Tolerance allocation by means of the polyhedral based tolerance analysis method

Abstract

The imperfection in the geometry and size of mechanical parts can lead to problems of assemblability and/or overall functionality. Defining acceptable tolerances for these imperfections is challenging because they impact how well the machine works and how much it costs to manufacture. In addition, tolerances for different parts often influence each other, contributing to a resultant tolerance.

This article presents a novel approach to tolerance allocation in mechanical design using the prismatic polyhedral approach and simulated annealing optimization. The prismatic polyhedral method effectively models deviations in complex mechanisms, while simulated annealing is used to optimize tolerance values considering both cost and functional compliance.

Methods based on sets of constraints, such as the prismatic polyhedral approach, can handle over- and iso-constrained mechanisms and, since it is feature based, it allows to model dependencies between rotational and translational deviations. However, they are often limited by high computational costs. To address this, the proposed methodology introduces a strategy to reduce the complexity of the contact graph reduction process, improving computational efficiency without sacrificing accuracy. Additionally, a new indicator of system compliance – the tolerance of circumscription – is introduced. This indicator has physical meaning and helps the designer to assess whether the system meets its functional conditions, as well as whether the total tolerance stack-up can be increased or needs to be tightened.