A scheme for mapping tolerance specifications to generalized deviation space for use in tolerance synthesis and analysis

Tolerances impose restrictions on the possible deviations of features from their nominal sizes/shapes. These variations of size/shape could be thought of as deviations of a set of generalized coordinates defined at some convenient point on a feature. Any tolerance specification for a feature imposes some kind of restrictions or constraints on its deviation parameters. These constraints, in general, define a bounded region in the deviation space. In this paper, a method has been presented for converting tolerance specifications as per maximum material condition (MMC)/least material condition (LMC)/regardless of feature size (RFS) material conditions for standard mating features (planar, cylindrical, and spherical) into a set of inequalities in a deviation space. Both virtual condition boundaries Virtual condition boundary: A constant boundary generated by the collective effects of a size feature´s specified MMC or LMC material condition and the geometric tolerance for that material condition. (VCB) and tolerance zones are utilized for these mappings. The mapping procedures have been illustrated with an example. Note to Practitioners-This paper deals with methods to convert tolerance specification as per ASME Y14.5M into a set of generalized deviation of features and vice-versa. These are intermediate relationships that are required for use in deviation-based tolerance synthesis methods. In this work, different examples have been presented to show how different tolerance specifications (such as positional tolerance at maximum material condition (MMC), least material condition (LMC), etc.) applied to different features could be treated on a generalized basis for tolerancing of manufactured parts.