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

Traditionally tolerances for manufactured parts are specified using symbolic schemes as per ASME or ISO standards. To use these tolerance specifications in computerized tolerance synthesis and analysis, we need information models to represent the tolerances. Tolerance specifications could be modeled as a class with its attributes and methods [ROY01]. Tolerances impose restrictions on the possible deviation of features from its nominal size/shape. These variations of shape/size of a feature could be modeled as deviation of a set of generalized coordinates defined at some convenient point on the feature [BAL98]. In this paper, we present a method for converting tolerance specifications as per MMC (Maximum Material Condition) / LMC (Least Material Condition) / RFS (Regardless of Feature Size) material conditions for standard mating features (planar, cylindrical, and spherical) into a set of inequalities in a deviation space for representation of deviation of a feature from it's nominal shape. We have used the virtual condition boundaries¹ (VCB) as well as tolerance zones (as the case may be) for these mappings. For the planar feature, these relations are linear and the bounded space is diamond shaped. For the other cases, the mapping is a set of nonlinear inequalities. The mapping transforms the tolerance specifications into a generalized coordinate frame as a set of inequalities. These are useful in tolerance synthesis, and analysis as well as in assemblability analysis in the generalized coordinate system (deviation space). In this paper, we also illustrate the mapping procedures with an example.