A Probabilistic Tolerance Analysis for Mechanical Assembly of Rotating Machines

Abstract

Due to inherent nature of manufacturing variability, the actual dimensions of manufactured components lie anywhere in the range of permissible variation randomly. The random manner by which the dimensional inaccuracies fall produce a pattern in which the variations are distributed within their tolerance zones. Mathematical modelling methods are presented and used to predict the statistical distributions of variations present in the complete assembly. This paper considers assemblies composed of axi-symmetric components and proposes a method to control assembly variation propagations using relative orientation technique. A relative orientation technique is a method in which individual components are re-orientated on a stage-by-stage basis to minimise the eccentricity from table-axis during the assembly of an engine rotor. Two straight-build assembly models are considered: i) Direct Build; and ii) Best Build for assemblies consisting of axi-symmetric components. Analytical expressions are determined for the probability density function (pdf) of the table-axis error for the complete assembly, and numerical comparisons are made with Monte Carlo simulation for the purposes of validation