A target ball roundness error measurement method and system based on the theodolite angle measurement principle

Abstract

The application provides a target ball roundness error measurement method and system based on the theodolite angle measurement principle, and comprises the following steps: setting a theodolite, directional lighting, aiming at a target ball contour point by using the theodolite, constructing a radius angle measurement model, linearizing the model, calculating the distance from a measurement station to the center of the target ball, and obtaining a target ball roundness error calibration result, etc. The theodolite aiming data is converted into a radius value based on a spherical triangle model, the non-contact roundness error measurement of the theodolite is realized for the first time, the center coordinates of the ball, the baseline length and the roundness error calibration can be synchronously completed in combination with the space three-dimensional intersection measurement, and the integrated efficient calibration of the three-dimensional baseline standard device "center coordinates of the ball-space baseline length-roundness error" can be realized.

Description

Technical Field

[0001] This invention relates to the field of large-scale engineering surveying technology, and in particular to a method and system for measuring the roundness error of a target sphere based on the theodolite angle measurement principle. Background Technology

[0002] In large-scale precision engineering surveying, such as bridge health monitoring and spacecraft assembly, high-precision applications require large-scale spatial measurement instruments like 3D laser scanners and photogrammetry systems to rely on a 3D baseline standard device composed of multiple target spheres for measurement traceability. The core metrological parameters of this device include the spatial coordinates of the target sphere centers, the standard value of the spatial baseline length between spheres, and the roundness error of the target spheres (i.e., the geometric deviation of the spherical profile). All three must be calibrated simultaneously to ensure the overall accuracy of the measurement system.

[0003] Current mainstream calibration methods have significant limitations: 1) Traditional laboratory contact measurements require disassembling the target sphere and using a coordinate measuring machine or length measuring machine for contact scanning. This method disrupts the original installation state, leading to the interruption of the traceability chain between the sphere center coordinates and the baseline length, and it cannot achieve in-situ calibration; 2) Although the method of using a laser tracker in conjunction with a spherical prism to contact the surface of the target sphere can obtain data in-situ, it relies on high-cost equipment with a unit price of over 2 million yuan, and the measurement personnel need to be in close contact with the target sphere. In large three-dimensional baseline standard devices, this can easily cause safety accidents such as falling and collisions. At the same time, contact measurement may introduce target sphere deformation errors; 3) Although structured light-based photogrammetry technology can achieve non-contact contour scanning, its measurement distance is usually less than 1 meter. Personnel still need to be close to the target sphere to operate, and the safety risks are comparable to those of laser trackers. Moreover, this method can only measure roundness errors and cannot simultaneously obtain the sphere center coordinates and baseline length, resulting in equipment utilization of less than 50% and significantly increasing the overall cost.

[0004] Currently, theodolite spatial 3D intersection measurement technology is commonly used in calibration sites to calibrate the sphere's center coordinates and baseline length. This technology offers advantages such as a long measurement range, safety (requiring no close-range operation by personnel), and cost, being only 10% of that of laser trackers. However, existing theodolite technology has a significant drawback—it cannot measure the target sphere's roundness error. This forces the 3D baseline device to perform calibration in steps: first, the theodolite is used to measure the sphere's center coordinates and baseline length, and then other methods (such as structured light or secondary disassembly) are used to separately measure the roundness error. This fragmented process reduces calibration efficiency by more than 60%, and the repeated operations further exacerbate safety risks. Especially in large-scale scenarios, the theodolite's safety and cost advantages are sharply contradicted by its functional limitations.

[0005] Therefore, there is an urgent need in this field to develop a target sphere roundness error measurement method based on the theodolite angle measurement principle. While retaining the advantages of theodolite in terms of large size adaptability, non-contact safety and low cost, this method can make up for its functional shortcomings and ultimately achieve integrated and efficient calibration of the three-dimensional baseline standard device in terms of "sphere center coordinates - spatial baseline length - roundness error". Summary of the Invention

[0006] This invention proposes a method and system for measuring the roundness error of a target sphere based on the theodolite angle measurement principle. It solves the problem that existing theodolite spatial three-dimensional intersection measurement systems lack non-contact measurement capabilities for the roundness error of the target sphere in large-scale calibration scenarios, thus failing to achieve integrated and efficient calibration of "sphere center coordinates + baseline length + roundness error". The technical solution of this invention is implemented as follows:

[0007] A method for measuring the roundness error of a target sphere based on the angle measurement principle of a theodolite, characterized by the following steps:

