Aviation tubes have been widely used in various systems of aerospace equipment owing to their excellent physical and chemical properties. It is important to ensure the manufacturing quality of aviation tubes for the safety of aircraft. Aviation tubes are manufactured by bending straight tubes. Under the action of the bending moment, the inner side of the tube is wrinkled and deformed owing to compressive instability. Although numerous researchers have investigated various manufacturing methods in the past few decades, wrinkle deformation is still unavoidable. The wrinkle degree of the tube is a key indicator of tube deformation, with the key geometric parameter being the wrinkle depth. Conventional manual inspection methods cannot guarantee the measurement efficiency and reliability of measurement results. Using a digital 3D measurement method can effectively avoid these shortcomings. Such methods quickly capture the surface shape data of the target object and have been widely used in welding seam detection and contour deformation detection.

The wrinkle degree can be measured using the scanning point cloud of the bent tube. First, combined with the shape characteristics of the bent tube, a tangent-arc-tangent model method is proposed to reconstruct the spine line of the tube and determine its shape parameters. It assumes that the spine line of the bent part is an arc, and the spine lines of the two straight tubes on both sides are the tangent lines of the end points on both sides of the arc. Thus, it ensures G1 smoothness between the straight and bent spine lines. By using the nonlinear least square method to optimize the distance between each spine line point and the corresponding spine line, the parameters of the spine line model are calculated. Subsequently, the contour lines are managed using the pole angle of each surface point under the respective spine line cross-section. Using this method, the contour line of the inner side of the bend can be quickly extracted, and distortion of the contour line in the wrinkle area can be avoided. Finally, a flattening method of the contour line is proposed. The wrinkle identification is not affected by the bent shape of the tube because of the flattened contour, so the peak and valley of each wrinkle can be correctly identified. The maximum wrinkle depth on the tube surface is then used to calculate the wrinkle degree.

Spine line reconstruction validation is performed by using two typical bent tubes with radii of 7.5 mm and 26 mm. For all five scans, the spine lines are successfully reconstructed and the contour lines are successfully extracted (Fig. 10). The model parameters before optimization are different from the actual parameters (Figs.11-12). There is a systematic deviation in the error of the spine line points. This is because there may be large deviations in the direction of the straight spine line. After optimization, the average error of the bending radius is -0.073-0.042 mm, and the average error of the bending angle is -0.114-0.195°. The average error of the spine line point is close to zero, and the root mean square error is reduced from 0.297-15.439 mm to 0.171-1.129 mm. The optimized spine line shape parameters reflect the real shape of the spine line well. The spine line error remains stable. The maximum depth of wrinkles can be accurately identified on the bent tube with obvious wrinkles (Fig. 14). Further, the accuracy of the wrinkle analysis is verified using the standard part (Fig. 15). The depth errors of different wrinkles are stable at 0.007 mm, and the wrinkle degree errors are stable at 0.011%. Therefore, the method proposed in this study can stably and reliably analyze wrinkle deformation of the bent tube.

To measure the wrinkle degree of bent tubes quickly and efficiently, a numerical analysis method based on the scanning point cloud of bent tubes is proposed. The effectiveness of the proposed method is verified using several typical tubes and a standard part. The experimental results show that the method proposed in this study can effectively identify the shape parameters of the bent tube and extract the contour lines. The reconstructed tube spine line fits well with the spine line points of each tube part. The contour flattening method proposed in this study can identify the wrinkle without any interference from the bending shape and accurately extract the wrinkle with the largest depth. Additionally, the proposed method can stably identify wrinkles with different depths on the standard part, with the wrinkle degree error stabilizing at 0.011%. Therefore, the proposed method can be used to accurately measure the wrinkle degree of bent tubes.