Statistical Assemblies with form Errors - A 2D Example

When dealing with precision in tolerancing of assembly systems, the modelling complexity of the mechanism increases. At first, one can distinguish the 1D tolerancing approach that only concerns variations of dimension. Then, several models are defined to set 3D tolerances, considering that the form error is negligible compared to the orientational and translational variations. Finally, some approaches are proposed to take into account the form variations in the tolerancing of mechanisms. However, some modelling approaches considers the form error as a tolerance zone to add to the 3D tolerances as defined by Rule#1 of the ASME standard, or ISO 8015. This paper proposes another point of view, considering the positioning of parts through contact points of their rigid deviation shapes under a defined assembly force and set-up. Rather than considering the positioning of a single part, here is proposed an approach of batch parts assembly by a statistical description of shapes. The result of the method is a statistical positioning error of one part on the other considering the form deviations of parts.