17), and take the maximum value as the coordinate system rotation error Δθ ₁ at that angle, as shown in formula (18).

Wherein, r _1js represents the sth element in the matrix ΔR _1j , j=1, 2, 3.

θ _m1j = arcsin(u ² +v ² +w ² ) (16)

j＝1，2，3。in,

j=1, 2, 3.

Δθ _1j =|θ _m1j -θ _r1 | (17)

Among them, j=1, 2, 3.

Δθ ₁ =max{Δθ ₁₁ ,Δθ ₁₂ ,Δθ ₁₃ } (18)

Step 6. According to the step θ, rotate the multi-tooth dividing table to the indicated values θ _r2 , θ _r3 , … , θ _rM in sequence, repeat steps 4 and 5, measure the coordinate system rotation errors Δθ _r2 , Δθ _r3 , … , Δθ _rM at each location, and take the maximum value as the coordinate system rotation error Δθ of this calibration, as shown in formula (19).

Δθ=max{Δθ ₁ , Δθ ₂ ,..., Δθ _M } (19).

Embodiment 2:

Taking a multi-instrument combined measurement system consisting of two measuring instruments as an example, the coordinate system translation error calibration of the multi-instrument combined measurement system is shown in Figure 3, including the following steps:

Step 1: Fix the first measuring instrument on the mobile workbench of the linear guide, and fix the second measuring instrument next to the linear guide. The overall layout of the two measuring instruments is consistent with their on-site application.

Step 2: Reset the laser interferometer, calibrate the external parameters of the two measuring instruments in the system according to the operation manual of the multi-instrument combination measurement system, and record the coordinate translation vector of the measuring instrument on the mobile workbench as T ₀ .

Step 3: Move the workbench along the linear guide rail for a displacement d, and record the indication d _r1 of the laser interferometer at this time.

Step 4: Calibrate the external parameters of the two measuring instruments in the system according to the operating manual of the multi-instrument combination measuring system, repeat three times, and record the coordinate system translation vectors of the measuring instruments on the mobile workbench as T ₁₁ , T ₁₂ , and T ₁₃ .

Step 5. Calculate the changes _ΔT11 , ΔT12, ΔT13 between the coordinate system translation vectors _T11 , _T12 , _T13 and _T0 respectively, as shown in formula (20), calculate the corresponding translations _dm11 , _dm12 , _dm13 in combination with the calculation formula of the vector modulus, as shown in formula (21), and calculate the differences _Δd11 , _Δd12 , _{Δd13 with dr1} , as shown in formula (22), and take the maximum value as the coordinate system translation error _Δd1 at that position, as shown in formula ( ₂₃ ).

Wherein, t _x1j , t _y1j , and t _z1j represent three elements in the vector ΔT _1j , and j=1, 2, and 3.

Among them, j=1, 2, 3.

Δd _1j ＝|d _m1j -d _r1 | (22)

Among them, j=1, 2, 3.

Δd ₁ =max{Δd ₁₁ ,Δd ₁₂ ,Δd ₁₃ } (23)

Step 6: Move the movable worktable to the indicated values d _r2 , d _r3 , …, d _rM along the linear guide rail in sequence according to the step d, repeat steps 4 and 5, measure the coordinate system translation errors Δd _r2 , Δd _r3 , …, Δd _rM at each location, and take the maximum value as the coordinate system translation error Δd of this calibration, as shown in formula (24).

Δd＝max{Δd ₁ ,Δd ₂ ,...,Δd _M } (24)

Embodiment three:

Taking a multi-instrument combined measurement system consisting of two measuring instruments and three length scales as an example, the calibration of the spatial length indication error of the common measuring point of the multi-instrument combined measurement system is shown in Figure 4, including the following steps:

Step 1: The multi-instrument combination measurement system consisting of two measuring instruments is placed according to the overall layout consistent with the on-site application. Three length rulers are arranged within the measurement range of the multi-instrument combination measurement system. A target holder is installed at each end of each length ruler, which can adapt to the targets of different measuring instruments in the multi-instrument combination measurement system and keep the measurement point unchanged with the change of target type. The directions of the length rulers include horizontal, vertical, inclined and other directions.

Step 2: Ensure that the measuring points at both ends of the three length scales can be measured by two measuring instruments in the multi-instrument combination measurement system. Take the measuring points at both ends of the length scales as common measuring points, and calibrate the external parameters of the multi-instrument combination measurement system in accordance with the operation manual of the multi-instrument combination measurement system in conjunction with other common measuring points, and calculate the coordinates of the common measuring points through data fusion. Repeat three times. The coordinates of the common measuring points at both ends of the i-th length scale in the j-th pass are recorded as ( _xi1j , _yi1j , _zi1j ) and ( _xi2j , _yi2j , _zi2j ), i = 1, 2, 3, j = 1, 2, 3.

