Target ball roundness error measurement method and system based on theodolite angle measurement principle

Abstract

The invention provides a target ball roundness error measurement method and system based on a theodolite angle measurement principle, and the method comprises the steps: setting a theodolite, carrying out the directional illumination, aiming at the contour point of a target ball through the theodolite, constructing a measurement model of a radius angle, carrying out the linearization of the model, and carrying out the calculation to obtain the distance from a measurement station to the center of the target ball and the roundness error calibration result of the target ball. Aiming data of the theodolite are converted into radius values based on a spherical triangle model, non-contact roundness error measurement of the theodolite is realized for the first time, and calibration of sphere center coordinates, baseline length and roundness errors can be synchronously completed in combination with spatial three-dimensional intersection measurement; and the integrated efficient calibration of the three-dimensional baseline standard device 'sphere center coordinate-space baseline length-roundness error' can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of large-scale engineering measurement, in particular to a target sphere roundness error measurement method and system based on theodolite angle measurement principle. Background Art

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

[0003] The current mainstream calibration methods have significant limitations: 1) Traditional laboratory contact measurement requires disassembly of the target sphere and contact scanning with the help of a coordinate measuring machine or a length measuring machine. This method destroys the original installation state, resulting in the interruption of the traceability chain between the sphere center coordinates and the baseline length, and in-situ calibration cannot be achieved; 2) Although the method of using a laser tracker with a spherical prism to contact the target sphere surface 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 come into close contact with the target sphere, which can easily cause safety accidents such as falling and collision in large-scale three-dimensional baseline standard devices. 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, and personnel still need to be close to the target sphere to operate. The safety risks are comparable to those of a laser tracker. In addition, this method can only measure roundness errors and is completely unable to synchronously obtain the sphere center coordinates and baseline length, resulting in equipment utilization rates below 50%, which greatly increases the overall cost.

[0004] Currently, calibration sites commonly use theodolite spatial 3D intersection measurement technology to calibrate the sphere center coordinates and baseline length. This technology offers the advantages of a long measurement range, the safety benefits of requiring no close proximity, and the cost of equipment at only 10% of that of a laser tracker. However, existing theodolite technology suffers from a significant drawback: it is completely incapable of measuring the roundness error of the target sphere. This forces the 3D baseline device to be calibrated in a separate process: first using theodolite to measure the sphere center coordinates and baseline length, and then using other methods (such as structured light or secondary disassembly) to separately measure the roundness error. This fragmented process reduces calibration efficiency by over 60%, and the repetitive operations further exacerbate safety risks. Especially in large-scale scenes, the safety and cost advantages of the theodolite conflict sharply with its functional limitations.

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

[0006] The present invention proposes a target sphere roundness error measurement method and system based on the theodolite angle measurement principle. This solves the problem that existing theodolite spatial three-dimensional intersection measurement systems lack the non-contact measurement capability of target sphere roundness error in large-scale calibration scenarios, and are unable to achieve integrated and efficient calibration of "sphere center coordinates + baseline length + roundness error". The technical solution of the present invention is achieved as follows: A method for measuring the roundness error of a target sphere based on theodolite angle measurement principle, characterized by comprising the following steps: S1: Set up at least three measuring stations at the measurement site and install theodolites at each measuring station; S2: Directional illumination is performed on the outline of the target ball to make the outline clearly imaged in the field of view of the theodolite; S3: Use the theodolite to aim at the contour point of the target ball and record the horizontal direction observation value h of the kth point of the jth target ball at the i-th measuring station ijk and the observed value of zenith distance v ijk ; S4: Based on the cosine theorem of spherical triangles, a measurement model for the radius angle is constructed:

[0007] Among them, h ij0 is the unknown horizontal observation value from the i-th station to the j-th target, v ij0 is the unknown observed value of the zenith distance from the i-th station to the j-th target sphere; S5: Linearize the measurement model into an error equation; S6: Convert the error measurement model into a matrix form and solve the radius angle by the least square method.

[0008] The radius angle r corresponding to the k-th sighting of the j-th target ball at the i-th measuring station ijk ;

[0009] S7: Based on the sine relationship Calculate the radius angle corresponding to the kth sighting of the jth target ball at the i-th measuring station Corresponding contour point radius value , can also be calculated by the following formula :: ; S8: Take all R of the same target ball ijk The range of the roundness error is taken as the single-station roundness error, and finally twice the maximum value of the multi-station roundness error is taken as the target ball roundness error calibration result.

[0010] As a preferred technical solution, the directional illumination in step S2 uses a side light source to illuminate the equatorial plane of the target sphere, so that the contour edge forms a high-contrast dark field image.

[0011] 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 measuring station to the center of the target sphere. ij , used to calculate the contour point radius value in step S7 .