[0008] S1: Set up at least 3 survey stations at the survey site and set up a theodolite at each survey station;

[0009] S2: Provide directional illumination to the outline of the target ball being measured, so that the outline is clearly imaged in the theodolite's field of view;

[0010] S3: Using a theodolite, aim at the outline of the target sphere and record the horizontal observation value h of the k-th point on the j-th target sphere at the i-th station. ijk and the observed zenith distance v ijk ;

[0011] S4: Based on the cosine theorem for spherical triangles, construct a measurement model for the radius angle:

[0012]

[0013] Among them, h ij0 It is the unknown horizontal observation value from the i-th station to the j-th target ball, v ij0 It is the unknown observed value of the zenith distance from the i-th station to the j-th target sphere;

[0014] S5: Linearize the measurement model into an error equation;

[0015] S6: Convert the error measurement model into matrix form and solve for the radius angle using the least squares method.

[0016] The radius angle r corresponding to the k-th aiming of the j-th target ball at the i-th station. ijk ;

[0017]

[0018] S7: Based on the sine relation Calculate the radius angle corresponding to the k-th aiming of the j-th target ball at the i-th station. Corresponding contour point radius value It can also be calculated using the following formula. ::

[0019] ;

[0020] S8: Take all R balls of the same target ball ijk The range of the values ​​is taken as the roundness error of a single station, and finally, twice the maximum roundness error of the target ball is taken as the calibration result of the roundness error of the target ball.

[0021] As a preferred technical solution, the directional illumination in step S2 uses a side light source to illuminate the equatorial surface of the target sphere, so that the contour edge forms a high-contrast dark field image.

[0022] As a preferred technical solution, step S3 further includes using the prism-free distance measurement function of the theodolite to obtain the distance value L from the center of the station to the center of the target ball. ij Used to calculate the radius value of the contour points in step S7. .

[0023] As a preferred technical solution, the linearization process in step S5 is specifically as follows:

[0024] 1) Define parameters: Let , ,

[0025] 2) Construct the error equation:

[0026]

[0027] 3) Convert the error measurement model into matrix form:

[0028]

[0029] in, , , .

[0030] As a preferred technical solution, the distance S in step S7 ij The results are obtained through spatial three-dimensional intersection calculations, and the intersection process does not participate in the roundness error calculation.

[0031] As a preferred technical solution, the range calculation in step S8 must meet the following requirements: the number of contour points sampled by a single target ball at a single station is ≥12 and they are uniformly distributed in the longitude direction.

[0032] As a preferred technical solution, h in step S4 ij0 vij0 The horizontal observation value h of the k-th point on the j-th target ball at the i-th station is determined as follows: ijk and the observed zenith distance v ijk Take the arithmetic mean; or measure directly by aiming at the center of the target ball's reflector.

[0033] A target sphere roundness error measurement system based on the theodolite angle measurement principle, characterized in that it includes:

[0034] At least three electronic theodolites were deployed at different survey stations;

[0035] A directional lighting module is used to project a light strip along the edge of the target sphere's outline.

[0036] The data processing unit is used to perform the following tasks:

[0037] 1) Construct and linearize the radius angle measurement model;

[0038] 2) Solve for the radius and angle parameters using least squares;

[0039] 3) Convert the radius value and calculate the range-type roundness error.

[0040] As a preferred technical solution, the data processing terminal can be configured to execute the following instructions:

[0041] Refuse to accept the sphere center coordinate data generated by spatial three-dimensional intersection;

[0042] As a preferred technical solution, the data processing unit can exclude the sphere center coordinate data obtained from three-dimensional spatial intersection when calculating the roundness error.

[0043] Compared with existing technologies, this solution has the following advantages:

[0044] (1) Based on the spherical triangle, a radius angle measurement model is constructed, and the contour aiming data is converted into radius values. This fills the technical gap that the theodolite cannot measure the roundness of the target sphere. For the first time, the full parameter calibration of sphere center coordinates, spatial baseline length and roundness error is completed simultaneously on a single device, which greatly improves calibration efficiency and avoids the safety risks of step-by-step operation.

[0045] (2) The equatorial surface of the directional illumination target sphere forms the boundary between light and dark. The theodolite optical aiming replaces contact scanning, and the surveyors do not need to enter high-risk areas, thus reducing the risk of accidents.

