Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments

Abstract

For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, profile tolerances have received the least attention for representation in computer models. The objective of this paper is to describe a new method of construction, using computer-aided geometric design, which can produce the T-Map for any line-profile. The new method requires decomposing a profile into segments, creating a solid-model T-Map primitive for each, and then combining these by Boolean intersection to generate the T-Map for a complete line profile of any shape. To economize on length, the scope of this paper is limited to line-profiles formed from circular arc-segments. The parts containing the line-profile features are considered to be rigid.

Allocation of geometric tolerances in one-dimensional stackup problems

“…With the objective of covering a wider spectrum of cases and assumptions, a further step is the development of procedures based on advanced concepts and mathematical models for the representation of geometric tolerances. These include the actual mating envelope [59], vectorial tolerancing [60], quantifier and virtual boundary [61], and the T-maps in progressively more detailed definitions [62][63][64][65][66]. On the opposite end, other approaches try to reduce the complexity involved by geometric tolerances by special assumptions or approaches; examples include measurements on prototypes in the study of an electrical device [67] and the definition of variables with multivariate normal distributions in an allocation strategy considering designer's preferences [68].…”