A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones

Abstract

The physical realization of any part always yields imperfect forms with respect to the ideal geometry specified in the engineering design. To describe and preserve functional requirements of design, the allowable variation is specified using modern geometric tolerances via tolerance zones. Specification using geometric tolerances is intended for unambiguous communication. Mathematically unambiguous specification is required for the application of computing machinery across manufacturing enterprises to lower costs and improve efficiency. Several computer-based tools have been developed to aid in tolerance specification and also in subsequent processing, or applications that utilize tolerance specification information, such as analysis, synthesis, manufacture and measurement. In order to execute these activities, the tolerance zones have to be unambiguously captured by computer programs. The geometric tolerance specification is complex and not completely free of ambiguities. These difficulties pose as challenges in realizing the tolerance zones and limit the applicability of any particular method developed so far. This paper presents a survey of the current computer based methods available to capture tolerance zones of parts. The limitations of the methods are analyzed based on the following criteria: the range of applicability, compatibility with standards, ease in realization and the effects of singularities in shapes that are application specific. Various assembly analysis techniques that utilize the tolerance zone construction and other recent approaches for tolerance design are also reported.