[0046] (3) Eliminate contact deformation error, and achieve a roundness measurement accuracy of ±0.03mm;

[0047] (4) Reuse the estimated value of the observation of the sphere's center direction Constructing a spatial three-dimensional intersection model enables data reuse, improves equipment utilization, and effectively enhances the accuracy of sphere center coordinates and spatial baseline length in spatial three-dimensional intersection measurements. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 A schematic diagram of the illumination method for the contour direction of the target ball under test according to the present invention;

[0050] Figure 2 This is a schematic diagram illustrating the lighting effect of the target ball under test in this invention.

[0051] Figure 3 This is a schematic diagram of the measurement model based on the cosine constant of a spherical triangle according to the present invention;

[0052] Figure 4 This invention calculates the radius angle r based on a sine relationship. ijk The corresponding radius R ijk Schematic diagram;

[0053] Figure 5 Radius residual distribution diagram of the target sphere roundness error measurement method of the present invention;

[0054] Figure 6 Radius angle residual distribution diagram of the target sphere roundness error measurement method of the present invention;

[0055] Figure 7 The flowchart of the target sphere roundness error measurement method based on the theodolite angle measurement principle of the present invention is shown in the figure. Detailed Implementation

[0056] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0057] Reference Figure 7 This invention proposes a method for measuring the roundness error of a target sphere based on the angle measurement principle of a theodolite, comprising the following steps:

[0058] S1: Design the theodolite stations at the survey site to ensure there are m stations, where m≥3. Deploy the theodolites at the stations, either by deploying m theodolites simultaneously or by deploying the same theodolite sequentially at m stations.

[0059] S2: Illuminate only the outline of the target sphere to ensure that the outline of the target sphere is clearly visible in the theodolite's field of view (see...). Figure 1 and Figure 2 );

[0060] S3: Using a theodolite, aim at the outline of the target ball, and sequentially measure and record the horizontal observation value h at the k-th point of the j-th target ball at the i-th station. ijk Observed value of zenith distance v ijk Simultaneously, the distance L between the center of the target ball and the center of the measuring station can be obtained using prism-free measurement. ij ;

[0061] S4: As Figure 3 As shown, based on the cosine theorem of spherical triangles, and using the contour observation data of the j-th target sphere at the i-th station, the radius angle r is constructed. ij Compared with the horizontal observation value h ijk Observed value of zenith distance v ijk Measurement model:

[0062]

[0063] Among them, h ij0 It is the unknown horizontal observation value from the i-th station to the j-th target ball, v ij0 It is the unknown observed value of the zenith distance from the i-th station to the j-th target sphere.

[0064] S5: Expand the measurement model and let , , The error measurement model can be obtained as follows:

[0065]

[0066] S6: Convert the error measurement model into matrix form:

[0067]

[0068] in,

[0069] , , .

[0070] S7: Perform least squares calculation:

[0071]

[0072] Further, we can obtain

[0073]

[0074]

[0075]

[0076] S8: Based on the measurement model in S4, substitute the parameter estimates to calculate the radius angle r corresponding to the k-th aiming of the j-th target ball at the i-th station. ijk :

[0077]

[0078] S9: such as Figure 4 As shown, the radius angle r is calculated based on the sine relation. ijk The corresponding radius R ijk :

[0079]

[0080] h can also be ij0 v ij0 Substituting this into the three-dimensional spatial intersection, the distance Sij from the station to the center of the target sphere is calculated, thus obtaining R. ijk :

[0081]

[0082] S10: Take the R value of the j-th target ball at the i-th measuring station. ijk The range of values ​​is taken as the roundness error of i stations, and finally twice the maximum roundness error of m stations is taken as the roundness error calibration result of the target ball.

[0083] To verify the beneficial effects of this scheme, two parameters, "radius angle residual" and "radius residual," were selected for testing:

[0084] The radius angle residual reflects the fitting quality of the measurement model, and the normal distribution can prove the rationality of the least squares solution; the radius residual directly reflects the distribution characteristics of the roundness error, and its uniformity indicates the sufficiency of the sampling of measurement points; by comparing the two, the effect of isolating the ranging error can be verified.

[0085] If the residuals follow a normal distribution, it indicates a good match between the spherical triangle model and the measured data, and that the least squares solution is effective. If the residuals approach 0, it confirms that the directional observations have high aiming accuracy and are free from systematic error interference. Figure 5 It can be concluded that the model is reasonably constructed and the algorithm can stably solve the radius angle parameters.

[0086] A uniform distribution of the radius residuals indicates that the contour points have been sampled sufficiently (e.g., ≥12 points in the longitude direction) and there are no measurement blind spots.

