Guiping Huang, Wenfang Zhu, Weifeng Wang, Xiaoliang Xie and Hewei Wang
(1. North China University of Water Resources and Electric Power, Zhengzhou 450046, China;2. China Gezhouba Group No. 3 Engineering Co., Ltd., Xi’an 710076, China;3. Yellow River Conservancy Technical Institute, Zhengzhou 475001, China;4. Zhonghang Industrial Shaanxi Aircraft Industry Co., Ltd, Hanzhong 723000, China;5. Zhengzhou Chenway Technology Co., Ltd, Zhengzhou 450000, China)
Abstract: According to the operational conditions of an aviation module reticule, a measurement mode is proposed, which is based on an industrial photogrammetry system, with matching by a measuring pen. Meanwhile, the factors affecting the accuracy of the measurement have been analyzed and verified by examples. The analysis is described as follows: ① Along the optical axis of the camera, the error is larger than the ones in other directions using the “single camera + measuring pen” mode; ② By avoiding the error along the optical axis of the camera, the accuracy of the“single camera + measuring pen” mode is better than 0.1 mm when the measuring pen is moving parallel to the optical axis.
Key words: module reticule;single camera+measuring pen;spatial resection of single images;repeatability;accuracy
Industrial photogrammetry involves taking photos of an object (to which a measurement target is passed) using one or more high-resolution digital cameras, and obtaining a plurality of two-dimensional digital images of the object, and obtaining the target point through camera orientation and computer image processing of its spatial three-dimensional coordinates. According to the number of cameras used in the measurement process, industrial photogrammetry systems are generally categorized into single camera industrial photogrammetry systems and multi-camera industrial photogrammetry systems[1-2]. China introduced an industrial photogrammetry system for the first time in 2005. With research and development, industrial photogrammetry has been applied in China’s aviation, aerospace, shipbuilding, and other industry fields because of its characteristics such as high precision, high efficiency,and ultra-portability[3-4].
At present, the new digital technology has been widely used in the design, manufacture and testing of mould tires. The detection methods for complex curved surfaces and the quality of the profile have seen qualitative leaps in accuracy[5-6].Among them, the aviation model tyre surface is complex, and the stencil trend is varied. There is little domestic research on how to complete the precision measurement of the mould tire scribe line, which remains in its experimental stage[7-8].Therefore, to meet the needs of domestic aviation unit mould line measurements (Fig.1), a new “single camera + measuring pen”[9-11]is proposed based on the MPS/S single camera industrial photogrammetry system (Zhengzhou Chenway Technology Co., Ltd). The “single camera +measuring pen ” mould tyre line measurement principle is shown in Fig.2. Through experiments, it is found that the mode is flexible, easy to operate, and the measurement accuracy is better than 0.1 mm, which made the method suitable for die-cutting measurement.
Fig.1 An aviation mould tyre
Fig.2 “Single camera + measuring pen” mould tyre line measurement principle
According to the conventional photogrammetric method, if only one camera is used and three-dimensional coordinates of a point are to be acquired, at least two different positions are required[12]. In the present paper, the “single camera + measuring pen” mode is used to capture a single photo to obtain three-dimensional coordinates of the measurement point, and verify that the measurement accuracy of the “single camera +measuring pen” mode is consistent with mould tyre scribe line tolerances.
The relocation of the single image space is based on a photograph and the mathematical relationship between a certain number of control points and the corresponding image points, and the process of solving the inner and outer orientation elements of the image[1,13](the inner orientation elements x0, y0, and f are pre-calibrated and can be considered as known values). For singlecamera measurement, the target points on the measuring pen are used as auxiliary control points, and the external orientation elements (Xs,Ys, Zs, ω, ψ, and κ) in the measuring pen coordinate system are obtained by a collinear equation
The three target points require six collinear equations to obtain the six external orientation elements. If there are more than three target points on the measuring pen, it can be solved by least squares adjustment
where
After the single image space resection, the outer orientation element in the measuring pen coordinate system (Fig.3) is obtained, thereby determining the relationship between the measuring pen coordinate system and the photogrammetric coordinate system.
Fig.3 Measuring pen
Let the coordinates of the pen tip of the measuring pen in the measuring pen coordinate system be (X′, Y′, Z′), and the coordinates in the photogrammetric coordinate system be (X,Y, Z ), then
Coordinate transformation can be used to obtain the coordinates of the measuring pen tip(the point to be touched) in the control field coordinate system.
Analysis of measurement errors and accuracy estimation of measurement results is an important aspect of evaluating the performance of a measurement system. Here, the error is analysed by measuring the direction of motion of the pen parallel, and perpendicular, to the optical axis.
From the law of error propagation:
Fig.4 Schematic diagram showing line of sight calculation
Since α is small, the value of csc2α tends to infinity, so even a small angular error will cause a large error in the y-axis direction, therefore in the single-camera mode measurement, the measured unknown point is parallel to the optical axis. The coordinate accuracy of the direction(the direction of the collimation axis) is low.
There are many indicators for measurement accuracy, including accuracy estimates, repeatability measurement accuracy, and external accuracy. Here, the “single camera + measuring pen”accuracy test starts from the two perspectives of repeatability measurement accuracy and length measurement error.
1.4.1 Repeatability measurement accuracy
Repeatability measurement accuracy refers to the consistency between measurement results when multiple observations are made of the same measurement object under the same observation condition, this is also called measurement repeatability and is used to detect the stability of a measurement system[14]. Let the measured values of each group be Xi, where i =1, 2, ···, n; and n is the number of measurement groups. Then
The measured values for each group in this paper are the gauge length and the width between the score lines. Using the experimental data, Eq. (6) is used to obtain the value of the measurement repeatability of the “single camera +measuring pen” system. The smaller the value,the better the stability of the measurement system.
