Date: 18 Nov 2012

Automatic evaluation of variational parameters for tolerance analysis of rigid parts based on graphs

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The present paper proposes a novel general approach to automatically calculate the variational parameters for planar or cylindrical features for a given set of tolerance specifications, according to ANSI or ISO Standards. Variational parameters correspond to those directions along/around which variation, in terms of small translation and rotation, may propagate for a given feature with tolerance specifications. A graph representation of these tolerance specifications is adopted and it is used along with screw theory and Davies’s laws to automatically calculate the variational parameters, and then the net variational space of each toleranced feature, by capturing nominal geometries directly from a CAD environment (SolidWorks). From screw theory, twist matrices, able to capture the motion properties of any kinematic joint in mechanical assemblies, are here adopted at part level and collected for every feature-to-datum relationship. Davies’s laws are then recalled to put those matrices together to calculate the variational parameters. In this way, both single-datum and multi-datum tolerance specifications can be handled. The proposed approach for the automatic calculation of variational parameters could be successfully implemented in a more general expert system for designing mechanical assemblies where an added-value interaction could allow user to detect relationships between geometric features. In this way, the leading of activities aimed to tolerance analysis could be accomplished both during the preliminary design stages and throughout the manufacturing and reviewing sessions.