A numerical approach to compute statistical assembly shift for patterns of fits: application to tolerance stack-up

Abstract This study introduces a numerical methodology for computing the statistical assembly shift in patterns of fits, addressing scenarios with variable numbers of elements and scrap caused by assembly failure. Using Monte Carlo simulations, the methodology estimates rejection rates, determines gap distributions, and calculates assembly shifts while considering both intrinsic and external datum systems. The findings indicate that adding more elements to a pattern reduces assembly shifts exponentially, presenting a design opportunity to control alignment and optimize component performance. A case study involving engine block and cylinder head alignment demonstrates the methodology’s applicability to real-world mechanical design. Three approaches for tolerance stack-up are evaluated: the standard Root Sum Square (RSS) method, where assembly shift is treated as a worst-case scenario; a proposed RSS method that models the assembly shift as a Gaussian distribution with a standard deviation derived from Monte Carlo simulations; and the Monte Carlo approach, which considers the full shape of the assembly shift distribution. By comparing these approaches, the study underscores the effectiveness of the proposed methodology in capturing the statistical behavior of assembly shifts. This work contributes a robust tool for tolerance analysis, advancing the precision and accuracy of pattern fit modeling and assembly shift evaluation in mechanical design. Graphical Abstract