1.4.2 Length measurement error
The length measurement error refers to the difference between the measured result and the measured true value, and is the most objective and true test of system measurement accuracy.In the ith measurement, the difference between the measured length and the standard length is ΔLi, where i=1, 2, ···, n, where n is the number of measurements. Recording the root mean square error of the length measurement as m△L,then
where Liis the measured value of the standard length at the ith measurement; L0represents the nominal value of the standard length.
Since the standard length has a calibration error, set it to mL0. From Eq. (7) and the error synthesis principle
The standard length calibration error mL0is much smaller than the measurement error of the measurement system, therefore, m△Lis approximately equal to the measurement error mLin the“single camera + measuring pen” mode. The smaller the error m△Lin the measurement, the higher the accuracy of the length measurement of the measuring system[15].
According to the measurement principle and accuracy evaluation index of the “single camera +measuring pen” mode, combined with the actual application requirements, the present research takes the single point repeatability and the measurement of the distance between the measuring block and the 20 mm scribe line in different measurement directions of the camera. The measurement accuracy of the “single camera + measuring pen” mode is explored and tested.
The control field of the test scheme selects a stable and interference-free ground. The control field measures 1.5 m × 1.5 m and 25 code points and several single points are distributed in Fig.5.The “single camera + measuring pen” test is performed on this control field.
Fig.5 Control field layout
To study the system performance of the“single camera + measuring pen ” mode, the single point repeatability measurement characteristics of this mode are studied. The measuring pen is fixed at one position of the control field,and the camera is fixed on the tripod to continuously measure the measuring pen 10 times, and three replicate measurements are conducted. The single point repeatability measurement data are shown in Tab. 1, where the axial distance is the difference between the maximum and minimum values of the plurality of sets of measurement data in the same axial direction, and the distance peak-to-peak value refers to the difference between the maximum and minimum values of the spatial distance of all points.
Tab. 1 Single point repeated measurementsmm
① The “single camera + measuring pen”mode has good repeatability of the axial distance in the X, Y, and Z axis directions; The “single camera + measuring pen” mode has a smaller axial distance in the X- and Z-axis directions(better than 0.03 mm), and the axial distance in the Y-direction is relatively large, with a maximum value exceeding 0.2 mm;
② In the actual measurement environment,the Y-axis direction is the Y-direction relative to the measured point in the quasi-axial direction,so the axial distance of the “single camera +measuring pen” mode is mainly concentrated in the direction of the collimating axis (optical axis), consistent with error analysis results (Section 1.3).
The 20 mm engraved line(Fig.6) refers to a scribed line with a distance of 20 mm between adjacent two engraved lines. The 20 mm engraved line is the same as the gauge block, that is, its length is the standard of the measurement instrument. The standard length of the score line used herein is 20 ± 0.002 mm.
Fig.6 20 mm engraved line
At a distance of 1.0 m to 1.2 m from the 20 mm scale line(Fig.7), A: the optical axis is perpendicular to the graticule direction and B:the optical axis is parallel to the graticule direction, and 40 photos are taken, wherein each of the scribe lines is uniform (using 10 points and taking a picture over a total of four lines). When shooting, the measuring pen is positioned perpendicular to the plane in which the score line is located. The experimental data of 20 mm scribe line measurement are shown in Tab. 2.
After calculation by experimental data: ①When the optical axis is taken in parallel with the graticule direction, the average value of the“single camera + measuring pen” measurement is 20.019 mm, the variance is 0.003; the length measurement error is at most 0.024 mm.
Fig.7 20 mm engraved line test design
Tab. 2 Experimental data of 20 mm scribe line measurement mm
② When the optical axis is taken perpendicular to the graticule direction, the average value of the “single camera + measuring pen” is 20.070 mm, the variance is 0.063; the length measurement error is at most 0.151 mm.
③ The photographic direction has an effect on the 20 mm scribe line experiment. The accuracy of the optical axis perpendicular to the scribe line is low, and the accuracy of the optical axis parallel to the scribe line is high.
④ In summary, the 20 mm scribe line measurement test further shows that the error is mainly concentrated in the direction of the sight axis. The accuracy of the optical axis parallel to the photographic direction of the graticule is optimal, so by circumventing the error of the optical axis direction of the “single camera + measuring pen” mode, the measurement accuracy thereof can reach 0.1 mm (as evinced by Eq. (5) in terms related to α).
According to the requirements of a certain model of the airline’s die-cutting line and on-site conditions, the “single camera + measuring pen”mode is used to take fast, accurate on-site measurements of a 2# moulded tyre workpiece, and the actual measured value is compared with the model to obtain point deviation data. The data(Tab. 3) are used to control the quality of mould tyres based on comparative data. It can be seen from the data that the RMS value of the point deviation is controlled within ± 0.1 mm, which verifies the feasibility of the “single camera +measuring pen” mode and the correctness of the conclusions herein. In addition, combined with the on-site implementation conditions, the “single camera + measuring pen ” mode is useful for measuring with two-dimensional high-precision;and it proves that this mode has the advantages of flexibility (in terms of measurement station),rapidity, and absence of spatial limitations.
Tab. 3 Comparison of point deviation datamm
According to the requirements of practical engineering applications and the principle of accuracy evaluation, the accuracy measurement method of “single camera + measuring pen ”mode, with measurement repeatability and length measurement accuracy as the evaluation indexes,is proposed. It is found that the “single camera +measuring pen” mode resulted into a large error along the optical axis of the camera, while the error in other directions is small; By avoiding the error in the optical axis direction of the “single camera + measuring pen” mode, the measurement accuracy thereof is better than 0.1 mm,which is of practical value in promoting the wider application of the method.
Journal of Beijing Institute of Technology2020年3期