Modeling and Simulation of Assembly Constraints in Tolerance Analysis of Rigid Part Assemblies

During last years variational models for tolerance analysis, both for rigid and compliant assemblies, have been implemented into CAT (Computer Aided Tolerancing) systems to verify the fulfilment of functional requirements, performing the virtual product validation from dimensional and geometrical point of view. In the present paper, starting from a numerical methodology, proposed by the same authors, that allows to simulate variational features, assembly constraints among parts are modelled and simulated. During assembly operations, an “object” part has to be moved to satisfy constraints of “target” parts. To do this, an assembly transformation matrix is calculated. By using geometric entities such as point, line and plane and their combinations, kinematic joints are modelled; then a numerical procedure is proposed to solve fully- and over-constrained assemblies. Therefore, the proposed model allows to take into account different assembly sequences. The best fit alignment among mating features is performed by using optimisation algorithms. Finally, two case studies are described and analysed.