Step 3: Using the coordinates (x _11j , y _11j , z _11j ) and (x _12j , y _12j , z _12j ), calculate the length l _m1j of the first length scale, as shown in formula (25), and calculate the difference Δl _1j between it and the reference value l _r1j of the length scale, as shown in formula (26). Take the maximum value of Δl ₁₁ , Δl ₁₂ , and Δl ₁₃ as the spatial length indication error Δl ₁ at the first length scale, as shown in formula (27).

Among them, j=1, 2, 3.

Δl _1j ＝|l _m1j -l _r1 | (26)

Among them, j=1, 2, 3.

Δl ₁ =max{Δl ₁₁ ,Δl ₁₂ ,Δl ₁₃ } (27)

Step 4: Repeat step 3 to calculate the spatial length indication error Δl _i at the remaining two length scales, i = 2, 3. The maximum value of the spatial length indication error at the three length scales is taken as the spatial length indication error Δl of the common measurement point of this calibration, as shown in formula (28).

Δl=max{Δl ₁ , Δl ₂ , Δl ₃ } (28).

Embodiment 4:

Taking a multi-instrument combined measurement system consisting of two measuring instruments and three length scales as an example, the calibration of the spatial length indication error of the non-public measuring points of the multi-instrument combined measurement system is shown in Figure 5, including the following steps:

Step 1: The multi-instrument combination measurement system consisting of two measuring instruments is placed according to the overall layout consistent with the field application, and the external parameters of the multi-instrument combination measurement system are calibrated according to the operation manual of the multi-instrument combination measurement system.

Step 2: Arrange three length scales within the measurement range of the multi-instrument combination measurement system. A target holder is installed at each end of each length scale, which can adapt to the targets of different measuring instruments in the multi-instrument combination measurement system and keep the measurement point unchanged with the change of target type. The directions of the length scales include horizontal, vertical, inclined and other directions.

Step 3: The multi-instrument combined measurement system measures the three length scales to ensure that the measurement points of each length scale are measured by only one measuring instrument, and the measurement points at both ends of the same length scale are not measured by the same measuring instrument, that is, the measurement points on the three length scales are all non-public measurement points. Complete data conversion according to the external parameters of the multi-instrument combined measurement system to obtain the coordinates of the non-public measurement points. Repeat three times. The coordinates of the public measurement points at both ends of the i-th length scale in the j-th pass are recorded as ( _xi1j , _yi1j , _zi1j ) and ( _xi2j , _yi2j , _zi2j ), i = 1, 2, 3, j = 1, 2, 3.

Step 4: Using the coordinates (x _11j , y _11j , z _11j ) and (x _12j , y _12j , z _12j ), calculate the length l _m1j of the first length scale, as shown in formula (25), and calculate the difference Δl _1j between it and the reference value l _r1j of the length scale, as shown in formula (26). Take the maximum value of Δl ₁₁ , Δl ₁₂ , and Δl ₁₃ as the spatial length indication error Δl ₁ at the first length scale, as shown in formula (27).

Step 5: Repeat step 4 to calculate the spatial length indication error Δl _i at the remaining two length scales, i = 2, 3. The maximum value of the spatial length indication error at the three length scales is taken as the spatial length indication error Δl of the non-public measurement point of this calibration, as shown in formula (28).

The reference numerals in the accompanying drawings 1-5 are as follows:

1First measuring instrument,

2 Second measuring instrument,

3Third measuring instrument,

4Fourth measuring instrument,

5 N-1th measuring instrument,

6th Nth measuring instrument,

7. Workpiece to be measured,

8 common measurement points,

9 laser interferometer,

10 linear guides,

11The first length scale,

12 second length scale,

13The third length scale,

14 non-public measurement points,

15 multi-tooth indexing table,

16 Mobile workbench.

Claims (1)

1. A method for calibrating a multi-instrument combined measurement system, comprising the steps of:

a multi-tooth indexing table is used as a standard for calibrating a coordinate system rotation error of a multi-instrument combined measurement system;

a linear guide rail with a laser interferometer is used as a standard to calibrate the coordinate system translation error of the multi-instrument combined measurement system;

using a length scale as a standard device to calibrate the space distance length errors of a public measuring point and a non-public measuring point of the multi-instrument combined measuring system;

the coordinate system rotation error calibration of the multi-instrument combined measurement system comprises the following steps:

step 1.1, a multi-instrument combined measuring system consisting of N measuring instruments is characterized in that 1 measuring instrument is fixed on a multi-tooth indexing table, the rest N-1 measuring instruments are fixed beside the multi-tooth indexing table, and the overall layout of the N measuring instruments is consistent with that of the N measuring instruments when the N measuring instruments are applied on site;

step 1.2, zeroing scale marks of the multi-tooth indexing table, calibrating external parameters of N measuring instruments in the system, and marking a coordinate system rotation matrix of the measuring instruments on the multi-tooth indexing table as R ₀ ；

