Mathematical model of laser tracker measur-ing system for multiple control of large constructions

Abstract

Laser trackers are widely used to non-contact measure large-scale aerospace products. If it is impossible to inspect the entire product with a single laser tracker with a fixed position, multi-station inspection is used. This paper aims todescribes the multi-station control of large-sized products geometry with using a laser tracker as a measuring tool. A three-segment welded cylindrical shell with a diameter of 4100 mm, a height of 1560 mm and a thickness of 24 mm is considered as an object of control. The coordinates of laser tracker and enhanced referring system points are determined from the conditions of their full visibility and the minimum measurement error. A mathematical model of the measuring system for large shell multi-station control for determining the relationship between the coordinates of points measured from different stations of the laser tracker is constructed. The reference points coordinates and laser tracker station coordinates of the measuring system are established in order to minimize the number of mathematical model unknown variables. The calculation results of the of the selected measuring system maximum allowable error was carried out. The experimental studies were carried out to confirm the main mathematical model assumptions. 276 points on the outer surface of the large shell were measured with laser tracker. To determine the deviation of the surface from the theoretical contour, a digital model of the theoretical contour of the assembly was built in the Spatial Analyzer software. The measured control points were compared with the surface of the digital model. The results of the experimental studies confirmed the main mathematical model approaches and showed that the error of the measuring system corresponds to the required values.