Parametric Modeling And Error Analysis Of Bent Tube Based On Point Cloud Data

Bent tubes are a kind of parts that are widely used in industry,and the inspection of the bent tube is a necessary step in the process of manufacturing.In the past,special gauges were designed specifically for different bend tubes,resulting in low efficiency.Besides,the measurement results cannot be quantified.In order to improve the inspection efficiency,the key technology in the non-contact,digital measurement of the bent tube are studied in this thesis.A method for identifying cylindrical sections and torus sections of the bend t ube is proposed for the scanning point cloud data to compute the parameters and reconstruct the model of bent tube.Then the profile error is obtained and analyzed by comparing with the CAD model.The main research contents include the follows:1.The basic properties of curved surfaces are extracted from the point cloud data.The initial value of the normal vector at each point is e stimated with principal component analysis.Then the local quadratic surface is fitted.Finally,the normal vector and the p rincipal curvature at each point are calculated based on differential geometry and matrix theory.2.Segmentation and processing of the point cloud.The principal curvature directions at each point is mapped to a unit sphere and the cylinder section is indentified by using data clustering algorithms.Each point of the point loud moves a radial length along its normal direction pointing to the inner of the bent tube,and the generated new points are considered to be located on the spine curve of the bent tube.Then,an ordered point set is extracted,and the original point cloud data are parameterized with the method of accumulating chord length.Finally,the point cloud data are reordered with the quick sort algorithm.3.Model reconstruction and error evaluation.The least-squares method is adopted to fit the cylindrical sections and the torus sections respectively based on the segmented data set obtained in the above step to get the parameters related to position,direction and size of every sections.The result of 3D reconstruction is showed with Open GL.In the end,the error is evaluated.Compared with the existing methods,it is unnecessary to acquire the point cloud data on the full surface by utilizing the symmetry of the bent tube surface,resulting in reduction of computation and improvement of inspection efficiency.