Groove modeling and digital simulation for intersecting structures of circular tubes based on coplanarity of vectors

In order to establish the groove model for intersecting structures of circular tubes, mathematical model of the intersecting line is established by the method of analytic geometry, and parametric equations are thus determined. The dihedral angle, groove angle and actual cutting angle for any position of the intersecting line are derived as well. In order to identify groove vectors for two pipes, a new analytical method, i.e. coplanarity of vectors, is further proposed to complete the groove model. The established model is virtually verified by programming and simulation calculation in the MATLAB environment. The results show that groove vectors of intersecting structures simulated by MATLAB are consistent with the theoretical groove model, indicating that the theoretical groove model established in this paper is accurate, and further proves that the proposed coplanarity of vectors for solving groove vectors is correct and feasible. Finally, a graphical user interface (GUI) is developed by MATLAB software to independently realize functions such as model drawing, variable calculation and data output. The research outcome provides a theoretical foundation for the actual welding of circular intersecting structures, and lays an essential basis for weld bead layout and path planning.