[0087] Amplitude range: directly reflects the range of roundness error. If it is ≤0.05mm, it meets the requirements for high-precision calibration.

[0088] In summary, based on Figure 5 Radius residual distribution diagram of the target sphere roundness error measurement method and Figure 6 The radius angle residual distribution diagram of the target sphere roundness error measurement method can verify the target sphere roundness error measurement method based on the theodolite angle measurement principle proposed in this scheme. It can make up for the shortcomings of spatial three-dimensional intersection measurement that only focuses on the sphere center coordinates and spatial baseline length standard value calibration. Based on the theodolite, it realizes large-scale, full-item, low-risk non-contact measurement of three-dimensional baseline standard device.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the roundness error of a target sphere based on the theodolite angle measurement principle, characterized in that, Includes the following steps: S1: Set up at least 3 survey stations at the survey site and set up a theodolite at each survey station; S2: Provide directional illumination to the outline of the target ball being measured, so that the outline is clearly imaged in the theodolite's field of view; S3: Using a theodolite, aim at the outline of the target sphere and record the horizontal observation value h of the k-th point on the j-th target sphere at the i-th station. ijk and the observed zenith distance v ijk ; S4: Based on the cosine theorem for spherical triangles, construct the radius angle. Measurement model: Among them, h ij0 It is the unknown horizontal observation value from the i-th station to the center of the j-th target ball, v ij0 It is the unknown observed value of the zenith distance from the i-th station to the center of the j-th target sphere; S5: Linearize the measurement model into an error equation; S6: Convert the error measurement model into matrix form, and solve for the radius angle r corresponding to the kth aiming of the j-th target ball at the i-th station using the least squares method. ijk ; S7: Based on the sine relation Calculate the radius angle corresponding to the k-th aiming of the j-th target ball at the i-th station. Corresponding contour point radius value It can also be calculated using the following formula. : ； S8: Take all R balls of the same target ball ijk The range of the values ​​is taken as the roundness error of a single station, and finally, twice the maximum roundness error of the target ball is taken as the calibration result of the roundness error of the target ball.

2. The target sphere roundness error measurement method based on the theodolite angle measurement principle as described in claim 1, characterized in that, In step S2, directional illumination uses a side light source to illuminate the equatorial surface of the target sphere, creating a high-contrast dark field image at the contour edge.

3. The target sphere roundness error measurement method based on the theodolite angle measurement principle as described in claim 1, wherein step S3 further includes obtaining the distance value L from the station center to the target sphere center using the prism-free distance measurement function of the theodolite. ij Used to calculate the radius value of the contour points in step S7. .

4. The target sphere roundness error measurement method based on the theodolite angle measurement principle as described in claim 1, characterized in that, The linearization process in step S5 is as follows: 1) Define parameters: Let , , , 2) Construct the error equation: 3) Convert the error measurement model into matrix form: in, , , .

5. The target sphere roundness error measurement method based on the theodolite angle measurement principle as described in claim 1, characterized in that, Distance S in step S7 ij It can be obtained through spatial three-dimensional intersection calculation, and the intersection process does not participate in the roundness error calculation.

6. The target sphere roundness error measurement method based on the theodolite angle measurement principle as described in claim 1, characterized in that, The range calculation in step S8 must meet the following conditions: the number of contour points sampled by a single target ball at a single station is ≥12 and they are uniformly distributed along the longitude direction.

7. The target sphere roundness error measurement method based on the theodolite angle measurement principle as described in claim 1, characterized in that, h in step S4 ij0 v ij0 These are unknown parameters, and their estimated values ​​can be obtained through the error model and least squares estimation in steps S5 and S6: 。 8. A target sphere roundness error measurement system based on the theodolite angle measurement principle for implementing any one of the methods described in any one of claims 1 to 7, characterized in that, include: At least three electronic theodolites were deployed at different survey stations; A directional lighting module is used to project a light strip along the edge of the target sphere's outline. The data processing unit is used to perform the following tasks: 1) Construct and linearize the radius angle measurement model; 2) Solve for the radius and angle parameters using least squares; 3) Convert the radius value and calculate the range-type roundness error.

9. The target sphere roundness error measurement system as described in claim 8, characterized in that, The data processing terminal can be configured to execute the following instructions: Refuse to accept the sphere center coordinate data generated by spatial three-dimensional intersection.

10. The target sphere roundness error measurement system as described in claim 8, characterized in that, When calculating the roundness error, the data processing unit can exclude the sphere center coordinate data obtained from three-dimensional spatial intersection.

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