Step 1.3, the rotation angle theta of the multi-tooth indexing table is recorded, and the indication value theta of the multi-tooth indexing table at the moment is recorded _r1 ；

Step 1.4, calibrating external parameters of N measuring instruments in the system, repeating for three times, and recording a coordinate system rotation matrix of the measuring instruments on the multi-tooth indexing table as R ₁₁ 、R ₁₂ 、R ₁₃ ；

Step 1.5, calculating a coordinate system rotation matrix R respectively ₁₁ 、R ₁₂ 、R ₁₃ And R is R ₀ The variation DeltaR between ₁₁ 、ΔR ₁₂ 、ΔR ₁₃ As shown in formula (1); calculating the corresponding rotation angle theta by combining the Rodrigues formula _m11 、θ _m12 、θ _m13 As shown in formula (2); and calculate the sum theta _r1 Is a difference delta theta of (2) ₁₁ 、Δθ ₁₂ 、Δθ ₁₃ As shown in formula (3); taking the maximum value as the coordinate system rotation error delta theta at the angle ₁ As shown in formula (4);

wherein ,r_1js Representation matrix DeltaR _1j J=1, 2,3;

θ _m1j ＝arcsin(u ² +v ² +w ² ) (2)；

wherein ,

Δθ _1j ＝|θ _m1j -θ _r1 | (3)；

wherein j=1, 2,3;

Δθ ₁ ＝max{Δθ ₁₁ ,Δθ ₁₂ ,Δθ ₁₃ } (4)；

step 1.6, sequentially rotating the multi-tooth indexing table to the indication value theta according to the step theta _r2 、θ _r3 、…、θ _rM Repeating the steps 1.4 and 1.5 to measure the rotation error delta theta of the coordinate system ₂ 、Δθ ₃ 、…、Δθ _M Taking the maximum value as the rotation error delta theta of the coordinate system in the calibration, as shown in a formula (5);

Δθ＝max{Δθ ₁ ,Δθ ₂ ,...,Δθ _M } (5)；

the coordinate system translation error calibration of the multi-instrument combined measurement system comprises the following steps:

step 2.1, a multi-instrument combined measuring system consisting of N measuring instruments is characterized in that 1 measuring instrument is fixed on a movable workbench of a linear guide rail, the rest N-1 measuring instruments are fixed beside the linear guide rail, and the overall layout of the N measuring instruments is consistent with that of the N measuring instruments when the N measuring instruments are applied on site;

step 2.2, resetting the laser interferometer, calibrating external parameters of N measuring instruments in the system, and recording a coordinate system translation vector of the measuring instrument on the movable workbench as T ₀ ；

Step 2.3, moving the workbench along the linear guide rail to move and displace d, and recording the indication value d of the laser interferometer at the moment _r1 ；

Step 2.4, calibrating external parameters of N measuring instruments in the system, repeating for three times, and recording a coordinate system translation vector of the measuring instrument on the movable workbench as T ₁₁ 、T ₁₂ 、T ₁₃ ；

Step 2.5, calculating the coordinate system translation vectors T respectively ₁₁ 、T ₁₂ 、T ₁₃ And T is ₀ The variation delta T between ₁₁ 、ΔT ₁₂ 、ΔT ₁₃ As shown in the formula (6), the corresponding translation d is calculated by combining a calculation formula of the vector mode _m11 、d _m12 、d _m13 As shown in formula (7), and calculate the sum d _r1 Is a difference Δd of (d) ₁₁ 、Δd ₁₂ 、Δd ₁₃ Taking the maximum value as the coordinate system translation error Δd at that position as shown in equation (8) ₁ As shown in formula (9);

wherein ,t_x1j 、t _y1j 、t _z1j Representing the vector DeltaT _1j J=1, 2,3;

wherein j=1, 2,3;

Δd _1j ＝|d _m1j -d _r1 | (8)；

wherein j=1, 2,3;

Δd ₁ ＝max{Δd ₁₁ ,Δd ₁₂ ,Δd ₁₃ } (9)；

step 2.6, moving the movable workbench to the indication value d along the linear guide rail in sequence according to the step d _r2 、d _r3 、…、d _rM Step 2.4 and step 2.5 are repeated to measure the translational error delta d of the coordinate system ₂ 、Δd ₃ 、…、Δd _M Taking the maximum value as the translation error delta d of the coordinate system in the calibration, as shown in a formula (10);

