Modelling spatial dimensional chains for CAD/CAM applications

Abstract

An analytical and computational procedure for modelling spatial dimensional chains (DC) is based on the kinematic interpretation both of nominal dimensions forming the DC and their errors. The goal of the investigation is to assess the accuracy of the closing link of the DC, taking into account the errors of the intermediate links of the DC. The three-stage procedure successively models the nominal DC, the actual DC with positional errors of the links, and the metrological estimations of the accuracy. The latter stage is undertaken using metrological models of accuracy, which brings the accuracy estimation into conformity with a nominal form of the boundaries of the DC’s closing link and the relative positions of the boundaries. The theoretical results apply to important design problems: evaluating closing tolerances, choosing compensating links, and structural optimization of the DC according to accuracy criteria. As an example, calculation of the spatial DC between two perpendicular bores is considered.