The effects of different specifications on the tolerance-maps for an angled face

A new mathematical model for representing geometric tolerances is applied to a part with an angled face and is extended to show its sensitivity to different specifications for dimensioning and tolerancing the part. The model is compatible with the ASME/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map ^®1, a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a plane which can arise from tolerances on size, position, form, and orientation. Every Tolerance-Map is a convex set. This model is one part of a bi-level model that we are developing for geometric tolerances. The new model makes stackup relations apparent in an assembly, and these can be used to allocate size and orientational tolerances; the same relations also can be used to identify sensitivities for these tolerances. All stackup relations can be met for 100% interchangeability or for a specified probability. This paper develops several Tolerance-Maps for a part with an angled end face for different tolerance specifications. These specifications are linear size, angularity, angular size, "linear size & angularity" and "linear & angular size" tolerance. Comparison of Tolerance-Maps for their content for these specifications led to the following conclusions: a) only angular size tolerance is not sufficient for tolerancing an angled face; b) if the value of tolerance remains the same, the allowable variation is more in a part having only an angularity tolerance than in one having only a size tolerance.