[0012] As a preferred technical solution, the linearization process of step S5 is specifically as follows: 1) Define parameters: Let , ,

[0013] 2) Construct error equation:

[0014] 3) Convert the error measurement model into matrix form:

[0015] in, , , .

[0016] As a preferred technical solution, the distance S in step S7 ij It is obtained through spatial three-dimensional intersection calculation, and the intersection process does not participate in the roundness error calculation.

[0017] As a preferred technical solution, the range calculation in step S8 must satisfy the following requirements: the number of contour point samples of a single target sphere at a single measuring station is ≥12 and is evenly distributed in the longitude direction.

[0018] As a preferred technical solution, h in step S4 ij0 、v ij0 Determine it in the following way: The horizontal direction observation value h of the kth point of the jth target ball at the i-th measuring station ijk and the observed value of zenith distance v ijk Take the arithmetic mean; or measure directly by aiming at the center of the target sphere reflector.

[0019] The target ball roundness error measurement system based on theodolite angle measurement principle is characterized by comprising: At least three electronic theodolites, deployed at different survey stations; Directional lighting module, used to project a light band around the edge of the target ball outline; Data processing unit, used to perform the following tasks: 1) Construct a radius angle measurement model and linearize it; 2) Least squares solution for radius angle parameters; 3) Convert the radius value and calculate the extreme roundness error.

[0020] As a preferred technical solution, the data processing terminal can be configured to execute the following instructions: Refuse to accept the spherical center coordinate data generated by three-dimensional spatial intersection; As a preferred technical solution, the data processing unit may exclude the spherical center coordinate data obtained by three-dimensional spatial intersection when calculating the roundness error.

[0021] Compared with the existing technology, this solution has the following beneficial effects: (1) A radius angle measurement model is constructed based on spherical triangles, and the contour aiming data is converted into radius values, filling the technical gap that the theodolite cannot measure the roundness of the target sphere. For the first time, the full parameter calibration of the sphere center coordinates + spatial baseline length + roundness error is completed simultaneously on a single device, which greatly improves the calibration efficiency and avoids the safety risks of step-by-step operation. (2) Directional illumination of the target sphere’s equatorial plane forms a light-dark boundary contour, and the optical aiming of the theodolite replaces contact scanning. Surveyors do not need to enter high-risk areas, thus reducing the risk of accidents. (3) Eliminate contact deformation error, and the roundness measurement accuracy reaches ±0.03mm; (4) Reusing the estimated value of the sphere center direction observation Constructing a spatial three-dimensional intersection model enables data reuse, improves equipment utilization, and can effectively improve the accuracy of the sphere center coordinates and spatial baseline length in spatial three-dimensional intersection measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0023] Figure 1 A schematic diagram of a method for illuminating the contour direction of a target sphere under test according to the present invention; Figure 2 Schematic diagram of the lighting effect of the target ball under test of the present invention; Figure 3 Schematic diagram of the measurement model based on the cosine of a spherical triangle according to the present invention; Figure 4 The present invention calculates the radius angle r according to the sinusoidal relationship ijk The corresponding radius R ijk Schematic diagram; Figure 5 Radius residual distribution diagram of the target ball roundness error measurement method of the present invention; Figure 6 Radius angle residual distribution diagram of the target ball roundness error measurement method of the present invention; Figure 7 A flow chart of a method for measuring the roundness error of a target sphere based on the theodolite angle measurement principle of the present invention. DETAILED DESCRIPTION

[0024] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the embodiments of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0025] Reference Figure 7 The present invention proposes a method for measuring the roundness error of a target sphere based on the principle of theodolite angle measurement, which includes the following steps: S1: Design theodolite stations at the survey site to ensure there are m stations, where m ≥ 3. Place theodolites at the stations. You can place m theodolites at the same time or place the same theodolite at m stations in sequence. S2: Only illuminate the outline of the target sphere to be measured, ensuring that the outline of the target sphere is clearly visible in the field of view of the theodolite (see Figure 1 and Figure 2 ); S3: Use the theodolite to aim at the outline of the target ball to be measured, and measure and record the horizontal direction observation value h of the kth point of the jth target ball at the i-th measuring station in sequence. ijk The observed value of the zenith distance v ijk At the same time, the distance value L between the center of the target sphere and the center of the measuring station can be obtained by prism-free measurement ij ; S4: As Figure 3 As shown, according to the cosine theorem of spherical triangles, the radius angle r is constructed based on the profile observation data of the jth target ball at the i-th measuring station. ij With the horizontal observation value h ijk The observed value of the zenith distance v ijk The measurement model:

[0026] Among them, h ij0 is the unknown horizontal observation value from the i-th station to the j-th target, v ij0 is the unknown observed value of the zenith distance from the i-th station to the j-th target sphere.

[0027] S5: Expand the measurement model and make , , , the error measurement model can be obtained:

[0028] S6: Convert the error measurement model into matrix form:

[0029] in, , , .

