Predicting the cumulative variation of 3-D mechanical assemblies using an ‘Idea Algebra’ framework

Improving productivity and performance of products require professional tolerance analysis and variation control and, in this context, to make sure the final product will achieve the aimed function, analysing the cumulative effects of component tolerances in an assembly is necessary. Such tolerance analysis generally involves complex and tedious calculations which take time and are susceptible to human error; therefore, for automating this process, computer-aided tolerance (CAT) systems have been used extensively. They are, however, complicated and also require relatively detailed definitions of an assembly (CAD models) before they can be used. In this paper, system topology with highly abstracted geometrical information is translated into an analytical vector model based on a semantic tool in the manner of an ‘idea algebra’. Tolerances may be defined at any level of the system (ranging from the component level to the system-level function), to more readily realise the design intent. This lightweight 3D-capable representation is possible already at an early concept stage, prior to CAD, and persists and is updated throughout the design process. Using a comparative numerical simulation-based study, it was demonstrated that the presented method provides quicker computation with equally accurate output as CAT, while requiring substantially lower complexity of input.