Variational modeling and assembly constraints in tolerance analysis of rigid part assemblies: planar and cylindrical features

In this paper, a general methodology to do tolerance analysis of rigid assemblies is proposed. Firstly, tolerance specification sets, according to GD&T or ISO specifications, are translated into variational features by using 4×4 homogenous transformation matrices. In particular, planar and cylindrical features are considered. Then, once all variational features are modeled, assembly constraints among parts are introduced. To solve assembly constraints, an assembly transformation matrix is evaluated. By using point, line, and plane entities and their combinations, kinematic joints are modeled. A numerical procedure is proposed to solve fully and over-constrained assemblies. The best-fit alignment among variational mating features is performed by using optimization algorithms. The proposed method for tolerance analysis of rigid part assemblies allows to simulate different assembly sequences. Finally, in order to show the effectiveness of the proposed methodology, three case studies are described and analyzed.