Δd＝max{Δd ₁ ,Δd ₂ ,...,Δd _M } (10)；

the error calibration of the spatial length indication value of the common measurement point of the multi-instrument combined measurement system comprises the following steps:

step 3.1, a multi-instrument combined measuring system consisting of N measuring instruments is placed according to the integral layout consistent with the field application, M length scales are arranged in the measuring range of the multi-instrument combined measuring system, two ends of each length scale are respectively provided with a target seat, targets of different measuring instruments in the multi-instrument combined measuring system can be adapted, measuring points are kept unchanged along with the change of target types, and the directions of the length scales comprise horizontal, vertical and inclined directions;

step 3.2, ensuring that the measuring points at the two ends of the M length scales can be measured by 2 or more measuring instruments in the multi-instrument combined measuring system, taking the measuring points at the two ends of the length scales as public measuring points, matching with other public measuring points, calibrating external parameters of the multi-instrument combined measuring system, and calculating coordinates of the public measuring points through data fusion; repeating three times, and respectively recording the coordinates of the common measuring points at the two ends of the ith length scale in the jth time as (x) _i1j ，y _i1j ，z _i1j) and (x_i2j ，y _i2j ，z _i2j )，i＝1，2，…，M，j＝1，2，3；

Step 3.3 using coordinates (x _11j ，y _11j ，z _11j )、(x _12j ，y _12j ，z _12j ) Calculate the length l of the 1 st length scale _m1j As shown in formula (11), and calculates a reference value l with the length scale _r1j Is a difference Deltal of (1) _1j As shown in formula (12); taking Deltal ₁₁ 、Δl ₁₂ 、Δl ₁₃ The maximum value of (1) is taken as the error Deltal of the space length indication value at the 1 st length scale ₁ As shown in formula (13);

wherein j=1, 2,3;

Δl _1j ＝|l _m1j -l _r1 | (12)；

wherein j=1, 2,3;

Δl ₁ ＝max{Δl ₁₁ ,Δl ₁₂ ,Δl ₁₃ } (13)；

step 3.4, repeating the step 3.3, and sequentially calculating the space length indication error Deltal at the position of the remaining M-1 length scales _i I=2, 3, …, M; taking the maximum value of the space length indication errors at the M length scales as the space length indication error Deltal of the common measurement point in the calibration, as shown in a formula (14);

Δl＝max{Δl ₁ ,Δl ₂ ,...,Δl _M } (14)；

the error calibration of the spatial length indication value of the non-common measurement point of the multi-instrument combined measurement system comprises the following steps:

step 4.1, a multi-instrument combined measurement system consisting of N measuring instruments is placed according to the integral layout consistent with the field application, and external parameters of the multi-instrument combined measurement system are calibrated;

step 4.2, arranging M length scales in the measuring range of the multi-instrument combined measuring system, wherein two ends of each length scale are respectively provided with a target seat, so that targets of different measuring instruments in the multi-instrument combined measuring system can be adapted, measuring points are kept unchanged along with the change of target types, and the directions of the length scales comprise horizontal, vertical and inclined directions;

step 4.3, the multi-instrument combined measuring system measures M length scales, so that the measuring points of each length scale are only measured by one measuring instrument, and the measuring points at two ends of the same length scale are not measured by the same measuring instrument, namely, the measuring points on the M length scales are all non-public measuring points; completing data conversion according to external parameters of the multi-instrument combined measurement system to obtain coordinates of non-public measurement points; repeating three times; the coordinates of the common measurement points at both ends of the ith length scale in the jth pass are respectively recorded as (x) _i1j ，y _i1j ，z _i1j) and (x_i2j ，y _i2j ，z _i2j )，i＝1，2，…，M，j＝1，2，3；

Step 4.4 using coordinates (x _i1j ，y _i1j ，z _i1j )、(x _i2j ，y _i2j ，z _i2j ) Calculate the length l of the 1 st length scale _m1j As shown in formula (11), and calculates a reference value l with the length scale _r1j Is a difference Deltal of (1) _1j As shown in formula (12); taking Deltal ₁₁ 、Δl ₁₂ 、Δl ₁₃ The maximum value of (1) is taken as the error Deltal of the space length indication value at the 1 st length scale ₁ As shown in formula (13);

step 4.5, repeating the step 4.4, and sequentially calculating the space length indication error Deltal at the position of the remaining M-1 length scales _i I=2, 3, …, M; taking the maximum value of the space length indication errors at the M length scales as the space length indication error Deltal of the non-common measurement point in the calibration, as shown in a formula (14);

n and M are positive integers.

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