Integrating GD&T into dimensional variation models for multistage machining processes

Recently, the modelling of variation propagation in multistage machining processes has drawn significant attention. In most of the recently developed variation propagation models, the dimensional variation is determined through kinematic analysis of the relationships among error sources and dimensional quality of the product, represented by homogeneous transformations of the actual location of a product's features from their nominal locations. In design and manufacturing, however, the dimensional quality is often evaluated using Geometric Dimensioning and Tolerancing (GD&T) standards. The method developed in this paper translates the GD&T characteristic of the features into a homogeneous transformation representation that can be integrated in existing variation propagation models for machining processes. A mathematical representation using homogeneous transformation matrices is developed for position, orientation and form characteristics as defined in ANSI Y14.5; further, a numerical case study is conducted to validate the developed methods.