Quantitative circularity tolerance analysis and design for 2D precision assemblies

Circular, cylindrical, or spherical features are fundamental geometric features in engineering. As precision requirement becomes more stringent, it is not sufficient to consider only size tolerance of circular and cylindrical parts. However, currently there is no quantitative and systematic way of assigning circularity and cylindricity tolerances. This paper investigates how to specify circularity tolerance quantitatively for 2D assemblies. Statistical matrices to quantify positioning error of two perfectly circular mating parts subject to size tolerance for both clearance and transition fit conditions are first developed. The analysis is then extended to nonideal profiles whose profile errors are assumed to deviate from a best-fit circle according to a normal distribution. The assumption of the normal distribution is then removed for more general results via computer simulation. For this purpose, an experimentally verified profile model is used to generate realistic profiles as those produced by various machining processes. Numerous pairs of these realistic profiles are then assembled virtually using Monte Carlo simulation to quantify their positioning errors. The simulation results and the analytical results are compared for cross-checking. Finally, systematic design procedures are proposed to assign circularity tolerance by prescribing a fit condition with a desirable process capability. By the nature of circularity tolerance, this paper addresses a 2D assembly. The result of this 2D analysis can be a foundation for more complicated 3D problems, such as assigning cylindricity tolerance. [Copyright &y& Elsevier]