[0030] S7: Perform least squares calculation:

[0031] Further available

[0032]

[0033]

[0034] S8: According to the S4 measurement model, substitute the parameter estimation value and calculate the radius angle r corresponding to the k-th sighting of the j-th target ball at the i-th measuring station ijk :

[0035] S9: As Figure 4 As shown, according to the sine relationship, the radius angle r is calculated ijk The corresponding radius R ijk :

[0036] You can also use h ij0 、v ij0 Substitute it into the three-dimensional space intersection and calculate the distance Sij from the measuring station to the center of the target sphere, thus obtaining R ijk :

[0037] S10: Get the R of the jth target ball at the i-th measuring station ijkThe range of the values ​​is taken as the roundness error of the i measuring stations, and finally twice the maximum value of the roundness error of the m measuring stations is taken as the roundness error calibration result of the target ball.

[0038] In order to verify the beneficial effect of this solution, two parameters, "radius angle residual" and "radius residual", were selected for testing: 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 adequacy of the measurement point sampling; by comparing the two, the effect of isolating the ranging error can be verified.

[0039] If it is normally distributed, it indicates that the spherical triangle model matches the measured data well and the least squares solution is effective. If the residual is close to 0, it proves that the direction observation value has high aiming accuracy and there is no systematic error interference. Figure 5 It can be concluded that the model is constructed reasonably and the algorithm can stably solve the radius angle parameters.

[0040] If the radius residual distribution is evenly distributed, it means that the contour points are fully sampled (e.g., ≥12 points in the longitude direction) and there are no measurement blind spots; Amplitude range: directly reflects the extreme roundness error. If it is ≤0.05mm, it meets the high-precision calibration requirements.

[0041] In summary, according to Figure 5 Radius residual distribution diagram of target ball 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, which can make up for the shortcomings of spatial three-dimensional intersection measurement that only focuses on the coordinates of the sphere center and the calibration of the standard value of the spatial baseline length. Based on the theodolite, large-scale, full-project, low-risk non-contact measurement of the three-dimensional baseline standard device is realized.

[0042] 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 in the scope of protection of the present invention.

Claims

1. A target ball roundness error measurement method based on theodolite angle measurement principle, characterized in that: The following steps are involved: S1: Set up at least three measuring stations at the measurement site and install theodolites at each measuring station; S2: Directional illumination is performed on the outline of the target ball to make the outline clearly imaged in the field of view of the theodolite; S3: Use the theodolite to aim at the contour point of the target ball and record the horizontal direction observation value h of the kth point of the jth target ball at the i-th measuring station ijk and the observed value of zenith distance v ijk ; S4: Constructing the radius angle based on the cosine theorem of spherical triangles The measurement model: Among them, h ij0 is the unknown horizontal observation value from the i-th station to the j-th target center, v ij0 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 a matrix form and solve the radius angle r corresponding to the k-th sighting of the j-th target ball at the i-th measuring station by the least square method. ijk ; S7: Based on the sine relationship , calculate the radius angle corresponding to the kth sighting of the jth target ball at the i-th station Corresponding contour point radius value , can also be calculated by the following formula : ； S8: Take all R of the same target ball ijk The range of the roundness error is taken as the single-station roundness error, and finally twice the maximum value of the multi-station roundness error is taken as the target ball roundness error calibration result.

2. The target sphere roundness error measurement method based on theodolite angle measurement principle according to claim 1, characterized in that: The directional illumination in step S2 uses a side light source to illuminate the equatorial plane of the target sphere, so that the contour edge forms a high-contrast dark field image.

3. The method for measuring the roundness error of a target sphere based on the theodolite angle measurement principle according to claim 1, wherein step S3 further comprises obtaining a distance value L from the center of the measuring station to the center of the target sphere using the prism-free distance measurement function of the theodolite. ij , used to calculate the contour point radius value in step S7 .

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

5. The target sphere roundness error measurement method based on theodolite angle measurement principle according to claim 1, characterized in that: The 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 theodolite angle measurement principle according to claim 1, characterized in that: The range calculation in step S8 must meet the following requirements: the number of contour point samples of a single target sphere at a single measuring station is ≥ 12 and is evenly distributed in the longitude direction.

7. The target sphere roundness error measurement method based on theodolite angle measurement principle according to claim 1, characterized in that: h in step S4 ij0 、v ij0 is an unknown parameter, and the parameter estimate 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 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, deployed at different survey stations; Directional lighting module, used to project a light band around the edge of the target ball outline; Data processing unit, used to perform the following tasks: 1) Construct a radius angle measurement model and linearize it; 2) Least squares solution for radius angle parameters; 3) Convert the radius value and calculate the extreme roundness error.

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

10. The target ball roundness error measurement system according to claim 8, characterized in that: When calculating the roundness error, the data processing unit may exclude the spherical center coordinate data obtained by the three-dimensional spatial intersection.

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