A Framework for Tolerance Modeling Based on Parametric Space Envelope

Abstract

Geometric dimensioning and tolerancing (GD&T) tolerance standards are widely used in industries across the world. A mathematical model to formulate tolerance specifications to enable comprehensive tolerance analysis is highly desirable but difficult to build. Existing methods have limited success on this with form and profile tolerance modeling as a known challenge. In this paper, we propose a novel tolerance modeling framework and methodology based upon parametric space envelope, a purposely built variation tool constructed from base parametric curve. Under proposal, geometric variation (deviation as well as deformation) is modeled and linked to envelope boundary control points’ movement. This indirect tolerance modeling brings various benefits. It is versatile and can handle full set of tolerances specified under GD&T standards including form, profile, and runout tolerance. The proposal can deal with complex manufacturing part and is capable of providing modeling accuracy required by many applications. The proposed approach has added advantage of facilitating integration of various computer-aided systems to meet emerging industry demands on tolerancing in a new era of digital manufacturing. The proposed methodology is illustrated and verified with an industrial case example on a two-part assembly.

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“…However, the rest of DT characterisation, such as bi-directional information flow during the lifecycle, was ignored here. The digital twin instance (DTI) refers to each individual instance of the object where it is created, including Geometric Dimensioning and Tolerancing (GD&T) [82][83][84]. The DT aggregate/environment (DTD/E) refers to multi-domain applications for employing the DT to meet various needs [82].…”

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“…It should be noted that each control point, in general, has different influence zone [55], i.e., r1 ≠ r2. Other tolerances under GD&T standards can also be modeled under the proposed modeling framework [56].…”

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