A probabilistic approach to variation propagation control for straight build in mechanical assembly

Random component variations have a significant influence on the quality of assembled products, and variation propagation control is one of the procedures used to improve product quality in the manufacturing assembly process. This paper considers straight-build assemblies composed of axi-symmetric components and proposes a novel variation propagation control method in which individual components are re-orientated on a stage-by-stage basis to optimise the table-axis error for the final component in the assembly. Mathematical modelling methods are developed to predict the statistical variations present in the complete assembly. Three straight-build assembly strategies are considered: (a) direct build, (b) best build and (c) worst build assembly. Analytical expressions are determined for the probability density function of the table-axis error for the final component in the assembly, and comparisons are made against Monte Carlo simulations for the purposes of validation. The results show that the proposed variation propagation control method offers good accuracy and efficiency, compared to the Monte Carlo simulations. The probability density functions are used to calculate the probability that the eccentricity will exceed a particular value and are useful for industrial applications and academic research in tolerance assignment and assembly process design. The proposed method is used to analyse the influence of different component tolerances on the build quality of an example originating in aero-engine sub-assembly.