Mesh-based tool path calculations for tubular joints

Manufacturing of large steel tube structures is faced with excessive welding, fit-up and rework times in tube joints, due to various types of deviation from nominal shape of the tubes. This article presents a procedure and geometry calculus for generating cutting and welding paths based on measured geometries. The procedure poses the two measured meshes as per construction specification and invokes a mesh intersection procedure to get the mesh intersection path; performs an optional smoothing; interpolates the smoothed path to a specified angular resolution; estimates the two surface normal vectors and the two surface tangents in the plane spanned by the normals at each interpolation point; calculates the cutting tool and welding tool approach directions for obtaining the specified welding groove geometry at each interpolation point; and finally stores all the data parameterized by the interpolation angle. Illustrations of results with both synthetic, representative meshes and meshes obtained from scanning of actual tubes at the shop-floor at a manufacturer are presented. The reference implementation for the developed software tool is based on Python and uses the mesh modeller from the 3D creation suite Blender as platform.

Application of Inverse Distance Weighted Interpolation Method in Finite Temperature Point Temperature Field

The paper introduces a kind of inverse distance weighted interpolation theoretical derivation and its solving way. The basic principle of this method is that to use known information limited data were interpolated to the unknown information for point, through the obtained interpolation point value to calculate the new interpolation point value. Thus, it is solved that the problem that limited number of temperature points can not be comprehensive description of temperature field, and the method is applied in the process of solving the unknown temperature points in the two dimensional temperature field. The characteristics of this method are simple, practical, less amount of calculation.

Triangle Interpolation on Discrete Point Set

An algorithm for triangle interpolation on discrete points is presented in the paper. It creates a square mesh which covers all the discrete points, then puts the points into the mesh and records the relationship between grids and points. When interpolating elevation of an interpolation point, it can fast find the discrete points which are near the interpolation point and these discrete points can be used to create a special triangle which contains the interpolation point. The elevation of the interpolation point can be obtained from the triangle. The method has the advantage of fast speed, high precision and needing less memory.

NURBS Curve Interpolation Algorithm Based on Motion Axis Control

This paper based on the interpolation point check calculation process, which uses the movement aixs of the CNC system on the velocity and acceleration components checking , instead of the traditional motion characteristics of the checking calculation. In this way, we can avoid complex NURBS curve derivative computation and simplify the process of the interpolation point calibration. Therefore, it also can ensure the precision of curve machining based on curve, at the same time, the interpolation speed and acceleration control strictly in the scope of the corresponding axis servo system capacity. Whats more, we can ensure that processing does not appear too large shock and vibration at any time.

High-Speed and High-Accuracy Schemes of Coordinate Calculation and End Point Judgment for Elliptic Interpolation

To implement high-speed and high-accuracy elliptic interpolation required in high-performance motion control, novel coordinate calculation and end point judgment schemes are proposed. Data Sample method is used for coordinate calculation. High accuracy is guaranteed by avoiding approximation calculation of interpolation points. Exact end point judgment is constructed based on the position relationship of the current interpolation point, the next interpolation point and the end point to avoid incomplete interpolation or over interpolation of elliptic trajectories. The proposed schemes feature fewer amounts of calculation and high accuracy and can produce any elliptic trajectories.

New Digital Differential Analyzer Linear Interpolation Program and Error Analysis

Common digital differential analyzer（DDA）linear interpolation error is lower than a pulse equivalent, and the output pulse along each axis is not uniform. New DDA linear interpolation flow chart was obtained by combining a quick algorithm of DDA interpolation and interpolating algorithm for pulses uniformization with common DDA linear interpolation principle. The relationship between interpolation error and pulse equivalent was demonstrated in detail. As the results shows, the new DDA with high precision machining but simple algorithm, increased interpolating speed; the new algorithm make the generation of uniform pulse series come true, which is of great importance to keep stepping motor rotating steadily without missing steps; At coordinate origin, interpolation error is lower than 0.42 pulse equivalent, while the interpolation point is not at coordinate origin, interpolation error is lower than 0.5 pulse equivalent.